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CHAPTER 2
ORGANIZING AND GRAPHING DATA
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Opening Example
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RAW DATA Definition Data recorded in the sequence in which they are collected
and before they are processed or ranked are called raw data
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Table 21 Ages of 50 Students
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Table 22 Status of 50 Students
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ORGANIZING AND GRAPHING DATA
Frequency Distributions Relative Frequency and Percentage Distributions Graphical Presentation of Qualitative Data
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Table 23 Types of Employment Students Intend to Engage In
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Frequency Distributions Definition A frequency distribution of a qualitative variable lists all
categories and the number of elements that belong to each of the categories
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-1
A sample of 30 persons who often consume donuts were asked what variety of donuts was their favorite The responses from these 30 persons were as follows
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Example 2-1
glazed filled other plain glazed other
frosted filled filled glazed other frosted
glazed plain other glazed glazed filled
frosted plain other other frosted filled
filled other frosted glazed glazed filled
Construct a frequency distribution table for these data
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Example 2-1 SolutionTable 24 Frequency Distribution of Favorite Donut Variety
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Relative Frequency and Percentage Distributions
Calculating Relative Frequency of a Category
sfrequencie all of Sum
category that ofFrequency category a offrequency lativeRe
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Relative Frequency and Percentage Distributions
Calculating Percentage Percentage = (Relative frequency) 100
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Example 2-2 Determine the relative frequency and percentage for the
data in Table 24
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Example 2-2 SolutionTable 25 Relative Frequency and Percentage Distributions of Favorite Donut Variety
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Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their Parents
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Graphical Presentation of Qualitative Data
Definition A graph made of bars whose heights represent the
frequencies of respective categories is called a bar graph
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Figure 21 Bar graph for the frequency distribution of Table 24
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Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
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Graphical Presentation of Qualitative Data Definition A circle divided into portions that represent the relative
frequencies or percentages of a population or a sample belonging to different categories is called a pie chart
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Table 26 Calculating Angle Sizes for the Pie Chart
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Figure 22 Pie chart for the percentage distribution of Table 25
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ORGANIZING AND GRAPHING QUANTITATIVE Frequency Distributions Constructing Frequency Distribution Tables Relative and Percentage Distributions Graphing Grouped Data
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Table 27 Weekly Earnings of 100 Employees of a Company
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Frequency Distributions Definition A frequency distribution for quantitative data lists all
the classes and the number of values that belong to each class Data presented in the form of a frequency distribution are called grouped data
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Frequency Distributions Definition The class boundary is given by the midpoint of the upper
limit of one class and the lower limit of the next class
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Frequency Distributions
Finding Class Width
Class width = Upper boundary ndash Lower boundary
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Frequency Distributions
Calculating Class Midpoint or Mark
2
limit Upper limit Lower markor midpoint Class
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Constructing Frequency Distribution Tables
Calculation of Class Width
classes ofNumber
alueSmallest v - lueLargest va widthclass eApproximat
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Table 28 Class Boundaries Class Widths and Class Midpoints for Table 27
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Example 2-3
The following data give the total number of iPodsreg sold by a mail order company on each of 30 days Construct a frequency distribution table
8 25 11 15 29 22 10 5 17 21
22 13 26 16 18 12 9 26 20 16
23 14 19 23 20 16 27 16 21 14
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Example 2-3 Solution
29 5Approximate width of each class 48
5
Now we round this approximate width to a convenient number say 5 The lower limit of the first class can be taken as 5 or any number less than 5 Suppose we take 5 as the lower limit of the first class Then our classes will be 5 ndash 9 10 ndash 14 15 ndash 19 20 ndash 24 and 25 ndash 29
The minimum value is 5 and the maximum value is 29 Suppose we decide to group these data using five classes of equal width Then
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Table 29 Frequency Distribution for the Data on iPods Sold
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Relative Frequency and Percentage Distributions
Calculating Relative Frequency and Percentage
100 frequency) (Relative Percentage
sfrequencie all of Sum
class that of Frequencyclass a of frequency Relative
f
f
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Example 2-4 Calculate the relative frequencies and percentages for
Table 29
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Example 2-4 SolutionTable 210 Relative Frequency and Percentage Distributions for Table 29
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Graphing Grouped Data Definition A histogram is a graph in which classes are marked on the
horizontal axis and the frequencies relative frequencies or percentages are marked on the vertical axis The frequencies relative frequencies or percentages are represented by the heights of the bars In a histogram the bars are drawn adjacent to each other
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Figure 23 Frequency histogram for Table 29
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Figure 24 Relative frequency histogram for Table 210
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Case Study 2-3 How Long Does Your Typical One-Way Commute Take
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Graphing Grouped Data Definition A graph formed by joining the midpoints of the tops of
successive bars in a histogram with straight lines is called a polygon
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Figure 25 Frequency polygon for Table 29
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Case Study 2-4 How Much Does it Cost to Insure a Car
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Figure 26 Frequency distribution curve
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Example 2-5 The percentage of the population working in the United
States peaked in 2000 but dropped to the lowest level in 30 years in 2010 Table 211 shows the percentage of the population working in each of the 50 states in 2010 These percentages exclude military personnel and self-employed persons (Source USA TODAY April 14 2011 Based on data from the US Census Bureau and US Bureau of Labor Statistics)
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Example 2-5
Construct a frequency distribution table Calculate the relative frequencies and percentages for all classes
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Example 2-5 Solution
The minimum value in the data set of Table 211 is 367 and the maximum value is 558 Suppose we decide to group these data using six classes of equal width Then
We round this to a more convenient number say 3 We can take a lower limit of the first class equal to 367 or any number lower than 367 If we start the first class at 36 the classes will be written as 36 to less than 39 39 to less than 42 and so on
119808119849119849119851119848119857119842119846119834119853119838119856119842119837119853119841119848119839 119834119836119845119834119852119852=558minus367
6=318
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Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
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Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
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Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
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Figure 27 Bar graph for Table 213
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Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
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SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
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Figure 28 Symmetric histograms
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Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
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Figure 210 A histogram with uniform distribution
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Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
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Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
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Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
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Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
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Figure 212 Ogive for the cumulative frequency distribution of Table 214
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STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
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Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
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Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
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Figure 213 Stem-and-leaf display
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Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
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Figure 214 Stem-and-leaf display of test scores
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Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
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Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
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Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
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Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
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Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
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Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
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Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
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Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
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DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
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Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
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Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
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Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
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Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
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Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
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Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
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Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
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Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
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TI-84
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TI-84
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Minitab
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Minitab
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Minitab
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Minitab
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Minitab
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Excel
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Excel
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- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Opening Example
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RAW DATA Definition Data recorded in the sequence in which they are collected
and before they are processed or ranked are called raw data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 21 Ages of 50 Students
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Table 22 Status of 50 Students
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ORGANIZING AND GRAPHING DATA
Frequency Distributions Relative Frequency and Percentage Distributions Graphical Presentation of Qualitative Data
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Table 23 Types of Employment Students Intend to Engage In
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Frequency Distributions Definition A frequency distribution of a qualitative variable lists all
categories and the number of elements that belong to each of the categories
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-1
A sample of 30 persons who often consume donuts were asked what variety of donuts was their favorite The responses from these 30 persons were as follows
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-1
glazed filled other plain glazed other
frosted filled filled glazed other frosted
glazed plain other glazed glazed filled
frosted plain other other frosted filled
filled other frosted glazed glazed filled
Construct a frequency distribution table for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-1 SolutionTable 24 Frequency Distribution of Favorite Donut Variety
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Relative Frequency and Percentage Distributions
Calculating Relative Frequency of a Category
sfrequencie all of Sum
category that ofFrequency category a offrequency lativeRe
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Relative Frequency and Percentage Distributions
Calculating Percentage Percentage = (Relative frequency) 100
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Example 2-2 Determine the relative frequency and percentage for the
data in Table 24
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Example 2-2 SolutionTable 25 Relative Frequency and Percentage Distributions of Favorite Donut Variety
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Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their Parents
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Graphical Presentation of Qualitative Data
Definition A graph made of bars whose heights represent the
frequencies of respective categories is called a bar graph
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Figure 21 Bar graph for the frequency distribution of Table 24
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Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
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Graphical Presentation of Qualitative Data Definition A circle divided into portions that represent the relative
frequencies or percentages of a population or a sample belonging to different categories is called a pie chart
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Table 26 Calculating Angle Sizes for the Pie Chart
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Figure 22 Pie chart for the percentage distribution of Table 25
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ORGANIZING AND GRAPHING QUANTITATIVE Frequency Distributions Constructing Frequency Distribution Tables Relative and Percentage Distributions Graphing Grouped Data
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Table 27 Weekly Earnings of 100 Employees of a Company
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Frequency Distributions Definition A frequency distribution for quantitative data lists all
the classes and the number of values that belong to each class Data presented in the form of a frequency distribution are called grouped data
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Frequency Distributions Definition The class boundary is given by the midpoint of the upper
limit of one class and the lower limit of the next class
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Frequency Distributions
Finding Class Width
Class width = Upper boundary ndash Lower boundary
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Frequency Distributions
Calculating Class Midpoint or Mark
2
limit Upper limit Lower markor midpoint Class
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Constructing Frequency Distribution Tables
Calculation of Class Width
classes ofNumber
alueSmallest v - lueLargest va widthclass eApproximat
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Table 28 Class Boundaries Class Widths and Class Midpoints for Table 27
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Example 2-3
The following data give the total number of iPodsreg sold by a mail order company on each of 30 days Construct a frequency distribution table
8 25 11 15 29 22 10 5 17 21
22 13 26 16 18 12 9 26 20 16
23 14 19 23 20 16 27 16 21 14
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Example 2-3 Solution
29 5Approximate width of each class 48
5
Now we round this approximate width to a convenient number say 5 The lower limit of the first class can be taken as 5 or any number less than 5 Suppose we take 5 as the lower limit of the first class Then our classes will be 5 ndash 9 10 ndash 14 15 ndash 19 20 ndash 24 and 25 ndash 29
The minimum value is 5 and the maximum value is 29 Suppose we decide to group these data using five classes of equal width Then
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Table 29 Frequency Distribution for the Data on iPods Sold
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Relative Frequency and Percentage Distributions
Calculating Relative Frequency and Percentage
100 frequency) (Relative Percentage
sfrequencie all of Sum
class that of Frequencyclass a of frequency Relative
f
f
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Example 2-4 Calculate the relative frequencies and percentages for
Table 29
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Example 2-4 SolutionTable 210 Relative Frequency and Percentage Distributions for Table 29
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Graphing Grouped Data Definition A histogram is a graph in which classes are marked on the
horizontal axis and the frequencies relative frequencies or percentages are marked on the vertical axis The frequencies relative frequencies or percentages are represented by the heights of the bars In a histogram the bars are drawn adjacent to each other
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Figure 23 Frequency histogram for Table 29
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Figure 24 Relative frequency histogram for Table 210
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Case Study 2-3 How Long Does Your Typical One-Way Commute Take
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Graphing Grouped Data Definition A graph formed by joining the midpoints of the tops of
successive bars in a histogram with straight lines is called a polygon
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Figure 25 Frequency polygon for Table 29
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Case Study 2-4 How Much Does it Cost to Insure a Car
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Figure 26 Frequency distribution curve
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Example 2-5 The percentage of the population working in the United
States peaked in 2000 but dropped to the lowest level in 30 years in 2010 Table 211 shows the percentage of the population working in each of the 50 states in 2010 These percentages exclude military personnel and self-employed persons (Source USA TODAY April 14 2011 Based on data from the US Census Bureau and US Bureau of Labor Statistics)
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Example 2-5
Construct a frequency distribution table Calculate the relative frequencies and percentages for all classes
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Example 2-5 Solution
The minimum value in the data set of Table 211 is 367 and the maximum value is 558 Suppose we decide to group these data using six classes of equal width Then
We round this to a more convenient number say 3 We can take a lower limit of the first class equal to 367 or any number lower than 367 If we start the first class at 36 the classes will be written as 36 to less than 39 39 to less than 42 and so on
119808119849119849119851119848119857119842119846119834119853119838119856119842119837119853119841119848119839 119834119836119845119834119852119852=558minus367
6=318
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Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
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Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
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Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
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Figure 27 Bar graph for Table 213
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Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
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SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
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Figure 28 Symmetric histograms
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Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
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Figure 210 A histogram with uniform distribution
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Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
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Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
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Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
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Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
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Figure 212 Ogive for the cumulative frequency distribution of Table 214
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STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
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Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
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Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
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Figure 213 Stem-and-leaf display
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Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
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Figure 214 Stem-and-leaf display of test scores
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Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
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Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
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Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
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Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
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Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
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Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
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Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
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Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
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DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
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Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
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Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
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Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
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Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
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Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
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Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
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Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
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Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
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TI-84
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TI-84
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Minitab
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Minitab
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Minitab
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Minitab
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Minitab
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Excel
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Excel
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- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
RAW DATA Definition Data recorded in the sequence in which they are collected
and before they are processed or ranked are called raw data
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Table 21 Ages of 50 Students
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Table 22 Status of 50 Students
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ORGANIZING AND GRAPHING DATA
Frequency Distributions Relative Frequency and Percentage Distributions Graphical Presentation of Qualitative Data
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Table 23 Types of Employment Students Intend to Engage In
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Frequency Distributions Definition A frequency distribution of a qualitative variable lists all
categories and the number of elements that belong to each of the categories
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Example 2-1
A sample of 30 persons who often consume donuts were asked what variety of donuts was their favorite The responses from these 30 persons were as follows
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Example 2-1
glazed filled other plain glazed other
frosted filled filled glazed other frosted
glazed plain other glazed glazed filled
frosted plain other other frosted filled
filled other frosted glazed glazed filled
Construct a frequency distribution table for these data
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Example 2-1 SolutionTable 24 Frequency Distribution of Favorite Donut Variety
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Relative Frequency and Percentage Distributions
Calculating Relative Frequency of a Category
sfrequencie all of Sum
category that ofFrequency category a offrequency lativeRe
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Relative Frequency and Percentage Distributions
Calculating Percentage Percentage = (Relative frequency) 100
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Example 2-2 Determine the relative frequency and percentage for the
data in Table 24
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Example 2-2 SolutionTable 25 Relative Frequency and Percentage Distributions of Favorite Donut Variety
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Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their Parents
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Graphical Presentation of Qualitative Data
Definition A graph made of bars whose heights represent the
frequencies of respective categories is called a bar graph
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Figure 21 Bar graph for the frequency distribution of Table 24
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Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
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Graphical Presentation of Qualitative Data Definition A circle divided into portions that represent the relative
frequencies or percentages of a population or a sample belonging to different categories is called a pie chart
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Table 26 Calculating Angle Sizes for the Pie Chart
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Figure 22 Pie chart for the percentage distribution of Table 25
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ORGANIZING AND GRAPHING QUANTITATIVE Frequency Distributions Constructing Frequency Distribution Tables Relative and Percentage Distributions Graphing Grouped Data
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Table 27 Weekly Earnings of 100 Employees of a Company
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Frequency Distributions Definition A frequency distribution for quantitative data lists all
the classes and the number of values that belong to each class Data presented in the form of a frequency distribution are called grouped data
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Frequency Distributions Definition The class boundary is given by the midpoint of the upper
limit of one class and the lower limit of the next class
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Frequency Distributions
Finding Class Width
Class width = Upper boundary ndash Lower boundary
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Frequency Distributions
Calculating Class Midpoint or Mark
2
limit Upper limit Lower markor midpoint Class
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Constructing Frequency Distribution Tables
Calculation of Class Width
classes ofNumber
alueSmallest v - lueLargest va widthclass eApproximat
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Table 28 Class Boundaries Class Widths and Class Midpoints for Table 27
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Example 2-3
The following data give the total number of iPodsreg sold by a mail order company on each of 30 days Construct a frequency distribution table
8 25 11 15 29 22 10 5 17 21
22 13 26 16 18 12 9 26 20 16
23 14 19 23 20 16 27 16 21 14
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Example 2-3 Solution
29 5Approximate width of each class 48
5
Now we round this approximate width to a convenient number say 5 The lower limit of the first class can be taken as 5 or any number less than 5 Suppose we take 5 as the lower limit of the first class Then our classes will be 5 ndash 9 10 ndash 14 15 ndash 19 20 ndash 24 and 25 ndash 29
The minimum value is 5 and the maximum value is 29 Suppose we decide to group these data using five classes of equal width Then
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Table 29 Frequency Distribution for the Data on iPods Sold
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Relative Frequency and Percentage Distributions
Calculating Relative Frequency and Percentage
100 frequency) (Relative Percentage
sfrequencie all of Sum
class that of Frequencyclass a of frequency Relative
f
f
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Example 2-4 Calculate the relative frequencies and percentages for
Table 29
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Example 2-4 SolutionTable 210 Relative Frequency and Percentage Distributions for Table 29
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Graphing Grouped Data Definition A histogram is a graph in which classes are marked on the
horizontal axis and the frequencies relative frequencies or percentages are marked on the vertical axis The frequencies relative frequencies or percentages are represented by the heights of the bars In a histogram the bars are drawn adjacent to each other
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Figure 23 Frequency histogram for Table 29
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Figure 24 Relative frequency histogram for Table 210
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Case Study 2-3 How Long Does Your Typical One-Way Commute Take
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Graphing Grouped Data Definition A graph formed by joining the midpoints of the tops of
successive bars in a histogram with straight lines is called a polygon
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Figure 25 Frequency polygon for Table 29
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Case Study 2-4 How Much Does it Cost to Insure a Car
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Figure 26 Frequency distribution curve
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Example 2-5 The percentage of the population working in the United
States peaked in 2000 but dropped to the lowest level in 30 years in 2010 Table 211 shows the percentage of the population working in each of the 50 states in 2010 These percentages exclude military personnel and self-employed persons (Source USA TODAY April 14 2011 Based on data from the US Census Bureau and US Bureau of Labor Statistics)
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Example 2-5
Construct a frequency distribution table Calculate the relative frequencies and percentages for all classes
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Example 2-5 Solution
The minimum value in the data set of Table 211 is 367 and the maximum value is 558 Suppose we decide to group these data using six classes of equal width Then
We round this to a more convenient number say 3 We can take a lower limit of the first class equal to 367 or any number lower than 367 If we start the first class at 36 the classes will be written as 36 to less than 39 39 to less than 42 and so on
119808119849119849119851119848119857119842119846119834119853119838119856119842119837119853119841119848119839 119834119836119845119834119852119852=558minus367
6=318
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Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
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Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
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Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
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Figure 27 Bar graph for Table 213
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Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
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SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
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Figure 28 Symmetric histograms
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Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
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Figure 210 A histogram with uniform distribution
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Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
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Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
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Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
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Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
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Figure 212 Ogive for the cumulative frequency distribution of Table 214
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STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
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Figure 213 Stem-and-leaf display
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Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
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Figure 214 Stem-and-leaf display of test scores
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Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
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Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
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Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
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Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
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DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
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Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
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Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
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Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
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Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
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Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
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Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
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Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
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Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
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TI-84
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TI-84
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Minitab
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Minitab
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Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Table 21 Ages of 50 Students
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Table 22 Status of 50 Students
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
ORGANIZING AND GRAPHING DATA
Frequency Distributions Relative Frequency and Percentage Distributions Graphical Presentation of Qualitative Data
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Table 23 Types of Employment Students Intend to Engage In
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Frequency Distributions Definition A frequency distribution of a qualitative variable lists all
categories and the number of elements that belong to each of the categories
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-1
A sample of 30 persons who often consume donuts were asked what variety of donuts was their favorite The responses from these 30 persons were as follows
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-1
glazed filled other plain glazed other
frosted filled filled glazed other frosted
glazed plain other glazed glazed filled
frosted plain other other frosted filled
filled other frosted glazed glazed filled
Construct a frequency distribution table for these data
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Example 2-1 SolutionTable 24 Frequency Distribution of Favorite Donut Variety
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Relative Frequency and Percentage Distributions
Calculating Relative Frequency of a Category
sfrequencie all of Sum
category that ofFrequency category a offrequency lativeRe
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Relative Frequency and Percentage Distributions
Calculating Percentage Percentage = (Relative frequency) 100
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Example 2-2 Determine the relative frequency and percentage for the
data in Table 24
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Example 2-2 SolutionTable 25 Relative Frequency and Percentage Distributions of Favorite Donut Variety
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Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their Parents
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Graphical Presentation of Qualitative Data
Definition A graph made of bars whose heights represent the
frequencies of respective categories is called a bar graph
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Figure 21 Bar graph for the frequency distribution of Table 24
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Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
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Graphical Presentation of Qualitative Data Definition A circle divided into portions that represent the relative
frequencies or percentages of a population or a sample belonging to different categories is called a pie chart
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Table 26 Calculating Angle Sizes for the Pie Chart
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Figure 22 Pie chart for the percentage distribution of Table 25
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ORGANIZING AND GRAPHING QUANTITATIVE Frequency Distributions Constructing Frequency Distribution Tables Relative and Percentage Distributions Graphing Grouped Data
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Table 27 Weekly Earnings of 100 Employees of a Company
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Frequency Distributions Definition A frequency distribution for quantitative data lists all
the classes and the number of values that belong to each class Data presented in the form of a frequency distribution are called grouped data
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Frequency Distributions Definition The class boundary is given by the midpoint of the upper
limit of one class and the lower limit of the next class
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Frequency Distributions
Finding Class Width
Class width = Upper boundary ndash Lower boundary
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Frequency Distributions
Calculating Class Midpoint or Mark
2
limit Upper limit Lower markor midpoint Class
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Constructing Frequency Distribution Tables
Calculation of Class Width
classes ofNumber
alueSmallest v - lueLargest va widthclass eApproximat
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Table 28 Class Boundaries Class Widths and Class Midpoints for Table 27
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-3
The following data give the total number of iPodsreg sold by a mail order company on each of 30 days Construct a frequency distribution table
8 25 11 15 29 22 10 5 17 21
22 13 26 16 18 12 9 26 20 16
23 14 19 23 20 16 27 16 21 14
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Example 2-3 Solution
29 5Approximate width of each class 48
5
Now we round this approximate width to a convenient number say 5 The lower limit of the first class can be taken as 5 or any number less than 5 Suppose we take 5 as the lower limit of the first class Then our classes will be 5 ndash 9 10 ndash 14 15 ndash 19 20 ndash 24 and 25 ndash 29
The minimum value is 5 and the maximum value is 29 Suppose we decide to group these data using five classes of equal width Then
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Table 29 Frequency Distribution for the Data on iPods Sold
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Relative Frequency and Percentage Distributions
Calculating Relative Frequency and Percentage
100 frequency) (Relative Percentage
sfrequencie all of Sum
class that of Frequencyclass a of frequency Relative
f
f
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Example 2-4 Calculate the relative frequencies and percentages for
Table 29
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Example 2-4 SolutionTable 210 Relative Frequency and Percentage Distributions for Table 29
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Graphing Grouped Data Definition A histogram is a graph in which classes are marked on the
horizontal axis and the frequencies relative frequencies or percentages are marked on the vertical axis The frequencies relative frequencies or percentages are represented by the heights of the bars In a histogram the bars are drawn adjacent to each other
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Figure 23 Frequency histogram for Table 29
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Figure 24 Relative frequency histogram for Table 210
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Case Study 2-3 How Long Does Your Typical One-Way Commute Take
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Graphing Grouped Data Definition A graph formed by joining the midpoints of the tops of
successive bars in a histogram with straight lines is called a polygon
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Figure 25 Frequency polygon for Table 29
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Case Study 2-4 How Much Does it Cost to Insure a Car
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Figure 26 Frequency distribution curve
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Example 2-5 The percentage of the population working in the United
States peaked in 2000 but dropped to the lowest level in 30 years in 2010 Table 211 shows the percentage of the population working in each of the 50 states in 2010 These percentages exclude military personnel and self-employed persons (Source USA TODAY April 14 2011 Based on data from the US Census Bureau and US Bureau of Labor Statistics)
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Example 2-5
Construct a frequency distribution table Calculate the relative frequencies and percentages for all classes
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Example 2-5 Solution
The minimum value in the data set of Table 211 is 367 and the maximum value is 558 Suppose we decide to group these data using six classes of equal width Then
We round this to a more convenient number say 3 We can take a lower limit of the first class equal to 367 or any number lower than 367 If we start the first class at 36 the classes will be written as 36 to less than 39 39 to less than 42 and so on
119808119849119849119851119848119857119842119846119834119853119838119856119842119837119853119841119848119839 119834119836119845119834119852119852=558minus367
6=318
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Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
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Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
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Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
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Figure 27 Bar graph for Table 213
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Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
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SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
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Figure 28 Symmetric histograms
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Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
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Figure 210 A histogram with uniform distribution
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Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
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Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
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Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
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Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
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Figure 212 Ogive for the cumulative frequency distribution of Table 214
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STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
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Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
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Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
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Figure 213 Stem-and-leaf display
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Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
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Figure 214 Stem-and-leaf display of test scores
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Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
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Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
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Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
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Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
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Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
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Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
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Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
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DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
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Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Table 22 Status of 50 Students
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
ORGANIZING AND GRAPHING DATA
Frequency Distributions Relative Frequency and Percentage Distributions Graphical Presentation of Qualitative Data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 23 Types of Employment Students Intend to Engage In
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Frequency Distributions Definition A frequency distribution of a qualitative variable lists all
categories and the number of elements that belong to each of the categories
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-1
A sample of 30 persons who often consume donuts were asked what variety of donuts was their favorite The responses from these 30 persons were as follows
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-1
glazed filled other plain glazed other
frosted filled filled glazed other frosted
glazed plain other glazed glazed filled
frosted plain other other frosted filled
filled other frosted glazed glazed filled
Construct a frequency distribution table for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-1 SolutionTable 24 Frequency Distribution of Favorite Donut Variety
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Relative Frequency and Percentage Distributions
Calculating Relative Frequency of a Category
sfrequencie all of Sum
category that ofFrequency category a offrequency lativeRe
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Relative Frequency and Percentage Distributions
Calculating Percentage Percentage = (Relative frequency) 100
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Example 2-2 Determine the relative frequency and percentage for the
data in Table 24
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Example 2-2 SolutionTable 25 Relative Frequency and Percentage Distributions of Favorite Donut Variety
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Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their Parents
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Graphical Presentation of Qualitative Data
Definition A graph made of bars whose heights represent the
frequencies of respective categories is called a bar graph
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Figure 21 Bar graph for the frequency distribution of Table 24
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Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
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Graphical Presentation of Qualitative Data Definition A circle divided into portions that represent the relative
frequencies or percentages of a population or a sample belonging to different categories is called a pie chart
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Table 26 Calculating Angle Sizes for the Pie Chart
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Figure 22 Pie chart for the percentage distribution of Table 25
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ORGANIZING AND GRAPHING QUANTITATIVE Frequency Distributions Constructing Frequency Distribution Tables Relative and Percentage Distributions Graphing Grouped Data
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Table 27 Weekly Earnings of 100 Employees of a Company
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Frequency Distributions Definition A frequency distribution for quantitative data lists all
the classes and the number of values that belong to each class Data presented in the form of a frequency distribution are called grouped data
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Frequency Distributions Definition The class boundary is given by the midpoint of the upper
limit of one class and the lower limit of the next class
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Frequency Distributions
Finding Class Width
Class width = Upper boundary ndash Lower boundary
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Frequency Distributions
Calculating Class Midpoint or Mark
2
limit Upper limit Lower markor midpoint Class
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Constructing Frequency Distribution Tables
Calculation of Class Width
classes ofNumber
alueSmallest v - lueLargest va widthclass eApproximat
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Table 28 Class Boundaries Class Widths and Class Midpoints for Table 27
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-3
The following data give the total number of iPodsreg sold by a mail order company on each of 30 days Construct a frequency distribution table
8 25 11 15 29 22 10 5 17 21
22 13 26 16 18 12 9 26 20 16
23 14 19 23 20 16 27 16 21 14
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Example 2-3 Solution
29 5Approximate width of each class 48
5
Now we round this approximate width to a convenient number say 5 The lower limit of the first class can be taken as 5 or any number less than 5 Suppose we take 5 as the lower limit of the first class Then our classes will be 5 ndash 9 10 ndash 14 15 ndash 19 20 ndash 24 and 25 ndash 29
The minimum value is 5 and the maximum value is 29 Suppose we decide to group these data using five classes of equal width Then
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Table 29 Frequency Distribution for the Data on iPods Sold
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Relative Frequency and Percentage Distributions
Calculating Relative Frequency and Percentage
100 frequency) (Relative Percentage
sfrequencie all of Sum
class that of Frequencyclass a of frequency Relative
f
f
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Example 2-4 Calculate the relative frequencies and percentages for
Table 29
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Example 2-4 SolutionTable 210 Relative Frequency and Percentage Distributions for Table 29
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Graphing Grouped Data Definition A histogram is a graph in which classes are marked on the
horizontal axis and the frequencies relative frequencies or percentages are marked on the vertical axis The frequencies relative frequencies or percentages are represented by the heights of the bars In a histogram the bars are drawn adjacent to each other
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Figure 23 Frequency histogram for Table 29
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Figure 24 Relative frequency histogram for Table 210
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Case Study 2-3 How Long Does Your Typical One-Way Commute Take
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Graphing Grouped Data Definition A graph formed by joining the midpoints of the tops of
successive bars in a histogram with straight lines is called a polygon
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Figure 25 Frequency polygon for Table 29
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Case Study 2-4 How Much Does it Cost to Insure a Car
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Figure 26 Frequency distribution curve
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Example 2-5 The percentage of the population working in the United
States peaked in 2000 but dropped to the lowest level in 30 years in 2010 Table 211 shows the percentage of the population working in each of the 50 states in 2010 These percentages exclude military personnel and self-employed persons (Source USA TODAY April 14 2011 Based on data from the US Census Bureau and US Bureau of Labor Statistics)
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5
Construct a frequency distribution table Calculate the relative frequencies and percentages for all classes
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Example 2-5 Solution
The minimum value in the data set of Table 211 is 367 and the maximum value is 558 Suppose we decide to group these data using six classes of equal width Then
We round this to a more convenient number say 3 We can take a lower limit of the first class equal to 367 or any number lower than 367 If we start the first class at 36 the classes will be written as 36 to less than 39 39 to less than 42 and so on
119808119849119849119851119848119857119842119846119834119853119838119856119842119837119853119841119848119839 119834119836119845119834119852119852=558minus367
6=318
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Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
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Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
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Figure 27 Bar graph for Table 213
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Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
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SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
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Figure 28 Symmetric histograms
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Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
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Figure 210 A histogram with uniform distribution
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Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
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Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
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Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
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Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
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Figure 212 Ogive for the cumulative frequency distribution of Table 214
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STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
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Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
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Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
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Figure 213 Stem-and-leaf display
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Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
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Figure 214 Stem-and-leaf display of test scores
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Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
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Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
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Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
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Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
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Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
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Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
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Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
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Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
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DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
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Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
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Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
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Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
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Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
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Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
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Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
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Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
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Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
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TI-84
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TI-84
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Minitab
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Minitab
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Minitab
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Minitab
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Minitab
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Excel
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Excel
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- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
ORGANIZING AND GRAPHING DATA
Frequency Distributions Relative Frequency and Percentage Distributions Graphical Presentation of Qualitative Data
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Table 23 Types of Employment Students Intend to Engage In
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Frequency Distributions Definition A frequency distribution of a qualitative variable lists all
categories and the number of elements that belong to each of the categories
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-1
A sample of 30 persons who often consume donuts were asked what variety of donuts was their favorite The responses from these 30 persons were as follows
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-1
glazed filled other plain glazed other
frosted filled filled glazed other frosted
glazed plain other glazed glazed filled
frosted plain other other frosted filled
filled other frosted glazed glazed filled
Construct a frequency distribution table for these data
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Example 2-1 SolutionTable 24 Frequency Distribution of Favorite Donut Variety
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Relative Frequency and Percentage Distributions
Calculating Relative Frequency of a Category
sfrequencie all of Sum
category that ofFrequency category a offrequency lativeRe
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Relative Frequency and Percentage Distributions
Calculating Percentage Percentage = (Relative frequency) 100
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-2 Determine the relative frequency and percentage for the
data in Table 24
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Example 2-2 SolutionTable 25 Relative Frequency and Percentage Distributions of Favorite Donut Variety
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Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their Parents
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Graphical Presentation of Qualitative Data
Definition A graph made of bars whose heights represent the
frequencies of respective categories is called a bar graph
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 21 Bar graph for the frequency distribution of Table 24
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Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Graphical Presentation of Qualitative Data Definition A circle divided into portions that represent the relative
frequencies or percentages of a population or a sample belonging to different categories is called a pie chart
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Table 26 Calculating Angle Sizes for the Pie Chart
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Figure 22 Pie chart for the percentage distribution of Table 25
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ORGANIZING AND GRAPHING QUANTITATIVE Frequency Distributions Constructing Frequency Distribution Tables Relative and Percentage Distributions Graphing Grouped Data
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Table 27 Weekly Earnings of 100 Employees of a Company
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Frequency Distributions Definition A frequency distribution for quantitative data lists all
the classes and the number of values that belong to each class Data presented in the form of a frequency distribution are called grouped data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Frequency Distributions Definition The class boundary is given by the midpoint of the upper
limit of one class and the lower limit of the next class
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Frequency Distributions
Finding Class Width
Class width = Upper boundary ndash Lower boundary
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Frequency Distributions
Calculating Class Midpoint or Mark
2
limit Upper limit Lower markor midpoint Class
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Constructing Frequency Distribution Tables
Calculation of Class Width
classes ofNumber
alueSmallest v - lueLargest va widthclass eApproximat
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 28 Class Boundaries Class Widths and Class Midpoints for Table 27
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-3
The following data give the total number of iPodsreg sold by a mail order company on each of 30 days Construct a frequency distribution table
8 25 11 15 29 22 10 5 17 21
22 13 26 16 18 12 9 26 20 16
23 14 19 23 20 16 27 16 21 14
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-3 Solution
29 5Approximate width of each class 48
5
Now we round this approximate width to a convenient number say 5 The lower limit of the first class can be taken as 5 or any number less than 5 Suppose we take 5 as the lower limit of the first class Then our classes will be 5 ndash 9 10 ndash 14 15 ndash 19 20 ndash 24 and 25 ndash 29
The minimum value is 5 and the maximum value is 29 Suppose we decide to group these data using five classes of equal width Then
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Table 29 Frequency Distribution for the Data on iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Relative Frequency and Percentage Distributions
Calculating Relative Frequency and Percentage
100 frequency) (Relative Percentage
sfrequencie all of Sum
class that of Frequencyclass a of frequency Relative
f
f
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Example 2-4 Calculate the relative frequencies and percentages for
Table 29
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Example 2-4 SolutionTable 210 Relative Frequency and Percentage Distributions for Table 29
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Graphing Grouped Data Definition A histogram is a graph in which classes are marked on the
horizontal axis and the frequencies relative frequencies or percentages are marked on the vertical axis The frequencies relative frequencies or percentages are represented by the heights of the bars In a histogram the bars are drawn adjacent to each other
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 23 Frequency histogram for Table 29
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Figure 24 Relative frequency histogram for Table 210
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Case Study 2-3 How Long Does Your Typical One-Way Commute Take
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Graphing Grouped Data Definition A graph formed by joining the midpoints of the tops of
successive bars in a histogram with straight lines is called a polygon
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Figure 25 Frequency polygon for Table 29
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Case Study 2-4 How Much Does it Cost to Insure a Car
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Figure 26 Frequency distribution curve
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Example 2-5 The percentage of the population working in the United
States peaked in 2000 but dropped to the lowest level in 30 years in 2010 Table 211 shows the percentage of the population working in each of the 50 states in 2010 These percentages exclude military personnel and self-employed persons (Source USA TODAY April 14 2011 Based on data from the US Census Bureau and US Bureau of Labor Statistics)
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5
Construct a frequency distribution table Calculate the relative frequencies and percentages for all classes
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Example 2-5 Solution
The minimum value in the data set of Table 211 is 367 and the maximum value is 558 Suppose we decide to group these data using six classes of equal width Then
We round this to a more convenient number say 3 We can take a lower limit of the first class equal to 367 or any number lower than 367 If we start the first class at 36 the classes will be written as 36 to less than 39 39 to less than 42 and so on
119808119849119849119851119848119857119842119846119834119853119838119856119842119837119853119841119848119839 119834119836119845119834119852119852=558minus367
6=318
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Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
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Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
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Figure 27 Bar graph for Table 213
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Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
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SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
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Figure 28 Symmetric histograms
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Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
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Figure 210 A histogram with uniform distribution
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Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
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Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
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Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
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Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
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Figure 212 Ogive for the cumulative frequency distribution of Table 214
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STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
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Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
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Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
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Figure 213 Stem-and-leaf display
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Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
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Figure 214 Stem-and-leaf display of test scores
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Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
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Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
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Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
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Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
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Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
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Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
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Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
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Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
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DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
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Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
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Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
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Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
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Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
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Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
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Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
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Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
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Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
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TI-84
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TI-84
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Minitab
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Minitab
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Minitab
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Minitab
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Minitab
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Excel
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Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Table 23 Types of Employment Students Intend to Engage In
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Frequency Distributions Definition A frequency distribution of a qualitative variable lists all
categories and the number of elements that belong to each of the categories
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Example 2-1
A sample of 30 persons who often consume donuts were asked what variety of donuts was their favorite The responses from these 30 persons were as follows
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Example 2-1
glazed filled other plain glazed other
frosted filled filled glazed other frosted
glazed plain other glazed glazed filled
frosted plain other other frosted filled
filled other frosted glazed glazed filled
Construct a frequency distribution table for these data
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Example 2-1 SolutionTable 24 Frequency Distribution of Favorite Donut Variety
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Relative Frequency and Percentage Distributions
Calculating Relative Frequency of a Category
sfrequencie all of Sum
category that ofFrequency category a offrequency lativeRe
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Relative Frequency and Percentage Distributions
Calculating Percentage Percentage = (Relative frequency) 100
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Example 2-2 Determine the relative frequency and percentage for the
data in Table 24
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Example 2-2 SolutionTable 25 Relative Frequency and Percentage Distributions of Favorite Donut Variety
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Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their Parents
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Graphical Presentation of Qualitative Data
Definition A graph made of bars whose heights represent the
frequencies of respective categories is called a bar graph
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Figure 21 Bar graph for the frequency distribution of Table 24
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Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
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Graphical Presentation of Qualitative Data Definition A circle divided into portions that represent the relative
frequencies or percentages of a population or a sample belonging to different categories is called a pie chart
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Table 26 Calculating Angle Sizes for the Pie Chart
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Figure 22 Pie chart for the percentage distribution of Table 25
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ORGANIZING AND GRAPHING QUANTITATIVE Frequency Distributions Constructing Frequency Distribution Tables Relative and Percentage Distributions Graphing Grouped Data
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Table 27 Weekly Earnings of 100 Employees of a Company
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Frequency Distributions Definition A frequency distribution for quantitative data lists all
the classes and the number of values that belong to each class Data presented in the form of a frequency distribution are called grouped data
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Frequency Distributions Definition The class boundary is given by the midpoint of the upper
limit of one class and the lower limit of the next class
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Frequency Distributions
Finding Class Width
Class width = Upper boundary ndash Lower boundary
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Frequency Distributions
Calculating Class Midpoint or Mark
2
limit Upper limit Lower markor midpoint Class
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Constructing Frequency Distribution Tables
Calculation of Class Width
classes ofNumber
alueSmallest v - lueLargest va widthclass eApproximat
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Table 28 Class Boundaries Class Widths and Class Midpoints for Table 27
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Example 2-3
The following data give the total number of iPodsreg sold by a mail order company on each of 30 days Construct a frequency distribution table
8 25 11 15 29 22 10 5 17 21
22 13 26 16 18 12 9 26 20 16
23 14 19 23 20 16 27 16 21 14
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Example 2-3 Solution
29 5Approximate width of each class 48
5
Now we round this approximate width to a convenient number say 5 The lower limit of the first class can be taken as 5 or any number less than 5 Suppose we take 5 as the lower limit of the first class Then our classes will be 5 ndash 9 10 ndash 14 15 ndash 19 20 ndash 24 and 25 ndash 29
The minimum value is 5 and the maximum value is 29 Suppose we decide to group these data using five classes of equal width Then
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Table 29 Frequency Distribution for the Data on iPods Sold
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Relative Frequency and Percentage Distributions
Calculating Relative Frequency and Percentage
100 frequency) (Relative Percentage
sfrequencie all of Sum
class that of Frequencyclass a of frequency Relative
f
f
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Example 2-4 Calculate the relative frequencies and percentages for
Table 29
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Example 2-4 SolutionTable 210 Relative Frequency and Percentage Distributions for Table 29
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Graphing Grouped Data Definition A histogram is a graph in which classes are marked on the
horizontal axis and the frequencies relative frequencies or percentages are marked on the vertical axis The frequencies relative frequencies or percentages are represented by the heights of the bars In a histogram the bars are drawn adjacent to each other
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Figure 23 Frequency histogram for Table 29
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Figure 24 Relative frequency histogram for Table 210
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Case Study 2-3 How Long Does Your Typical One-Way Commute Take
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Graphing Grouped Data Definition A graph formed by joining the midpoints of the tops of
successive bars in a histogram with straight lines is called a polygon
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Figure 25 Frequency polygon for Table 29
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Case Study 2-4 How Much Does it Cost to Insure a Car
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Figure 26 Frequency distribution curve
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Example 2-5 The percentage of the population working in the United
States peaked in 2000 but dropped to the lowest level in 30 years in 2010 Table 211 shows the percentage of the population working in each of the 50 states in 2010 These percentages exclude military personnel and self-employed persons (Source USA TODAY April 14 2011 Based on data from the US Census Bureau and US Bureau of Labor Statistics)
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Example 2-5
Construct a frequency distribution table Calculate the relative frequencies and percentages for all classes
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Example 2-5 Solution
The minimum value in the data set of Table 211 is 367 and the maximum value is 558 Suppose we decide to group these data using six classes of equal width Then
We round this to a more convenient number say 3 We can take a lower limit of the first class equal to 367 or any number lower than 367 If we start the first class at 36 the classes will be written as 36 to less than 39 39 to less than 42 and so on
119808119849119849119851119848119857119842119846119834119853119838119856119842119837119853119841119848119839 119834119836119845119834119852119852=558minus367
6=318
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Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
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Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
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Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
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Figure 27 Bar graph for Table 213
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Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
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SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
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Figure 28 Symmetric histograms
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Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
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Figure 210 A histogram with uniform distribution
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Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
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Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
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Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
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Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
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Figure 212 Ogive for the cumulative frequency distribution of Table 214
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STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
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Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
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Figure 213 Stem-and-leaf display
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Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
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Figure 214 Stem-and-leaf display of test scores
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Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
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Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
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Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
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Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
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Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
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Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
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Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
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DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
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Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
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Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
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Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
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Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
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Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Frequency Distributions Definition A frequency distribution of a qualitative variable lists all
categories and the number of elements that belong to each of the categories
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-1
A sample of 30 persons who often consume donuts were asked what variety of donuts was their favorite The responses from these 30 persons were as follows
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-1
glazed filled other plain glazed other
frosted filled filled glazed other frosted
glazed plain other glazed glazed filled
frosted plain other other frosted filled
filled other frosted glazed glazed filled
Construct a frequency distribution table for these data
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Example 2-1 SolutionTable 24 Frequency Distribution of Favorite Donut Variety
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Relative Frequency and Percentage Distributions
Calculating Relative Frequency of a Category
sfrequencie all of Sum
category that ofFrequency category a offrequency lativeRe
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Relative Frequency and Percentage Distributions
Calculating Percentage Percentage = (Relative frequency) 100
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Example 2-2 Determine the relative frequency and percentage for the
data in Table 24
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Example 2-2 SolutionTable 25 Relative Frequency and Percentage Distributions of Favorite Donut Variety
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Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their Parents
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Graphical Presentation of Qualitative Data
Definition A graph made of bars whose heights represent the
frequencies of respective categories is called a bar graph
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Figure 21 Bar graph for the frequency distribution of Table 24
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Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
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Graphical Presentation of Qualitative Data Definition A circle divided into portions that represent the relative
frequencies or percentages of a population or a sample belonging to different categories is called a pie chart
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Table 26 Calculating Angle Sizes for the Pie Chart
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Figure 22 Pie chart for the percentage distribution of Table 25
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ORGANIZING AND GRAPHING QUANTITATIVE Frequency Distributions Constructing Frequency Distribution Tables Relative and Percentage Distributions Graphing Grouped Data
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Table 27 Weekly Earnings of 100 Employees of a Company
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Frequency Distributions Definition A frequency distribution for quantitative data lists all
the classes and the number of values that belong to each class Data presented in the form of a frequency distribution are called grouped data
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Frequency Distributions Definition The class boundary is given by the midpoint of the upper
limit of one class and the lower limit of the next class
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Frequency Distributions
Finding Class Width
Class width = Upper boundary ndash Lower boundary
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Frequency Distributions
Calculating Class Midpoint or Mark
2
limit Upper limit Lower markor midpoint Class
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Constructing Frequency Distribution Tables
Calculation of Class Width
classes ofNumber
alueSmallest v - lueLargest va widthclass eApproximat
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Table 28 Class Boundaries Class Widths and Class Midpoints for Table 27
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Example 2-3
The following data give the total number of iPodsreg sold by a mail order company on each of 30 days Construct a frequency distribution table
8 25 11 15 29 22 10 5 17 21
22 13 26 16 18 12 9 26 20 16
23 14 19 23 20 16 27 16 21 14
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Example 2-3 Solution
29 5Approximate width of each class 48
5
Now we round this approximate width to a convenient number say 5 The lower limit of the first class can be taken as 5 or any number less than 5 Suppose we take 5 as the lower limit of the first class Then our classes will be 5 ndash 9 10 ndash 14 15 ndash 19 20 ndash 24 and 25 ndash 29
The minimum value is 5 and the maximum value is 29 Suppose we decide to group these data using five classes of equal width Then
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Table 29 Frequency Distribution for the Data on iPods Sold
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Relative Frequency and Percentage Distributions
Calculating Relative Frequency and Percentage
100 frequency) (Relative Percentage
sfrequencie all of Sum
class that of Frequencyclass a of frequency Relative
f
f
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Example 2-4 Calculate the relative frequencies and percentages for
Table 29
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Example 2-4 SolutionTable 210 Relative Frequency and Percentage Distributions for Table 29
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Graphing Grouped Data Definition A histogram is a graph in which classes are marked on the
horizontal axis and the frequencies relative frequencies or percentages are marked on the vertical axis The frequencies relative frequencies or percentages are represented by the heights of the bars In a histogram the bars are drawn adjacent to each other
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Figure 23 Frequency histogram for Table 29
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Figure 24 Relative frequency histogram for Table 210
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Case Study 2-3 How Long Does Your Typical One-Way Commute Take
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Graphing Grouped Data Definition A graph formed by joining the midpoints of the tops of
successive bars in a histogram with straight lines is called a polygon
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Figure 25 Frequency polygon for Table 29
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Case Study 2-4 How Much Does it Cost to Insure a Car
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Figure 26 Frequency distribution curve
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Example 2-5 The percentage of the population working in the United
States peaked in 2000 but dropped to the lowest level in 30 years in 2010 Table 211 shows the percentage of the population working in each of the 50 states in 2010 These percentages exclude military personnel and self-employed persons (Source USA TODAY April 14 2011 Based on data from the US Census Bureau and US Bureau of Labor Statistics)
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Example 2-5
Construct a frequency distribution table Calculate the relative frequencies and percentages for all classes
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Example 2-5 Solution
The minimum value in the data set of Table 211 is 367 and the maximum value is 558 Suppose we decide to group these data using six classes of equal width Then
We round this to a more convenient number say 3 We can take a lower limit of the first class equal to 367 or any number lower than 367 If we start the first class at 36 the classes will be written as 36 to less than 39 39 to less than 42 and so on
119808119849119849119851119848119857119842119846119834119853119838119856119842119837119853119841119848119839 119834119836119845119834119852119852=558minus367
6=318
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Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
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Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
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Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
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Figure 27 Bar graph for Table 213
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Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
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SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
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Figure 28 Symmetric histograms
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Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
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Figure 210 A histogram with uniform distribution
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Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
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Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
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Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
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Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
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Figure 212 Ogive for the cumulative frequency distribution of Table 214
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STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
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Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
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Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
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Figure 213 Stem-and-leaf display
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Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
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Figure 214 Stem-and-leaf display of test scores
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Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
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Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
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Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
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Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
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Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
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Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
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Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
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Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
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DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
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Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
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Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
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Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
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Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
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Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
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Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
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Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
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TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Example 2-1
A sample of 30 persons who often consume donuts were asked what variety of donuts was their favorite The responses from these 30 persons were as follows
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-1
glazed filled other plain glazed other
frosted filled filled glazed other frosted
glazed plain other glazed glazed filled
frosted plain other other frosted filled
filled other frosted glazed glazed filled
Construct a frequency distribution table for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-1 SolutionTable 24 Frequency Distribution of Favorite Donut Variety
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Relative Frequency and Percentage Distributions
Calculating Relative Frequency of a Category
sfrequencie all of Sum
category that ofFrequency category a offrequency lativeRe
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Relative Frequency and Percentage Distributions
Calculating Percentage Percentage = (Relative frequency) 100
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-2 Determine the relative frequency and percentage for the
data in Table 24
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Example 2-2 SolutionTable 25 Relative Frequency and Percentage Distributions of Favorite Donut Variety
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Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their Parents
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Graphical Presentation of Qualitative Data
Definition A graph made of bars whose heights represent the
frequencies of respective categories is called a bar graph
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 21 Bar graph for the frequency distribution of Table 24
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Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Graphical Presentation of Qualitative Data Definition A circle divided into portions that represent the relative
frequencies or percentages of a population or a sample belonging to different categories is called a pie chart
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 26 Calculating Angle Sizes for the Pie Chart
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Figure 22 Pie chart for the percentage distribution of Table 25
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ORGANIZING AND GRAPHING QUANTITATIVE Frequency Distributions Constructing Frequency Distribution Tables Relative and Percentage Distributions Graphing Grouped Data
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Table 27 Weekly Earnings of 100 Employees of a Company
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Frequency Distributions Definition A frequency distribution for quantitative data lists all
the classes and the number of values that belong to each class Data presented in the form of a frequency distribution are called grouped data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Frequency Distributions Definition The class boundary is given by the midpoint of the upper
limit of one class and the lower limit of the next class
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Frequency Distributions
Finding Class Width
Class width = Upper boundary ndash Lower boundary
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Frequency Distributions
Calculating Class Midpoint or Mark
2
limit Upper limit Lower markor midpoint Class
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Constructing Frequency Distribution Tables
Calculation of Class Width
classes ofNumber
alueSmallest v - lueLargest va widthclass eApproximat
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 28 Class Boundaries Class Widths and Class Midpoints for Table 27
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-3
The following data give the total number of iPodsreg sold by a mail order company on each of 30 days Construct a frequency distribution table
8 25 11 15 29 22 10 5 17 21
22 13 26 16 18 12 9 26 20 16
23 14 19 23 20 16 27 16 21 14
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-3 Solution
29 5Approximate width of each class 48
5
Now we round this approximate width to a convenient number say 5 The lower limit of the first class can be taken as 5 or any number less than 5 Suppose we take 5 as the lower limit of the first class Then our classes will be 5 ndash 9 10 ndash 14 15 ndash 19 20 ndash 24 and 25 ndash 29
The minimum value is 5 and the maximum value is 29 Suppose we decide to group these data using five classes of equal width Then
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 29 Frequency Distribution for the Data on iPods Sold
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Relative Frequency and Percentage Distributions
Calculating Relative Frequency and Percentage
100 frequency) (Relative Percentage
sfrequencie all of Sum
class that of Frequencyclass a of frequency Relative
f
f
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Example 2-4 Calculate the relative frequencies and percentages for
Table 29
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Example 2-4 SolutionTable 210 Relative Frequency and Percentage Distributions for Table 29
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Graphing Grouped Data Definition A histogram is a graph in which classes are marked on the
horizontal axis and the frequencies relative frequencies or percentages are marked on the vertical axis The frequencies relative frequencies or percentages are represented by the heights of the bars In a histogram the bars are drawn adjacent to each other
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Figure 23 Frequency histogram for Table 29
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Figure 24 Relative frequency histogram for Table 210
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Case Study 2-3 How Long Does Your Typical One-Way Commute Take
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Graphing Grouped Data Definition A graph formed by joining the midpoints of the tops of
successive bars in a histogram with straight lines is called a polygon
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Figure 25 Frequency polygon for Table 29
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Case Study 2-4 How Much Does it Cost to Insure a Car
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Figure 26 Frequency distribution curve
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Example 2-5 The percentage of the population working in the United
States peaked in 2000 but dropped to the lowest level in 30 years in 2010 Table 211 shows the percentage of the population working in each of the 50 states in 2010 These percentages exclude military personnel and self-employed persons (Source USA TODAY April 14 2011 Based on data from the US Census Bureau and US Bureau of Labor Statistics)
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Example 2-5
Construct a frequency distribution table Calculate the relative frequencies and percentages for all classes
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Example 2-5 Solution
The minimum value in the data set of Table 211 is 367 and the maximum value is 558 Suppose we decide to group these data using six classes of equal width Then
We round this to a more convenient number say 3 We can take a lower limit of the first class equal to 367 or any number lower than 367 If we start the first class at 36 the classes will be written as 36 to less than 39 39 to less than 42 and so on
119808119849119849119851119848119857119842119846119834119853119838119856119842119837119853119841119848119839 119834119836119845119834119852119852=558minus367
6=318
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Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
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Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
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Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
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Figure 27 Bar graph for Table 213
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Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
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SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
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Figure 28 Symmetric histograms
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Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
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Figure 210 A histogram with uniform distribution
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Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
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Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
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Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
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Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
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Figure 212 Ogive for the cumulative frequency distribution of Table 214
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STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
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Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
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Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
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Figure 213 Stem-and-leaf display
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Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
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Figure 214 Stem-and-leaf display of test scores
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Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
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Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
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Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
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Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
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Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
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Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
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Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
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Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
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DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
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Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
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Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
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Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
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Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
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Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
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Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
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Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
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Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
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TI-84
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TI-84
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Minitab
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Minitab
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Minitab
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Minitab
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Minitab
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Excel
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Excel
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- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Example 2-1
glazed filled other plain glazed other
frosted filled filled glazed other frosted
glazed plain other glazed glazed filled
frosted plain other other frosted filled
filled other frosted glazed glazed filled
Construct a frequency distribution table for these data
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Example 2-1 SolutionTable 24 Frequency Distribution of Favorite Donut Variety
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Relative Frequency and Percentage Distributions
Calculating Relative Frequency of a Category
sfrequencie all of Sum
category that ofFrequency category a offrequency lativeRe
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Relative Frequency and Percentage Distributions
Calculating Percentage Percentage = (Relative frequency) 100
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Example 2-2 Determine the relative frequency and percentage for the
data in Table 24
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Example 2-2 SolutionTable 25 Relative Frequency and Percentage Distributions of Favorite Donut Variety
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Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their Parents
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Graphical Presentation of Qualitative Data
Definition A graph made of bars whose heights represent the
frequencies of respective categories is called a bar graph
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Figure 21 Bar graph for the frequency distribution of Table 24
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Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
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Graphical Presentation of Qualitative Data Definition A circle divided into portions that represent the relative
frequencies or percentages of a population or a sample belonging to different categories is called a pie chart
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Table 26 Calculating Angle Sizes for the Pie Chart
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Figure 22 Pie chart for the percentage distribution of Table 25
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ORGANIZING AND GRAPHING QUANTITATIVE Frequency Distributions Constructing Frequency Distribution Tables Relative and Percentage Distributions Graphing Grouped Data
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Table 27 Weekly Earnings of 100 Employees of a Company
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Frequency Distributions Definition A frequency distribution for quantitative data lists all
the classes and the number of values that belong to each class Data presented in the form of a frequency distribution are called grouped data
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Frequency Distributions Definition The class boundary is given by the midpoint of the upper
limit of one class and the lower limit of the next class
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Frequency Distributions
Finding Class Width
Class width = Upper boundary ndash Lower boundary
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Frequency Distributions
Calculating Class Midpoint or Mark
2
limit Upper limit Lower markor midpoint Class
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Constructing Frequency Distribution Tables
Calculation of Class Width
classes ofNumber
alueSmallest v - lueLargest va widthclass eApproximat
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Table 28 Class Boundaries Class Widths and Class Midpoints for Table 27
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Example 2-3
The following data give the total number of iPodsreg sold by a mail order company on each of 30 days Construct a frequency distribution table
8 25 11 15 29 22 10 5 17 21
22 13 26 16 18 12 9 26 20 16
23 14 19 23 20 16 27 16 21 14
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Example 2-3 Solution
29 5Approximate width of each class 48
5
Now we round this approximate width to a convenient number say 5 The lower limit of the first class can be taken as 5 or any number less than 5 Suppose we take 5 as the lower limit of the first class Then our classes will be 5 ndash 9 10 ndash 14 15 ndash 19 20 ndash 24 and 25 ndash 29
The minimum value is 5 and the maximum value is 29 Suppose we decide to group these data using five classes of equal width Then
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Table 29 Frequency Distribution for the Data on iPods Sold
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Relative Frequency and Percentage Distributions
Calculating Relative Frequency and Percentage
100 frequency) (Relative Percentage
sfrequencie all of Sum
class that of Frequencyclass a of frequency Relative
f
f
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Example 2-4 Calculate the relative frequencies and percentages for
Table 29
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Example 2-4 SolutionTable 210 Relative Frequency and Percentage Distributions for Table 29
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Graphing Grouped Data Definition A histogram is a graph in which classes are marked on the
horizontal axis and the frequencies relative frequencies or percentages are marked on the vertical axis The frequencies relative frequencies or percentages are represented by the heights of the bars In a histogram the bars are drawn adjacent to each other
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Figure 23 Frequency histogram for Table 29
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Figure 24 Relative frequency histogram for Table 210
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Case Study 2-3 How Long Does Your Typical One-Way Commute Take
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Graphing Grouped Data Definition A graph formed by joining the midpoints of the tops of
successive bars in a histogram with straight lines is called a polygon
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Figure 25 Frequency polygon for Table 29
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Case Study 2-4 How Much Does it Cost to Insure a Car
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Figure 26 Frequency distribution curve
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Example 2-5 The percentage of the population working in the United
States peaked in 2000 but dropped to the lowest level in 30 years in 2010 Table 211 shows the percentage of the population working in each of the 50 states in 2010 These percentages exclude military personnel and self-employed persons (Source USA TODAY April 14 2011 Based on data from the US Census Bureau and US Bureau of Labor Statistics)
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5
Construct a frequency distribution table Calculate the relative frequencies and percentages for all classes
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Example 2-5 Solution
The minimum value in the data set of Table 211 is 367 and the maximum value is 558 Suppose we decide to group these data using six classes of equal width Then
We round this to a more convenient number say 3 We can take a lower limit of the first class equal to 367 or any number lower than 367 If we start the first class at 36 the classes will be written as 36 to less than 39 39 to less than 42 and so on
119808119849119849119851119848119857119842119846119834119853119838119856119842119837119853119841119848119839 119834119836119845119834119852119852=558minus367
6=318
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Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
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Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
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Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
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Figure 27 Bar graph for Table 213
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Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
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SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
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Figure 28 Symmetric histograms
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Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
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Figure 210 A histogram with uniform distribution
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Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
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Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
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Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
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Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
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Figure 212 Ogive for the cumulative frequency distribution of Table 214
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STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
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Figure 213 Stem-and-leaf display
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Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
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Figure 214 Stem-and-leaf display of test scores
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Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
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Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
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Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
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Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
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Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
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Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
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DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
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Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
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Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
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Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
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Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
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Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
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Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
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Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
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Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
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TI-84
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TI-84
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Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Example 2-1 SolutionTable 24 Frequency Distribution of Favorite Donut Variety
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Relative Frequency and Percentage Distributions
Calculating Relative Frequency of a Category
sfrequencie all of Sum
category that ofFrequency category a offrequency lativeRe
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Relative Frequency and Percentage Distributions
Calculating Percentage Percentage = (Relative frequency) 100
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Example 2-2 Determine the relative frequency and percentage for the
data in Table 24
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Example 2-2 SolutionTable 25 Relative Frequency and Percentage Distributions of Favorite Donut Variety
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Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their Parents
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Graphical Presentation of Qualitative Data
Definition A graph made of bars whose heights represent the
frequencies of respective categories is called a bar graph
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Figure 21 Bar graph for the frequency distribution of Table 24
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Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Graphical Presentation of Qualitative Data Definition A circle divided into portions that represent the relative
frequencies or percentages of a population or a sample belonging to different categories is called a pie chart
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Table 26 Calculating Angle Sizes for the Pie Chart
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Figure 22 Pie chart for the percentage distribution of Table 25
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ORGANIZING AND GRAPHING QUANTITATIVE Frequency Distributions Constructing Frequency Distribution Tables Relative and Percentage Distributions Graphing Grouped Data
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Table 27 Weekly Earnings of 100 Employees of a Company
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Frequency Distributions Definition A frequency distribution for quantitative data lists all
the classes and the number of values that belong to each class Data presented in the form of a frequency distribution are called grouped data
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Frequency Distributions Definition The class boundary is given by the midpoint of the upper
limit of one class and the lower limit of the next class
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Frequency Distributions
Finding Class Width
Class width = Upper boundary ndash Lower boundary
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Frequency Distributions
Calculating Class Midpoint or Mark
2
limit Upper limit Lower markor midpoint Class
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Constructing Frequency Distribution Tables
Calculation of Class Width
classes ofNumber
alueSmallest v - lueLargest va widthclass eApproximat
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Table 28 Class Boundaries Class Widths and Class Midpoints for Table 27
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Example 2-3
The following data give the total number of iPodsreg sold by a mail order company on each of 30 days Construct a frequency distribution table
8 25 11 15 29 22 10 5 17 21
22 13 26 16 18 12 9 26 20 16
23 14 19 23 20 16 27 16 21 14
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Example 2-3 Solution
29 5Approximate width of each class 48
5
Now we round this approximate width to a convenient number say 5 The lower limit of the first class can be taken as 5 or any number less than 5 Suppose we take 5 as the lower limit of the first class Then our classes will be 5 ndash 9 10 ndash 14 15 ndash 19 20 ndash 24 and 25 ndash 29
The minimum value is 5 and the maximum value is 29 Suppose we decide to group these data using five classes of equal width Then
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Table 29 Frequency Distribution for the Data on iPods Sold
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Relative Frequency and Percentage Distributions
Calculating Relative Frequency and Percentage
100 frequency) (Relative Percentage
sfrequencie all of Sum
class that of Frequencyclass a of frequency Relative
f
f
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Example 2-4 Calculate the relative frequencies and percentages for
Table 29
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Example 2-4 SolutionTable 210 Relative Frequency and Percentage Distributions for Table 29
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Graphing Grouped Data Definition A histogram is a graph in which classes are marked on the
horizontal axis and the frequencies relative frequencies or percentages are marked on the vertical axis The frequencies relative frequencies or percentages are represented by the heights of the bars In a histogram the bars are drawn adjacent to each other
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Figure 23 Frequency histogram for Table 29
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Figure 24 Relative frequency histogram for Table 210
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Case Study 2-3 How Long Does Your Typical One-Way Commute Take
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Graphing Grouped Data Definition A graph formed by joining the midpoints of the tops of
successive bars in a histogram with straight lines is called a polygon
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Figure 25 Frequency polygon for Table 29
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Case Study 2-4 How Much Does it Cost to Insure a Car
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Figure 26 Frequency distribution curve
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Example 2-5 The percentage of the population working in the United
States peaked in 2000 but dropped to the lowest level in 30 years in 2010 Table 211 shows the percentage of the population working in each of the 50 states in 2010 These percentages exclude military personnel and self-employed persons (Source USA TODAY April 14 2011 Based on data from the US Census Bureau and US Bureau of Labor Statistics)
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Example 2-5
Construct a frequency distribution table Calculate the relative frequencies and percentages for all classes
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Example 2-5 Solution
The minimum value in the data set of Table 211 is 367 and the maximum value is 558 Suppose we decide to group these data using six classes of equal width Then
We round this to a more convenient number say 3 We can take a lower limit of the first class equal to 367 or any number lower than 367 If we start the first class at 36 the classes will be written as 36 to less than 39 39 to less than 42 and so on
119808119849119849119851119848119857119842119846119834119853119838119856119842119837119853119841119848119839 119834119836119845119834119852119852=558minus367
6=318
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Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
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Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
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Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
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Figure 27 Bar graph for Table 213
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Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
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SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
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Figure 28 Symmetric histograms
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Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
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Figure 210 A histogram with uniform distribution
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Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
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Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
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Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
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Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
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Figure 212 Ogive for the cumulative frequency distribution of Table 214
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STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
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Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
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Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
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Figure 213 Stem-and-leaf display
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Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
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Figure 214 Stem-and-leaf display of test scores
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Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
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Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
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Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
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Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
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Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
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Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
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Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
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DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
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Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
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Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
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Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
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Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
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Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Relative Frequency and Percentage Distributions
Calculating Relative Frequency of a Category
sfrequencie all of Sum
category that ofFrequency category a offrequency lativeRe
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Relative Frequency and Percentage Distributions
Calculating Percentage Percentage = (Relative frequency) 100
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-2 Determine the relative frequency and percentage for the
data in Table 24
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-2 SolutionTable 25 Relative Frequency and Percentage Distributions of Favorite Donut Variety
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their Parents
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Graphical Presentation of Qualitative Data
Definition A graph made of bars whose heights represent the
frequencies of respective categories is called a bar graph
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 21 Bar graph for the frequency distribution of Table 24
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Graphical Presentation of Qualitative Data Definition A circle divided into portions that represent the relative
frequencies or percentages of a population or a sample belonging to different categories is called a pie chart
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Table 26 Calculating Angle Sizes for the Pie Chart
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Figure 22 Pie chart for the percentage distribution of Table 25
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ORGANIZING AND GRAPHING QUANTITATIVE Frequency Distributions Constructing Frequency Distribution Tables Relative and Percentage Distributions Graphing Grouped Data
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Table 27 Weekly Earnings of 100 Employees of a Company
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Frequency Distributions Definition A frequency distribution for quantitative data lists all
the classes and the number of values that belong to each class Data presented in the form of a frequency distribution are called grouped data
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Frequency Distributions Definition The class boundary is given by the midpoint of the upper
limit of one class and the lower limit of the next class
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Frequency Distributions
Finding Class Width
Class width = Upper boundary ndash Lower boundary
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Frequency Distributions
Calculating Class Midpoint or Mark
2
limit Upper limit Lower markor midpoint Class
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Constructing Frequency Distribution Tables
Calculation of Class Width
classes ofNumber
alueSmallest v - lueLargest va widthclass eApproximat
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Table 28 Class Boundaries Class Widths and Class Midpoints for Table 27
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Example 2-3
The following data give the total number of iPodsreg sold by a mail order company on each of 30 days Construct a frequency distribution table
8 25 11 15 29 22 10 5 17 21
22 13 26 16 18 12 9 26 20 16
23 14 19 23 20 16 27 16 21 14
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Example 2-3 Solution
29 5Approximate width of each class 48
5
Now we round this approximate width to a convenient number say 5 The lower limit of the first class can be taken as 5 or any number less than 5 Suppose we take 5 as the lower limit of the first class Then our classes will be 5 ndash 9 10 ndash 14 15 ndash 19 20 ndash 24 and 25 ndash 29
The minimum value is 5 and the maximum value is 29 Suppose we decide to group these data using five classes of equal width Then
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Table 29 Frequency Distribution for the Data on iPods Sold
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Relative Frequency and Percentage Distributions
Calculating Relative Frequency and Percentage
100 frequency) (Relative Percentage
sfrequencie all of Sum
class that of Frequencyclass a of frequency Relative
f
f
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Example 2-4 Calculate the relative frequencies and percentages for
Table 29
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Example 2-4 SolutionTable 210 Relative Frequency and Percentage Distributions for Table 29
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Graphing Grouped Data Definition A histogram is a graph in which classes are marked on the
horizontal axis and the frequencies relative frequencies or percentages are marked on the vertical axis The frequencies relative frequencies or percentages are represented by the heights of the bars In a histogram the bars are drawn adjacent to each other
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Figure 23 Frequency histogram for Table 29
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Figure 24 Relative frequency histogram for Table 210
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Case Study 2-3 How Long Does Your Typical One-Way Commute Take
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Graphing Grouped Data Definition A graph formed by joining the midpoints of the tops of
successive bars in a histogram with straight lines is called a polygon
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Figure 25 Frequency polygon for Table 29
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Case Study 2-4 How Much Does it Cost to Insure a Car
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Figure 26 Frequency distribution curve
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Example 2-5 The percentage of the population working in the United
States peaked in 2000 but dropped to the lowest level in 30 years in 2010 Table 211 shows the percentage of the population working in each of the 50 states in 2010 These percentages exclude military personnel and self-employed persons (Source USA TODAY April 14 2011 Based on data from the US Census Bureau and US Bureau of Labor Statistics)
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Example 2-5
Construct a frequency distribution table Calculate the relative frequencies and percentages for all classes
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Example 2-5 Solution
The minimum value in the data set of Table 211 is 367 and the maximum value is 558 Suppose we decide to group these data using six classes of equal width Then
We round this to a more convenient number say 3 We can take a lower limit of the first class equal to 367 or any number lower than 367 If we start the first class at 36 the classes will be written as 36 to less than 39 39 to less than 42 and so on
119808119849119849119851119848119857119842119846119834119853119838119856119842119837119853119841119848119839 119834119836119845119834119852119852=558minus367
6=318
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Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
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Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
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Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
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Figure 27 Bar graph for Table 213
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Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
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SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
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Figure 28 Symmetric histograms
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Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
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Figure 210 A histogram with uniform distribution
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Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
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Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
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Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
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Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
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Figure 212 Ogive for the cumulative frequency distribution of Table 214
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STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
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Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
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Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
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Figure 213 Stem-and-leaf display
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Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
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Figure 214 Stem-and-leaf display of test scores
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Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
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Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
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Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
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Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
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Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
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Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
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Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
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Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
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DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
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Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
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Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
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Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
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Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
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Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
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Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
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Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
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Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
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TI-84
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TI-84
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Minitab
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Minitab
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Minitab
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Minitab
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Minitab
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Excel
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Excel
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- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Relative Frequency and Percentage Distributions
Calculating Percentage Percentage = (Relative frequency) 100
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Example 2-2 Determine the relative frequency and percentage for the
data in Table 24
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Example 2-2 SolutionTable 25 Relative Frequency and Percentage Distributions of Favorite Donut Variety
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Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their Parents
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Graphical Presentation of Qualitative Data
Definition A graph made of bars whose heights represent the
frequencies of respective categories is called a bar graph
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Figure 21 Bar graph for the frequency distribution of Table 24
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Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
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Graphical Presentation of Qualitative Data Definition A circle divided into portions that represent the relative
frequencies or percentages of a population or a sample belonging to different categories is called a pie chart
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Table 26 Calculating Angle Sizes for the Pie Chart
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Figure 22 Pie chart for the percentage distribution of Table 25
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ORGANIZING AND GRAPHING QUANTITATIVE Frequency Distributions Constructing Frequency Distribution Tables Relative and Percentage Distributions Graphing Grouped Data
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Table 27 Weekly Earnings of 100 Employees of a Company
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Frequency Distributions Definition A frequency distribution for quantitative data lists all
the classes and the number of values that belong to each class Data presented in the form of a frequency distribution are called grouped data
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Frequency Distributions Definition The class boundary is given by the midpoint of the upper
limit of one class and the lower limit of the next class
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Frequency Distributions
Finding Class Width
Class width = Upper boundary ndash Lower boundary
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Frequency Distributions
Calculating Class Midpoint or Mark
2
limit Upper limit Lower markor midpoint Class
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Constructing Frequency Distribution Tables
Calculation of Class Width
classes ofNumber
alueSmallest v - lueLargest va widthclass eApproximat
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Table 28 Class Boundaries Class Widths and Class Midpoints for Table 27
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Example 2-3
The following data give the total number of iPodsreg sold by a mail order company on each of 30 days Construct a frequency distribution table
8 25 11 15 29 22 10 5 17 21
22 13 26 16 18 12 9 26 20 16
23 14 19 23 20 16 27 16 21 14
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Example 2-3 Solution
29 5Approximate width of each class 48
5
Now we round this approximate width to a convenient number say 5 The lower limit of the first class can be taken as 5 or any number less than 5 Suppose we take 5 as the lower limit of the first class Then our classes will be 5 ndash 9 10 ndash 14 15 ndash 19 20 ndash 24 and 25 ndash 29
The minimum value is 5 and the maximum value is 29 Suppose we decide to group these data using five classes of equal width Then
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Table 29 Frequency Distribution for the Data on iPods Sold
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Relative Frequency and Percentage Distributions
Calculating Relative Frequency and Percentage
100 frequency) (Relative Percentage
sfrequencie all of Sum
class that of Frequencyclass a of frequency Relative
f
f
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Example 2-4 Calculate the relative frequencies and percentages for
Table 29
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Example 2-4 SolutionTable 210 Relative Frequency and Percentage Distributions for Table 29
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Graphing Grouped Data Definition A histogram is a graph in which classes are marked on the
horizontal axis and the frequencies relative frequencies or percentages are marked on the vertical axis The frequencies relative frequencies or percentages are represented by the heights of the bars In a histogram the bars are drawn adjacent to each other
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Figure 23 Frequency histogram for Table 29
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Figure 24 Relative frequency histogram for Table 210
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Case Study 2-3 How Long Does Your Typical One-Way Commute Take
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Graphing Grouped Data Definition A graph formed by joining the midpoints of the tops of
successive bars in a histogram with straight lines is called a polygon
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Figure 25 Frequency polygon for Table 29
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Case Study 2-4 How Much Does it Cost to Insure a Car
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Figure 26 Frequency distribution curve
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Example 2-5 The percentage of the population working in the United
States peaked in 2000 but dropped to the lowest level in 30 years in 2010 Table 211 shows the percentage of the population working in each of the 50 states in 2010 These percentages exclude military personnel and self-employed persons (Source USA TODAY April 14 2011 Based on data from the US Census Bureau and US Bureau of Labor Statistics)
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5
Construct a frequency distribution table Calculate the relative frequencies and percentages for all classes
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Example 2-5 Solution
The minimum value in the data set of Table 211 is 367 and the maximum value is 558 Suppose we decide to group these data using six classes of equal width Then
We round this to a more convenient number say 3 We can take a lower limit of the first class equal to 367 or any number lower than 367 If we start the first class at 36 the classes will be written as 36 to less than 39 39 to less than 42 and so on
119808119849119849119851119848119857119842119846119834119853119838119856119842119837119853119841119848119839 119834119836119845119834119852119852=558minus367
6=318
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Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
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Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
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Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
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Figure 27 Bar graph for Table 213
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Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
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SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
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Figure 28 Symmetric histograms
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Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
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Figure 210 A histogram with uniform distribution
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Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
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Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
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Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
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Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
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Figure 212 Ogive for the cumulative frequency distribution of Table 214
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STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
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Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
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Figure 213 Stem-and-leaf display
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Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
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Figure 214 Stem-and-leaf display of test scores
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Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
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Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
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Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
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Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
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Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
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Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
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Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
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Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
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DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
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Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
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Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
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Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
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Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
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Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
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Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
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Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
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Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
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TI-84
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TI-84
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Minitab
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Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Example 2-2 Determine the relative frequency and percentage for the
data in Table 24
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Example 2-2 SolutionTable 25 Relative Frequency and Percentage Distributions of Favorite Donut Variety
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Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their Parents
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Graphical Presentation of Qualitative Data
Definition A graph made of bars whose heights represent the
frequencies of respective categories is called a bar graph
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Figure 21 Bar graph for the frequency distribution of Table 24
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Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
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Graphical Presentation of Qualitative Data Definition A circle divided into portions that represent the relative
frequencies or percentages of a population or a sample belonging to different categories is called a pie chart
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Table 26 Calculating Angle Sizes for the Pie Chart
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Figure 22 Pie chart for the percentage distribution of Table 25
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ORGANIZING AND GRAPHING QUANTITATIVE Frequency Distributions Constructing Frequency Distribution Tables Relative and Percentage Distributions Graphing Grouped Data
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Table 27 Weekly Earnings of 100 Employees of a Company
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Frequency Distributions Definition A frequency distribution for quantitative data lists all
the classes and the number of values that belong to each class Data presented in the form of a frequency distribution are called grouped data
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Frequency Distributions Definition The class boundary is given by the midpoint of the upper
limit of one class and the lower limit of the next class
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Frequency Distributions
Finding Class Width
Class width = Upper boundary ndash Lower boundary
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Frequency Distributions
Calculating Class Midpoint or Mark
2
limit Upper limit Lower markor midpoint Class
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Constructing Frequency Distribution Tables
Calculation of Class Width
classes ofNumber
alueSmallest v - lueLargest va widthclass eApproximat
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Table 28 Class Boundaries Class Widths and Class Midpoints for Table 27
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Example 2-3
The following data give the total number of iPodsreg sold by a mail order company on each of 30 days Construct a frequency distribution table
8 25 11 15 29 22 10 5 17 21
22 13 26 16 18 12 9 26 20 16
23 14 19 23 20 16 27 16 21 14
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Example 2-3 Solution
29 5Approximate width of each class 48
5
Now we round this approximate width to a convenient number say 5 The lower limit of the first class can be taken as 5 or any number less than 5 Suppose we take 5 as the lower limit of the first class Then our classes will be 5 ndash 9 10 ndash 14 15 ndash 19 20 ndash 24 and 25 ndash 29
The minimum value is 5 and the maximum value is 29 Suppose we decide to group these data using five classes of equal width Then
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Table 29 Frequency Distribution for the Data on iPods Sold
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Relative Frequency and Percentage Distributions
Calculating Relative Frequency and Percentage
100 frequency) (Relative Percentage
sfrequencie all of Sum
class that of Frequencyclass a of frequency Relative
f
f
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Example 2-4 Calculate the relative frequencies and percentages for
Table 29
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Example 2-4 SolutionTable 210 Relative Frequency and Percentage Distributions for Table 29
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Graphing Grouped Data Definition A histogram is a graph in which classes are marked on the
horizontal axis and the frequencies relative frequencies or percentages are marked on the vertical axis The frequencies relative frequencies or percentages are represented by the heights of the bars In a histogram the bars are drawn adjacent to each other
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Figure 23 Frequency histogram for Table 29
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Figure 24 Relative frequency histogram for Table 210
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Case Study 2-3 How Long Does Your Typical One-Way Commute Take
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Graphing Grouped Data Definition A graph formed by joining the midpoints of the tops of
successive bars in a histogram with straight lines is called a polygon
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Figure 25 Frequency polygon for Table 29
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Case Study 2-4 How Much Does it Cost to Insure a Car
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Figure 26 Frequency distribution curve
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Example 2-5 The percentage of the population working in the United
States peaked in 2000 but dropped to the lowest level in 30 years in 2010 Table 211 shows the percentage of the population working in each of the 50 states in 2010 These percentages exclude military personnel and self-employed persons (Source USA TODAY April 14 2011 Based on data from the US Census Bureau and US Bureau of Labor Statistics)
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Example 2-5
Construct a frequency distribution table Calculate the relative frequencies and percentages for all classes
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Example 2-5 Solution
The minimum value in the data set of Table 211 is 367 and the maximum value is 558 Suppose we decide to group these data using six classes of equal width Then
We round this to a more convenient number say 3 We can take a lower limit of the first class equal to 367 or any number lower than 367 If we start the first class at 36 the classes will be written as 36 to less than 39 39 to less than 42 and so on
119808119849119849119851119848119857119842119846119834119853119838119856119842119837119853119841119848119839 119834119836119845119834119852119852=558minus367
6=318
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Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
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Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
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Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
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Figure 27 Bar graph for Table 213
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Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
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SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
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Figure 28 Symmetric histograms
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Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
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Figure 210 A histogram with uniform distribution
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Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
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Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
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Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
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Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
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Figure 212 Ogive for the cumulative frequency distribution of Table 214
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STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
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Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
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Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
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Figure 213 Stem-and-leaf display
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Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
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Figure 214 Stem-and-leaf display of test scores
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Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
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Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
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Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
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Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
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Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
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Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
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DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
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Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
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Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
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Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
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Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
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Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
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TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Example 2-2 SolutionTable 25 Relative Frequency and Percentage Distributions of Favorite Donut Variety
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their Parents
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Graphical Presentation of Qualitative Data
Definition A graph made of bars whose heights represent the
frequencies of respective categories is called a bar graph
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Figure 21 Bar graph for the frequency distribution of Table 24
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Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
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Graphical Presentation of Qualitative Data Definition A circle divided into portions that represent the relative
frequencies or percentages of a population or a sample belonging to different categories is called a pie chart
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Table 26 Calculating Angle Sizes for the Pie Chart
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Figure 22 Pie chart for the percentage distribution of Table 25
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ORGANIZING AND GRAPHING QUANTITATIVE Frequency Distributions Constructing Frequency Distribution Tables Relative and Percentage Distributions Graphing Grouped Data
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Table 27 Weekly Earnings of 100 Employees of a Company
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Frequency Distributions Definition A frequency distribution for quantitative data lists all
the classes and the number of values that belong to each class Data presented in the form of a frequency distribution are called grouped data
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Frequency Distributions Definition The class boundary is given by the midpoint of the upper
limit of one class and the lower limit of the next class
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Frequency Distributions
Finding Class Width
Class width = Upper boundary ndash Lower boundary
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Frequency Distributions
Calculating Class Midpoint or Mark
2
limit Upper limit Lower markor midpoint Class
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Constructing Frequency Distribution Tables
Calculation of Class Width
classes ofNumber
alueSmallest v - lueLargest va widthclass eApproximat
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Table 28 Class Boundaries Class Widths and Class Midpoints for Table 27
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-3
The following data give the total number of iPodsreg sold by a mail order company on each of 30 days Construct a frequency distribution table
8 25 11 15 29 22 10 5 17 21
22 13 26 16 18 12 9 26 20 16
23 14 19 23 20 16 27 16 21 14
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Example 2-3 Solution
29 5Approximate width of each class 48
5
Now we round this approximate width to a convenient number say 5 The lower limit of the first class can be taken as 5 or any number less than 5 Suppose we take 5 as the lower limit of the first class Then our classes will be 5 ndash 9 10 ndash 14 15 ndash 19 20 ndash 24 and 25 ndash 29
The minimum value is 5 and the maximum value is 29 Suppose we decide to group these data using five classes of equal width Then
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Table 29 Frequency Distribution for the Data on iPods Sold
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Relative Frequency and Percentage Distributions
Calculating Relative Frequency and Percentage
100 frequency) (Relative Percentage
sfrequencie all of Sum
class that of Frequencyclass a of frequency Relative
f
f
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Example 2-4 Calculate the relative frequencies and percentages for
Table 29
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Example 2-4 SolutionTable 210 Relative Frequency and Percentage Distributions for Table 29
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Graphing Grouped Data Definition A histogram is a graph in which classes are marked on the
horizontal axis and the frequencies relative frequencies or percentages are marked on the vertical axis The frequencies relative frequencies or percentages are represented by the heights of the bars In a histogram the bars are drawn adjacent to each other
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Figure 23 Frequency histogram for Table 29
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Figure 24 Relative frequency histogram for Table 210
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Case Study 2-3 How Long Does Your Typical One-Way Commute Take
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Graphing Grouped Data Definition A graph formed by joining the midpoints of the tops of
successive bars in a histogram with straight lines is called a polygon
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Figure 25 Frequency polygon for Table 29
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Case Study 2-4 How Much Does it Cost to Insure a Car
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Figure 26 Frequency distribution curve
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Example 2-5 The percentage of the population working in the United
States peaked in 2000 but dropped to the lowest level in 30 years in 2010 Table 211 shows the percentage of the population working in each of the 50 states in 2010 These percentages exclude military personnel and self-employed persons (Source USA TODAY April 14 2011 Based on data from the US Census Bureau and US Bureau of Labor Statistics)
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5
Construct a frequency distribution table Calculate the relative frequencies and percentages for all classes
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Example 2-5 Solution
The minimum value in the data set of Table 211 is 367 and the maximum value is 558 Suppose we decide to group these data using six classes of equal width Then
We round this to a more convenient number say 3 We can take a lower limit of the first class equal to 367 or any number lower than 367 If we start the first class at 36 the classes will be written as 36 to less than 39 39 to less than 42 and so on
119808119849119849119851119848119857119842119846119834119853119838119856119842119837119853119841119848119839 119834119836119845119834119852119852=558minus367
6=318
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Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
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Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
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Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
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Figure 27 Bar graph for Table 213
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Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
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SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
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Figure 28 Symmetric histograms
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Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
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Figure 210 A histogram with uniform distribution
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Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
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Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
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Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
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Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
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Figure 212 Ogive for the cumulative frequency distribution of Table 214
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STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
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Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
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Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
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Figure 213 Stem-and-leaf display
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Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
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Figure 214 Stem-and-leaf display of test scores
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Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
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Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
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Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
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Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
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Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
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Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
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Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
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Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
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DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
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Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
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Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
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Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
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Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
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Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
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Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
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Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
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Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
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TI-84
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TI-84
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Minitab
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Minitab
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Minitab
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Minitab
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Minitab
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Excel
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Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their Parents
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Graphical Presentation of Qualitative Data
Definition A graph made of bars whose heights represent the
frequencies of respective categories is called a bar graph
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 21 Bar graph for the frequency distribution of Table 24
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Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Graphical Presentation of Qualitative Data Definition A circle divided into portions that represent the relative
frequencies or percentages of a population or a sample belonging to different categories is called a pie chart
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 26 Calculating Angle Sizes for the Pie Chart
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Figure 22 Pie chart for the percentage distribution of Table 25
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ORGANIZING AND GRAPHING QUANTITATIVE Frequency Distributions Constructing Frequency Distribution Tables Relative and Percentage Distributions Graphing Grouped Data
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Table 27 Weekly Earnings of 100 Employees of a Company
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Frequency Distributions Definition A frequency distribution for quantitative data lists all
the classes and the number of values that belong to each class Data presented in the form of a frequency distribution are called grouped data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Frequency Distributions Definition The class boundary is given by the midpoint of the upper
limit of one class and the lower limit of the next class
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Frequency Distributions
Finding Class Width
Class width = Upper boundary ndash Lower boundary
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Frequency Distributions
Calculating Class Midpoint or Mark
2
limit Upper limit Lower markor midpoint Class
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Constructing Frequency Distribution Tables
Calculation of Class Width
classes ofNumber
alueSmallest v - lueLargest va widthclass eApproximat
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Table 28 Class Boundaries Class Widths and Class Midpoints for Table 27
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-3
The following data give the total number of iPodsreg sold by a mail order company on each of 30 days Construct a frequency distribution table
8 25 11 15 29 22 10 5 17 21
22 13 26 16 18 12 9 26 20 16
23 14 19 23 20 16 27 16 21 14
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-3 Solution
29 5Approximate width of each class 48
5
Now we round this approximate width to a convenient number say 5 The lower limit of the first class can be taken as 5 or any number less than 5 Suppose we take 5 as the lower limit of the first class Then our classes will be 5 ndash 9 10 ndash 14 15 ndash 19 20 ndash 24 and 25 ndash 29
The minimum value is 5 and the maximum value is 29 Suppose we decide to group these data using five classes of equal width Then
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Table 29 Frequency Distribution for the Data on iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Relative Frequency and Percentage Distributions
Calculating Relative Frequency and Percentage
100 frequency) (Relative Percentage
sfrequencie all of Sum
class that of Frequencyclass a of frequency Relative
f
f
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Example 2-4 Calculate the relative frequencies and percentages for
Table 29
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Example 2-4 SolutionTable 210 Relative Frequency and Percentage Distributions for Table 29
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Graphing Grouped Data Definition A histogram is a graph in which classes are marked on the
horizontal axis and the frequencies relative frequencies or percentages are marked on the vertical axis The frequencies relative frequencies or percentages are represented by the heights of the bars In a histogram the bars are drawn adjacent to each other
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 23 Frequency histogram for Table 29
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Figure 24 Relative frequency histogram for Table 210
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Case Study 2-3 How Long Does Your Typical One-Way Commute Take
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Graphing Grouped Data Definition A graph formed by joining the midpoints of the tops of
successive bars in a histogram with straight lines is called a polygon
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Figure 25 Frequency polygon for Table 29
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Case Study 2-4 How Much Does it Cost to Insure a Car
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Figure 26 Frequency distribution curve
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Example 2-5 The percentage of the population working in the United
States peaked in 2000 but dropped to the lowest level in 30 years in 2010 Table 211 shows the percentage of the population working in each of the 50 states in 2010 These percentages exclude military personnel and self-employed persons (Source USA TODAY April 14 2011 Based on data from the US Census Bureau and US Bureau of Labor Statistics)
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5
Construct a frequency distribution table Calculate the relative frequencies and percentages for all classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5 Solution
The minimum value in the data set of Table 211 is 367 and the maximum value is 558 Suppose we decide to group these data using six classes of equal width Then
We round this to a more convenient number say 3 We can take a lower limit of the first class equal to 367 or any number lower than 367 If we start the first class at 36 the classes will be written as 36 to less than 39 39 to less than 42 and so on
119808119849119849119851119848119857119842119846119834119853119838119856119842119837119853119841119848119839 119834119836119845119834119852119852=558minus367
6=318
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Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
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Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
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Figure 27 Bar graph for Table 213
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Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
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SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
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Figure 28 Symmetric histograms
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Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
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Figure 210 A histogram with uniform distribution
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Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
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Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
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Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
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Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 212 Ogive for the cumulative frequency distribution of Table 214
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STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
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Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
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Figure 213 Stem-and-leaf display
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Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
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Figure 214 Stem-and-leaf display of test scores
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Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
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Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
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Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
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Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
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Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
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Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
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Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
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Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
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DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
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Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
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Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
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Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
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Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
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Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
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Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
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Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
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Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
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TI-84
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TI-84
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Minitab
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Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
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Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Graphical Presentation of Qualitative Data
Definition A graph made of bars whose heights represent the
frequencies of respective categories is called a bar graph
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Figure 21 Bar graph for the frequency distribution of Table 24
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Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
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Graphical Presentation of Qualitative Data Definition A circle divided into portions that represent the relative
frequencies or percentages of a population or a sample belonging to different categories is called a pie chart
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Table 26 Calculating Angle Sizes for the Pie Chart
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Figure 22 Pie chart for the percentage distribution of Table 25
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ORGANIZING AND GRAPHING QUANTITATIVE Frequency Distributions Constructing Frequency Distribution Tables Relative and Percentage Distributions Graphing Grouped Data
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Table 27 Weekly Earnings of 100 Employees of a Company
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Frequency Distributions Definition A frequency distribution for quantitative data lists all
the classes and the number of values that belong to each class Data presented in the form of a frequency distribution are called grouped data
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Frequency Distributions Definition The class boundary is given by the midpoint of the upper
limit of one class and the lower limit of the next class
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Frequency Distributions
Finding Class Width
Class width = Upper boundary ndash Lower boundary
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Frequency Distributions
Calculating Class Midpoint or Mark
2
limit Upper limit Lower markor midpoint Class
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Constructing Frequency Distribution Tables
Calculation of Class Width
classes ofNumber
alueSmallest v - lueLargest va widthclass eApproximat
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Table 28 Class Boundaries Class Widths and Class Midpoints for Table 27
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Example 2-3
The following data give the total number of iPodsreg sold by a mail order company on each of 30 days Construct a frequency distribution table
8 25 11 15 29 22 10 5 17 21
22 13 26 16 18 12 9 26 20 16
23 14 19 23 20 16 27 16 21 14
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Example 2-3 Solution
29 5Approximate width of each class 48
5
Now we round this approximate width to a convenient number say 5 The lower limit of the first class can be taken as 5 or any number less than 5 Suppose we take 5 as the lower limit of the first class Then our classes will be 5 ndash 9 10 ndash 14 15 ndash 19 20 ndash 24 and 25 ndash 29
The minimum value is 5 and the maximum value is 29 Suppose we decide to group these data using five classes of equal width Then
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Table 29 Frequency Distribution for the Data on iPods Sold
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Relative Frequency and Percentage Distributions
Calculating Relative Frequency and Percentage
100 frequency) (Relative Percentage
sfrequencie all of Sum
class that of Frequencyclass a of frequency Relative
f
f
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Example 2-4 Calculate the relative frequencies and percentages for
Table 29
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Example 2-4 SolutionTable 210 Relative Frequency and Percentage Distributions for Table 29
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Graphing Grouped Data Definition A histogram is a graph in which classes are marked on the
horizontal axis and the frequencies relative frequencies or percentages are marked on the vertical axis The frequencies relative frequencies or percentages are represented by the heights of the bars In a histogram the bars are drawn adjacent to each other
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Figure 23 Frequency histogram for Table 29
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Figure 24 Relative frequency histogram for Table 210
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Case Study 2-3 How Long Does Your Typical One-Way Commute Take
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Graphing Grouped Data Definition A graph formed by joining the midpoints of the tops of
successive bars in a histogram with straight lines is called a polygon
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Figure 25 Frequency polygon for Table 29
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Case Study 2-4 How Much Does it Cost to Insure a Car
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Figure 26 Frequency distribution curve
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Example 2-5 The percentage of the population working in the United
States peaked in 2000 but dropped to the lowest level in 30 years in 2010 Table 211 shows the percentage of the population working in each of the 50 states in 2010 These percentages exclude military personnel and self-employed persons (Source USA TODAY April 14 2011 Based on data from the US Census Bureau and US Bureau of Labor Statistics)
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Example 2-5
Construct a frequency distribution table Calculate the relative frequencies and percentages for all classes
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Example 2-5 Solution
The minimum value in the data set of Table 211 is 367 and the maximum value is 558 Suppose we decide to group these data using six classes of equal width Then
We round this to a more convenient number say 3 We can take a lower limit of the first class equal to 367 or any number lower than 367 If we start the first class at 36 the classes will be written as 36 to less than 39 39 to less than 42 and so on
119808119849119849119851119848119857119842119846119834119853119838119856119842119837119853119841119848119839 119834119836119845119834119852119852=558minus367
6=318
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Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
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Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
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Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
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Figure 27 Bar graph for Table 213
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Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
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SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
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Figure 28 Symmetric histograms
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Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
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Figure 210 A histogram with uniform distribution
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Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
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Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
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Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
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Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
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Figure 212 Ogive for the cumulative frequency distribution of Table 214
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STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
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Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
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Figure 213 Stem-and-leaf display
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Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
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Figure 214 Stem-and-leaf display of test scores
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Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
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Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
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Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
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Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
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Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
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Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
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DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
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Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
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Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
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Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
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Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
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TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Figure 21 Bar graph for the frequency distribution of Table 24
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Graphical Presentation of Qualitative Data Definition A circle divided into portions that represent the relative
frequencies or percentages of a population or a sample belonging to different categories is called a pie chart
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 26 Calculating Angle Sizes for the Pie Chart
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Figure 22 Pie chart for the percentage distribution of Table 25
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ORGANIZING AND GRAPHING QUANTITATIVE Frequency Distributions Constructing Frequency Distribution Tables Relative and Percentage Distributions Graphing Grouped Data
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Table 27 Weekly Earnings of 100 Employees of a Company
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Frequency Distributions Definition A frequency distribution for quantitative data lists all
the classes and the number of values that belong to each class Data presented in the form of a frequency distribution are called grouped data
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Frequency Distributions Definition The class boundary is given by the midpoint of the upper
limit of one class and the lower limit of the next class
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Frequency Distributions
Finding Class Width
Class width = Upper boundary ndash Lower boundary
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Frequency Distributions
Calculating Class Midpoint or Mark
2
limit Upper limit Lower markor midpoint Class
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Constructing Frequency Distribution Tables
Calculation of Class Width
classes ofNumber
alueSmallest v - lueLargest va widthclass eApproximat
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Table 28 Class Boundaries Class Widths and Class Midpoints for Table 27
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Example 2-3
The following data give the total number of iPodsreg sold by a mail order company on each of 30 days Construct a frequency distribution table
8 25 11 15 29 22 10 5 17 21
22 13 26 16 18 12 9 26 20 16
23 14 19 23 20 16 27 16 21 14
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Example 2-3 Solution
29 5Approximate width of each class 48
5
Now we round this approximate width to a convenient number say 5 The lower limit of the first class can be taken as 5 or any number less than 5 Suppose we take 5 as the lower limit of the first class Then our classes will be 5 ndash 9 10 ndash 14 15 ndash 19 20 ndash 24 and 25 ndash 29
The minimum value is 5 and the maximum value is 29 Suppose we decide to group these data using five classes of equal width Then
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Table 29 Frequency Distribution for the Data on iPods Sold
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Relative Frequency and Percentage Distributions
Calculating Relative Frequency and Percentage
100 frequency) (Relative Percentage
sfrequencie all of Sum
class that of Frequencyclass a of frequency Relative
f
f
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Example 2-4 Calculate the relative frequencies and percentages for
Table 29
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Example 2-4 SolutionTable 210 Relative Frequency and Percentage Distributions for Table 29
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Graphing Grouped Data Definition A histogram is a graph in which classes are marked on the
horizontal axis and the frequencies relative frequencies or percentages are marked on the vertical axis The frequencies relative frequencies or percentages are represented by the heights of the bars In a histogram the bars are drawn adjacent to each other
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Figure 23 Frequency histogram for Table 29
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Figure 24 Relative frequency histogram for Table 210
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Case Study 2-3 How Long Does Your Typical One-Way Commute Take
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Graphing Grouped Data Definition A graph formed by joining the midpoints of the tops of
successive bars in a histogram with straight lines is called a polygon
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Figure 25 Frequency polygon for Table 29
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Case Study 2-4 How Much Does it Cost to Insure a Car
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Figure 26 Frequency distribution curve
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Example 2-5 The percentage of the population working in the United
States peaked in 2000 but dropped to the lowest level in 30 years in 2010 Table 211 shows the percentage of the population working in each of the 50 states in 2010 These percentages exclude military personnel and self-employed persons (Source USA TODAY April 14 2011 Based on data from the US Census Bureau and US Bureau of Labor Statistics)
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Example 2-5
Construct a frequency distribution table Calculate the relative frequencies and percentages for all classes
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Example 2-5 Solution
The minimum value in the data set of Table 211 is 367 and the maximum value is 558 Suppose we decide to group these data using six classes of equal width Then
We round this to a more convenient number say 3 We can take a lower limit of the first class equal to 367 or any number lower than 367 If we start the first class at 36 the classes will be written as 36 to less than 39 39 to less than 42 and so on
119808119849119849119851119848119857119842119846119834119853119838119856119842119837119853119841119848119839 119834119836119845119834119852119852=558minus367
6=318
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Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
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Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
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Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
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Figure 27 Bar graph for Table 213
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Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
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SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
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Figure 28 Symmetric histograms
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Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
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Figure 210 A histogram with uniform distribution
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Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
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Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
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Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
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Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
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Figure 212 Ogive for the cumulative frequency distribution of Table 214
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STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
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Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
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Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
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Figure 213 Stem-and-leaf display
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Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
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Figure 214 Stem-and-leaf display of test scores
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Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
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Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
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Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
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Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
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Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
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Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
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Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
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Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
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DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
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Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
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Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
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Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
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Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
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Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
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Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
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Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
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Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
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TI-84
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TI-84
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Minitab
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Minitab
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Minitab
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Minitab
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Minitab
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Excel
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Excel
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- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
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Graphical Presentation of Qualitative Data Definition A circle divided into portions that represent the relative
frequencies or percentages of a population or a sample belonging to different categories is called a pie chart
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Table 26 Calculating Angle Sizes for the Pie Chart
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Figure 22 Pie chart for the percentage distribution of Table 25
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ORGANIZING AND GRAPHING QUANTITATIVE Frequency Distributions Constructing Frequency Distribution Tables Relative and Percentage Distributions Graphing Grouped Data
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Table 27 Weekly Earnings of 100 Employees of a Company
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Frequency Distributions Definition A frequency distribution for quantitative data lists all
the classes and the number of values that belong to each class Data presented in the form of a frequency distribution are called grouped data
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Frequency Distributions Definition The class boundary is given by the midpoint of the upper
limit of one class and the lower limit of the next class
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Frequency Distributions
Finding Class Width
Class width = Upper boundary ndash Lower boundary
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Frequency Distributions
Calculating Class Midpoint or Mark
2
limit Upper limit Lower markor midpoint Class
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Constructing Frequency Distribution Tables
Calculation of Class Width
classes ofNumber
alueSmallest v - lueLargest va widthclass eApproximat
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Table 28 Class Boundaries Class Widths and Class Midpoints for Table 27
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Example 2-3
The following data give the total number of iPodsreg sold by a mail order company on each of 30 days Construct a frequency distribution table
8 25 11 15 29 22 10 5 17 21
22 13 26 16 18 12 9 26 20 16
23 14 19 23 20 16 27 16 21 14
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Example 2-3 Solution
29 5Approximate width of each class 48
5
Now we round this approximate width to a convenient number say 5 The lower limit of the first class can be taken as 5 or any number less than 5 Suppose we take 5 as the lower limit of the first class Then our classes will be 5 ndash 9 10 ndash 14 15 ndash 19 20 ndash 24 and 25 ndash 29
The minimum value is 5 and the maximum value is 29 Suppose we decide to group these data using five classes of equal width Then
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Table 29 Frequency Distribution for the Data on iPods Sold
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Relative Frequency and Percentage Distributions
Calculating Relative Frequency and Percentage
100 frequency) (Relative Percentage
sfrequencie all of Sum
class that of Frequencyclass a of frequency Relative
f
f
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Example 2-4 Calculate the relative frequencies and percentages for
Table 29
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Example 2-4 SolutionTable 210 Relative Frequency and Percentage Distributions for Table 29
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Graphing Grouped Data Definition A histogram is a graph in which classes are marked on the
horizontal axis and the frequencies relative frequencies or percentages are marked on the vertical axis The frequencies relative frequencies or percentages are represented by the heights of the bars In a histogram the bars are drawn adjacent to each other
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Figure 23 Frequency histogram for Table 29
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Figure 24 Relative frequency histogram for Table 210
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Case Study 2-3 How Long Does Your Typical One-Way Commute Take
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Graphing Grouped Data Definition A graph formed by joining the midpoints of the tops of
successive bars in a histogram with straight lines is called a polygon
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Figure 25 Frequency polygon for Table 29
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Case Study 2-4 How Much Does it Cost to Insure a Car
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Figure 26 Frequency distribution curve
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Example 2-5 The percentage of the population working in the United
States peaked in 2000 but dropped to the lowest level in 30 years in 2010 Table 211 shows the percentage of the population working in each of the 50 states in 2010 These percentages exclude military personnel and self-employed persons (Source USA TODAY April 14 2011 Based on data from the US Census Bureau and US Bureau of Labor Statistics)
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Example 2-5
Construct a frequency distribution table Calculate the relative frequencies and percentages for all classes
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Example 2-5 Solution
The minimum value in the data set of Table 211 is 367 and the maximum value is 558 Suppose we decide to group these data using six classes of equal width Then
We round this to a more convenient number say 3 We can take a lower limit of the first class equal to 367 or any number lower than 367 If we start the first class at 36 the classes will be written as 36 to less than 39 39 to less than 42 and so on
119808119849119849119851119848119857119842119846119834119853119838119856119842119837119853119841119848119839 119834119836119845119834119852119852=558minus367
6=318
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Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
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Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
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Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
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Figure 27 Bar graph for Table 213
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Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
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SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
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Figure 28 Symmetric histograms
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Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
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Figure 210 A histogram with uniform distribution
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Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
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Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
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Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
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Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
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Figure 212 Ogive for the cumulative frequency distribution of Table 214
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STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
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Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
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Figure 213 Stem-and-leaf display
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Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
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Figure 214 Stem-and-leaf display of test scores
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Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
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Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
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Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
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Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
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Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
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Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
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Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
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Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
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DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
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Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
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Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
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Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
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Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
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Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
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Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
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Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
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Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
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TI-84
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TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
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Minitab
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Minitab
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Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Graphical Presentation of Qualitative Data Definition A circle divided into portions that represent the relative
frequencies or percentages of a population or a sample belonging to different categories is called a pie chart
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Table 26 Calculating Angle Sizes for the Pie Chart
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Figure 22 Pie chart for the percentage distribution of Table 25
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ORGANIZING AND GRAPHING QUANTITATIVE Frequency Distributions Constructing Frequency Distribution Tables Relative and Percentage Distributions Graphing Grouped Data
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Table 27 Weekly Earnings of 100 Employees of a Company
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Frequency Distributions Definition A frequency distribution for quantitative data lists all
the classes and the number of values that belong to each class Data presented in the form of a frequency distribution are called grouped data
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Frequency Distributions Definition The class boundary is given by the midpoint of the upper
limit of one class and the lower limit of the next class
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Frequency Distributions
Finding Class Width
Class width = Upper boundary ndash Lower boundary
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Frequency Distributions
Calculating Class Midpoint or Mark
2
limit Upper limit Lower markor midpoint Class
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Constructing Frequency Distribution Tables
Calculation of Class Width
classes ofNumber
alueSmallest v - lueLargest va widthclass eApproximat
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Table 28 Class Boundaries Class Widths and Class Midpoints for Table 27
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-3
The following data give the total number of iPodsreg sold by a mail order company on each of 30 days Construct a frequency distribution table
8 25 11 15 29 22 10 5 17 21
22 13 26 16 18 12 9 26 20 16
23 14 19 23 20 16 27 16 21 14
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Example 2-3 Solution
29 5Approximate width of each class 48
5
Now we round this approximate width to a convenient number say 5 The lower limit of the first class can be taken as 5 or any number less than 5 Suppose we take 5 as the lower limit of the first class Then our classes will be 5 ndash 9 10 ndash 14 15 ndash 19 20 ndash 24 and 25 ndash 29
The minimum value is 5 and the maximum value is 29 Suppose we decide to group these data using five classes of equal width Then
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Table 29 Frequency Distribution for the Data on iPods Sold
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Relative Frequency and Percentage Distributions
Calculating Relative Frequency and Percentage
100 frequency) (Relative Percentage
sfrequencie all of Sum
class that of Frequencyclass a of frequency Relative
f
f
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Example 2-4 Calculate the relative frequencies and percentages for
Table 29
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Example 2-4 SolutionTable 210 Relative Frequency and Percentage Distributions for Table 29
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Graphing Grouped Data Definition A histogram is a graph in which classes are marked on the
horizontal axis and the frequencies relative frequencies or percentages are marked on the vertical axis The frequencies relative frequencies or percentages are represented by the heights of the bars In a histogram the bars are drawn adjacent to each other
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Figure 23 Frequency histogram for Table 29
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Figure 24 Relative frequency histogram for Table 210
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Case Study 2-3 How Long Does Your Typical One-Way Commute Take
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Graphing Grouped Data Definition A graph formed by joining the midpoints of the tops of
successive bars in a histogram with straight lines is called a polygon
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Figure 25 Frequency polygon for Table 29
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Case Study 2-4 How Much Does it Cost to Insure a Car
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Figure 26 Frequency distribution curve
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Example 2-5 The percentage of the population working in the United
States peaked in 2000 but dropped to the lowest level in 30 years in 2010 Table 211 shows the percentage of the population working in each of the 50 states in 2010 These percentages exclude military personnel and self-employed persons (Source USA TODAY April 14 2011 Based on data from the US Census Bureau and US Bureau of Labor Statistics)
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Example 2-5
Construct a frequency distribution table Calculate the relative frequencies and percentages for all classes
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Example 2-5 Solution
The minimum value in the data set of Table 211 is 367 and the maximum value is 558 Suppose we decide to group these data using six classes of equal width Then
We round this to a more convenient number say 3 We can take a lower limit of the first class equal to 367 or any number lower than 367 If we start the first class at 36 the classes will be written as 36 to less than 39 39 to less than 42 and so on
119808119849119849119851119848119857119842119846119834119853119838119856119842119837119853119841119848119839 119834119836119845119834119852119852=558minus367
6=318
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Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
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Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
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Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
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Figure 27 Bar graph for Table 213
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Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
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SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
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Figure 28 Symmetric histograms
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Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
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Figure 210 A histogram with uniform distribution
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Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
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Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
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Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
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Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
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Figure 212 Ogive for the cumulative frequency distribution of Table 214
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STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
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Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
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Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
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Figure 213 Stem-and-leaf display
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Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
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Figure 214 Stem-and-leaf display of test scores
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Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
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Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
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Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
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Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
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Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
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Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
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Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
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DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
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Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
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Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
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Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
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Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
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Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
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TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Table 26 Calculating Angle Sizes for the Pie Chart
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 22 Pie chart for the percentage distribution of Table 25
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ORGANIZING AND GRAPHING QUANTITATIVE Frequency Distributions Constructing Frequency Distribution Tables Relative and Percentage Distributions Graphing Grouped Data
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Table 27 Weekly Earnings of 100 Employees of a Company
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Frequency Distributions Definition A frequency distribution for quantitative data lists all
the classes and the number of values that belong to each class Data presented in the form of a frequency distribution are called grouped data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Frequency Distributions Definition The class boundary is given by the midpoint of the upper
limit of one class and the lower limit of the next class
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Frequency Distributions
Finding Class Width
Class width = Upper boundary ndash Lower boundary
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Frequency Distributions
Calculating Class Midpoint or Mark
2
limit Upper limit Lower markor midpoint Class
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Constructing Frequency Distribution Tables
Calculation of Class Width
classes ofNumber
alueSmallest v - lueLargest va widthclass eApproximat
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 28 Class Boundaries Class Widths and Class Midpoints for Table 27
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-3
The following data give the total number of iPodsreg sold by a mail order company on each of 30 days Construct a frequency distribution table
8 25 11 15 29 22 10 5 17 21
22 13 26 16 18 12 9 26 20 16
23 14 19 23 20 16 27 16 21 14
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-3 Solution
29 5Approximate width of each class 48
5
Now we round this approximate width to a convenient number say 5 The lower limit of the first class can be taken as 5 or any number less than 5 Suppose we take 5 as the lower limit of the first class Then our classes will be 5 ndash 9 10 ndash 14 15 ndash 19 20 ndash 24 and 25 ndash 29
The minimum value is 5 and the maximum value is 29 Suppose we decide to group these data using five classes of equal width Then
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Table 29 Frequency Distribution for the Data on iPods Sold
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Relative Frequency and Percentage Distributions
Calculating Relative Frequency and Percentage
100 frequency) (Relative Percentage
sfrequencie all of Sum
class that of Frequencyclass a of frequency Relative
f
f
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Example 2-4 Calculate the relative frequencies and percentages for
Table 29
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Example 2-4 SolutionTable 210 Relative Frequency and Percentage Distributions for Table 29
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Graphing Grouped Data Definition A histogram is a graph in which classes are marked on the
horizontal axis and the frequencies relative frequencies or percentages are marked on the vertical axis The frequencies relative frequencies or percentages are represented by the heights of the bars In a histogram the bars are drawn adjacent to each other
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Figure 23 Frequency histogram for Table 29
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Figure 24 Relative frequency histogram for Table 210
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Case Study 2-3 How Long Does Your Typical One-Way Commute Take
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Graphing Grouped Data Definition A graph formed by joining the midpoints of the tops of
successive bars in a histogram with straight lines is called a polygon
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Figure 25 Frequency polygon for Table 29
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Case Study 2-4 How Much Does it Cost to Insure a Car
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Figure 26 Frequency distribution curve
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Example 2-5 The percentage of the population working in the United
States peaked in 2000 but dropped to the lowest level in 30 years in 2010 Table 211 shows the percentage of the population working in each of the 50 states in 2010 These percentages exclude military personnel and self-employed persons (Source USA TODAY April 14 2011 Based on data from the US Census Bureau and US Bureau of Labor Statistics)
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Example 2-5
Construct a frequency distribution table Calculate the relative frequencies and percentages for all classes
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Example 2-5 Solution
The minimum value in the data set of Table 211 is 367 and the maximum value is 558 Suppose we decide to group these data using six classes of equal width Then
We round this to a more convenient number say 3 We can take a lower limit of the first class equal to 367 or any number lower than 367 If we start the first class at 36 the classes will be written as 36 to less than 39 39 to less than 42 and so on
119808119849119849119851119848119857119842119846119834119853119838119856119842119837119853119841119848119839 119834119836119845119834119852119852=558minus367
6=318
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Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
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Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
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Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
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Figure 27 Bar graph for Table 213
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Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
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SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
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Figure 28 Symmetric histograms
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Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
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Figure 210 A histogram with uniform distribution
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Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
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Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
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Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
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Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
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Figure 212 Ogive for the cumulative frequency distribution of Table 214
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STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
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Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
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Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
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Figure 213 Stem-and-leaf display
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Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
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Figure 214 Stem-and-leaf display of test scores
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Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
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Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
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Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
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Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
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Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
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Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
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Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
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Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
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DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
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Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
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Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
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Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
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Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
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Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
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Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
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Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
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Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
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TI-84
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TI-84
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Minitab
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Minitab
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Minitab
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Minitab
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Minitab
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Excel
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Excel
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- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Figure 22 Pie chart for the percentage distribution of Table 25
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ORGANIZING AND GRAPHING QUANTITATIVE Frequency Distributions Constructing Frequency Distribution Tables Relative and Percentage Distributions Graphing Grouped Data
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Table 27 Weekly Earnings of 100 Employees of a Company
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Frequency Distributions Definition A frequency distribution for quantitative data lists all
the classes and the number of values that belong to each class Data presented in the form of a frequency distribution are called grouped data
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Frequency Distributions Definition The class boundary is given by the midpoint of the upper
limit of one class and the lower limit of the next class
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Frequency Distributions
Finding Class Width
Class width = Upper boundary ndash Lower boundary
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Frequency Distributions
Calculating Class Midpoint or Mark
2
limit Upper limit Lower markor midpoint Class
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Constructing Frequency Distribution Tables
Calculation of Class Width
classes ofNumber
alueSmallest v - lueLargest va widthclass eApproximat
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Table 28 Class Boundaries Class Widths and Class Midpoints for Table 27
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Example 2-3
The following data give the total number of iPodsreg sold by a mail order company on each of 30 days Construct a frequency distribution table
8 25 11 15 29 22 10 5 17 21
22 13 26 16 18 12 9 26 20 16
23 14 19 23 20 16 27 16 21 14
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Example 2-3 Solution
29 5Approximate width of each class 48
5
Now we round this approximate width to a convenient number say 5 The lower limit of the first class can be taken as 5 or any number less than 5 Suppose we take 5 as the lower limit of the first class Then our classes will be 5 ndash 9 10 ndash 14 15 ndash 19 20 ndash 24 and 25 ndash 29
The minimum value is 5 and the maximum value is 29 Suppose we decide to group these data using five classes of equal width Then
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Table 29 Frequency Distribution for the Data on iPods Sold
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Relative Frequency and Percentage Distributions
Calculating Relative Frequency and Percentage
100 frequency) (Relative Percentage
sfrequencie all of Sum
class that of Frequencyclass a of frequency Relative
f
f
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Example 2-4 Calculate the relative frequencies and percentages for
Table 29
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Example 2-4 SolutionTable 210 Relative Frequency and Percentage Distributions for Table 29
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Graphing Grouped Data Definition A histogram is a graph in which classes are marked on the
horizontal axis and the frequencies relative frequencies or percentages are marked on the vertical axis The frequencies relative frequencies or percentages are represented by the heights of the bars In a histogram the bars are drawn adjacent to each other
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Figure 23 Frequency histogram for Table 29
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Figure 24 Relative frequency histogram for Table 210
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Case Study 2-3 How Long Does Your Typical One-Way Commute Take
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Graphing Grouped Data Definition A graph formed by joining the midpoints of the tops of
successive bars in a histogram with straight lines is called a polygon
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Figure 25 Frequency polygon for Table 29
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Case Study 2-4 How Much Does it Cost to Insure a Car
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Figure 26 Frequency distribution curve
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Example 2-5 The percentage of the population working in the United
States peaked in 2000 but dropped to the lowest level in 30 years in 2010 Table 211 shows the percentage of the population working in each of the 50 states in 2010 These percentages exclude military personnel and self-employed persons (Source USA TODAY April 14 2011 Based on data from the US Census Bureau and US Bureau of Labor Statistics)
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Example 2-5
Construct a frequency distribution table Calculate the relative frequencies and percentages for all classes
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Example 2-5 Solution
The minimum value in the data set of Table 211 is 367 and the maximum value is 558 Suppose we decide to group these data using six classes of equal width Then
We round this to a more convenient number say 3 We can take a lower limit of the first class equal to 367 or any number lower than 367 If we start the first class at 36 the classes will be written as 36 to less than 39 39 to less than 42 and so on
119808119849119849119851119848119857119842119846119834119853119838119856119842119837119853119841119848119839 119834119836119845119834119852119852=558minus367
6=318
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Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
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Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
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Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
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Figure 27 Bar graph for Table 213
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Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
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SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
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Figure 28 Symmetric histograms
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Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
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Figure 210 A histogram with uniform distribution
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Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
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Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
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Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
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Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
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Figure 212 Ogive for the cumulative frequency distribution of Table 214
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STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
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Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
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Figure 213 Stem-and-leaf display
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Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
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Figure 214 Stem-and-leaf display of test scores
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Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
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Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
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Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
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Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
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Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
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Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
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Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
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Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
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DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
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Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
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Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
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Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
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Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
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Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
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Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
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TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
ORGANIZING AND GRAPHING QUANTITATIVE Frequency Distributions Constructing Frequency Distribution Tables Relative and Percentage Distributions Graphing Grouped Data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 27 Weekly Earnings of 100 Employees of a Company
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Frequency Distributions Definition A frequency distribution for quantitative data lists all
the classes and the number of values that belong to each class Data presented in the form of a frequency distribution are called grouped data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Frequency Distributions Definition The class boundary is given by the midpoint of the upper
limit of one class and the lower limit of the next class
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Frequency Distributions
Finding Class Width
Class width = Upper boundary ndash Lower boundary
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Frequency Distributions
Calculating Class Midpoint or Mark
2
limit Upper limit Lower markor midpoint Class
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Constructing Frequency Distribution Tables
Calculation of Class Width
classes ofNumber
alueSmallest v - lueLargest va widthclass eApproximat
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Table 28 Class Boundaries Class Widths and Class Midpoints for Table 27
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-3
The following data give the total number of iPodsreg sold by a mail order company on each of 30 days Construct a frequency distribution table
8 25 11 15 29 22 10 5 17 21
22 13 26 16 18 12 9 26 20 16
23 14 19 23 20 16 27 16 21 14
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Example 2-3 Solution
29 5Approximate width of each class 48
5
Now we round this approximate width to a convenient number say 5 The lower limit of the first class can be taken as 5 or any number less than 5 Suppose we take 5 as the lower limit of the first class Then our classes will be 5 ndash 9 10 ndash 14 15 ndash 19 20 ndash 24 and 25 ndash 29
The minimum value is 5 and the maximum value is 29 Suppose we decide to group these data using five classes of equal width Then
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Table 29 Frequency Distribution for the Data on iPods Sold
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Relative Frequency and Percentage Distributions
Calculating Relative Frequency and Percentage
100 frequency) (Relative Percentage
sfrequencie all of Sum
class that of Frequencyclass a of frequency Relative
f
f
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Example 2-4 Calculate the relative frequencies and percentages for
Table 29
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Example 2-4 SolutionTable 210 Relative Frequency and Percentage Distributions for Table 29
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Graphing Grouped Data Definition A histogram is a graph in which classes are marked on the
horizontal axis and the frequencies relative frequencies or percentages are marked on the vertical axis The frequencies relative frequencies or percentages are represented by the heights of the bars In a histogram the bars are drawn adjacent to each other
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Figure 23 Frequency histogram for Table 29
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Figure 24 Relative frequency histogram for Table 210
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Case Study 2-3 How Long Does Your Typical One-Way Commute Take
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Graphing Grouped Data Definition A graph formed by joining the midpoints of the tops of
successive bars in a histogram with straight lines is called a polygon
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Figure 25 Frequency polygon for Table 29
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Case Study 2-4 How Much Does it Cost to Insure a Car
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Figure 26 Frequency distribution curve
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Example 2-5 The percentage of the population working in the United
States peaked in 2000 but dropped to the lowest level in 30 years in 2010 Table 211 shows the percentage of the population working in each of the 50 states in 2010 These percentages exclude military personnel and self-employed persons (Source USA TODAY April 14 2011 Based on data from the US Census Bureau and US Bureau of Labor Statistics)
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5
Construct a frequency distribution table Calculate the relative frequencies and percentages for all classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5 Solution
The minimum value in the data set of Table 211 is 367 and the maximum value is 558 Suppose we decide to group these data using six classes of equal width Then
We round this to a more convenient number say 3 We can take a lower limit of the first class equal to 367 or any number lower than 367 If we start the first class at 36 the classes will be written as 36 to less than 39 39 to less than 42 and so on
119808119849119849119851119848119857119842119846119834119853119838119856119842119837119853119841119848119839 119834119836119845119834119852119852=558minus367
6=318
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Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
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Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
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Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
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Figure 27 Bar graph for Table 213
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Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
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SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
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Figure 28 Symmetric histograms
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Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
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Figure 210 A histogram with uniform distribution
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Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
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Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
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Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
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Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
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Figure 212 Ogive for the cumulative frequency distribution of Table 214
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STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
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Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
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Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
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Figure 213 Stem-and-leaf display
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Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
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Figure 214 Stem-and-leaf display of test scores
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Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
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Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
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Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
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Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
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Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
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Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
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Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
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Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
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DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
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Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
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Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
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Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
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Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
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Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Table 27 Weekly Earnings of 100 Employees of a Company
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Frequency Distributions Definition A frequency distribution for quantitative data lists all
the classes and the number of values that belong to each class Data presented in the form of a frequency distribution are called grouped data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Frequency Distributions Definition The class boundary is given by the midpoint of the upper
limit of one class and the lower limit of the next class
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Frequency Distributions
Finding Class Width
Class width = Upper boundary ndash Lower boundary
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Frequency Distributions
Calculating Class Midpoint or Mark
2
limit Upper limit Lower markor midpoint Class
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Constructing Frequency Distribution Tables
Calculation of Class Width
classes ofNumber
alueSmallest v - lueLargest va widthclass eApproximat
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 28 Class Boundaries Class Widths and Class Midpoints for Table 27
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-3
The following data give the total number of iPodsreg sold by a mail order company on each of 30 days Construct a frequency distribution table
8 25 11 15 29 22 10 5 17 21
22 13 26 16 18 12 9 26 20 16
23 14 19 23 20 16 27 16 21 14
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-3 Solution
29 5Approximate width of each class 48
5
Now we round this approximate width to a convenient number say 5 The lower limit of the first class can be taken as 5 or any number less than 5 Suppose we take 5 as the lower limit of the first class Then our classes will be 5 ndash 9 10 ndash 14 15 ndash 19 20 ndash 24 and 25 ndash 29
The minimum value is 5 and the maximum value is 29 Suppose we decide to group these data using five classes of equal width Then
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 29 Frequency Distribution for the Data on iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Relative Frequency and Percentage Distributions
Calculating Relative Frequency and Percentage
100 frequency) (Relative Percentage
sfrequencie all of Sum
class that of Frequencyclass a of frequency Relative
f
f
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-4 Calculate the relative frequencies and percentages for
Table 29
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Example 2-4 SolutionTable 210 Relative Frequency and Percentage Distributions for Table 29
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Graphing Grouped Data Definition A histogram is a graph in which classes are marked on the
horizontal axis and the frequencies relative frequencies or percentages are marked on the vertical axis The frequencies relative frequencies or percentages are represented by the heights of the bars In a histogram the bars are drawn adjacent to each other
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 23 Frequency histogram for Table 29
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Figure 24 Relative frequency histogram for Table 210
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Case Study 2-3 How Long Does Your Typical One-Way Commute Take
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Graphing Grouped Data Definition A graph formed by joining the midpoints of the tops of
successive bars in a histogram with straight lines is called a polygon
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Figure 25 Frequency polygon for Table 29
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Case Study 2-4 How Much Does it Cost to Insure a Car
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Figure 26 Frequency distribution curve
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Example 2-5 The percentage of the population working in the United
States peaked in 2000 but dropped to the lowest level in 30 years in 2010 Table 211 shows the percentage of the population working in each of the 50 states in 2010 These percentages exclude military personnel and self-employed persons (Source USA TODAY April 14 2011 Based on data from the US Census Bureau and US Bureau of Labor Statistics)
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5
Construct a frequency distribution table Calculate the relative frequencies and percentages for all classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5 Solution
The minimum value in the data set of Table 211 is 367 and the maximum value is 558 Suppose we decide to group these data using six classes of equal width Then
We round this to a more convenient number say 3 We can take a lower limit of the first class equal to 367 or any number lower than 367 If we start the first class at 36 the classes will be written as 36 to less than 39 39 to less than 42 and so on
119808119849119849119851119848119857119842119846119834119853119838119856119842119837119853119841119848119839 119834119836119845119834119852119852=558minus367
6=318
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Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
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Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
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Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
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Figure 27 Bar graph for Table 213
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Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
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SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
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Figure 28 Symmetric histograms
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Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
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Figure 210 A histogram with uniform distribution
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Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
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Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
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Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
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Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
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Figure 212 Ogive for the cumulative frequency distribution of Table 214
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STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
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Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
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Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
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Figure 213 Stem-and-leaf display
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Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
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Figure 214 Stem-and-leaf display of test scores
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Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
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Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
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Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
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Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
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Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
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Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
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Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
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Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
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DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
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Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
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Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
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Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
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Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
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Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
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Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
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Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
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Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
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TI-84
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TI-84
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Minitab
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Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Frequency Distributions Definition A frequency distribution for quantitative data lists all
the classes and the number of values that belong to each class Data presented in the form of a frequency distribution are called grouped data
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Frequency Distributions Definition The class boundary is given by the midpoint of the upper
limit of one class and the lower limit of the next class
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Frequency Distributions
Finding Class Width
Class width = Upper boundary ndash Lower boundary
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Frequency Distributions
Calculating Class Midpoint or Mark
2
limit Upper limit Lower markor midpoint Class
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Constructing Frequency Distribution Tables
Calculation of Class Width
classes ofNumber
alueSmallest v - lueLargest va widthclass eApproximat
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Table 28 Class Boundaries Class Widths and Class Midpoints for Table 27
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Example 2-3
The following data give the total number of iPodsreg sold by a mail order company on each of 30 days Construct a frequency distribution table
8 25 11 15 29 22 10 5 17 21
22 13 26 16 18 12 9 26 20 16
23 14 19 23 20 16 27 16 21 14
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Example 2-3 Solution
29 5Approximate width of each class 48
5
Now we round this approximate width to a convenient number say 5 The lower limit of the first class can be taken as 5 or any number less than 5 Suppose we take 5 as the lower limit of the first class Then our classes will be 5 ndash 9 10 ndash 14 15 ndash 19 20 ndash 24 and 25 ndash 29
The minimum value is 5 and the maximum value is 29 Suppose we decide to group these data using five classes of equal width Then
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Table 29 Frequency Distribution for the Data on iPods Sold
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Relative Frequency and Percentage Distributions
Calculating Relative Frequency and Percentage
100 frequency) (Relative Percentage
sfrequencie all of Sum
class that of Frequencyclass a of frequency Relative
f
f
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Example 2-4 Calculate the relative frequencies and percentages for
Table 29
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Example 2-4 SolutionTable 210 Relative Frequency and Percentage Distributions for Table 29
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Graphing Grouped Data Definition A histogram is a graph in which classes are marked on the
horizontal axis and the frequencies relative frequencies or percentages are marked on the vertical axis The frequencies relative frequencies or percentages are represented by the heights of the bars In a histogram the bars are drawn adjacent to each other
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Figure 23 Frequency histogram for Table 29
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Figure 24 Relative frequency histogram for Table 210
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Case Study 2-3 How Long Does Your Typical One-Way Commute Take
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Graphing Grouped Data Definition A graph formed by joining the midpoints of the tops of
successive bars in a histogram with straight lines is called a polygon
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Figure 25 Frequency polygon for Table 29
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Case Study 2-4 How Much Does it Cost to Insure a Car
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Figure 26 Frequency distribution curve
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Example 2-5 The percentage of the population working in the United
States peaked in 2000 but dropped to the lowest level in 30 years in 2010 Table 211 shows the percentage of the population working in each of the 50 states in 2010 These percentages exclude military personnel and self-employed persons (Source USA TODAY April 14 2011 Based on data from the US Census Bureau and US Bureau of Labor Statistics)
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Example 2-5
Construct a frequency distribution table Calculate the relative frequencies and percentages for all classes
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Example 2-5 Solution
The minimum value in the data set of Table 211 is 367 and the maximum value is 558 Suppose we decide to group these data using six classes of equal width Then
We round this to a more convenient number say 3 We can take a lower limit of the first class equal to 367 or any number lower than 367 If we start the first class at 36 the classes will be written as 36 to less than 39 39 to less than 42 and so on
119808119849119849119851119848119857119842119846119834119853119838119856119842119837119853119841119848119839 119834119836119845119834119852119852=558minus367
6=318
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Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
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Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
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Figure 27 Bar graph for Table 213
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Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
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SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
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Figure 28 Symmetric histograms
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Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
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Figure 210 A histogram with uniform distribution
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Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
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Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
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Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
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Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
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Figure 212 Ogive for the cumulative frequency distribution of Table 214
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STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
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Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
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Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
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Figure 213 Stem-and-leaf display
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Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
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Figure 214 Stem-and-leaf display of test scores
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Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
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Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
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Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
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Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
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Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
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Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
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Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
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Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
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DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
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Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
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Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
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Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
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Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
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Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
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TI-84
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TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Frequency Distributions Definition The class boundary is given by the midpoint of the upper
limit of one class and the lower limit of the next class
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Frequency Distributions
Finding Class Width
Class width = Upper boundary ndash Lower boundary
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Frequency Distributions
Calculating Class Midpoint or Mark
2
limit Upper limit Lower markor midpoint Class
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Constructing Frequency Distribution Tables
Calculation of Class Width
classes ofNumber
alueSmallest v - lueLargest va widthclass eApproximat
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Table 28 Class Boundaries Class Widths and Class Midpoints for Table 27
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Example 2-3
The following data give the total number of iPodsreg sold by a mail order company on each of 30 days Construct a frequency distribution table
8 25 11 15 29 22 10 5 17 21
22 13 26 16 18 12 9 26 20 16
23 14 19 23 20 16 27 16 21 14
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Example 2-3 Solution
29 5Approximate width of each class 48
5
Now we round this approximate width to a convenient number say 5 The lower limit of the first class can be taken as 5 or any number less than 5 Suppose we take 5 as the lower limit of the first class Then our classes will be 5 ndash 9 10 ndash 14 15 ndash 19 20 ndash 24 and 25 ndash 29
The minimum value is 5 and the maximum value is 29 Suppose we decide to group these data using five classes of equal width Then
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Table 29 Frequency Distribution for the Data on iPods Sold
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Relative Frequency and Percentage Distributions
Calculating Relative Frequency and Percentage
100 frequency) (Relative Percentage
sfrequencie all of Sum
class that of Frequencyclass a of frequency Relative
f
f
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Example 2-4 Calculate the relative frequencies and percentages for
Table 29
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Example 2-4 SolutionTable 210 Relative Frequency and Percentage Distributions for Table 29
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Graphing Grouped Data Definition A histogram is a graph in which classes are marked on the
horizontal axis and the frequencies relative frequencies or percentages are marked on the vertical axis The frequencies relative frequencies or percentages are represented by the heights of the bars In a histogram the bars are drawn adjacent to each other
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Figure 23 Frequency histogram for Table 29
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Figure 24 Relative frequency histogram for Table 210
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Case Study 2-3 How Long Does Your Typical One-Way Commute Take
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Graphing Grouped Data Definition A graph formed by joining the midpoints of the tops of
successive bars in a histogram with straight lines is called a polygon
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Figure 25 Frequency polygon for Table 29
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Case Study 2-4 How Much Does it Cost to Insure a Car
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Figure 26 Frequency distribution curve
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Example 2-5 The percentage of the population working in the United
States peaked in 2000 but dropped to the lowest level in 30 years in 2010 Table 211 shows the percentage of the population working in each of the 50 states in 2010 These percentages exclude military personnel and self-employed persons (Source USA TODAY April 14 2011 Based on data from the US Census Bureau and US Bureau of Labor Statistics)
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Example 2-5
Construct a frequency distribution table Calculate the relative frequencies and percentages for all classes
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Example 2-5 Solution
The minimum value in the data set of Table 211 is 367 and the maximum value is 558 Suppose we decide to group these data using six classes of equal width Then
We round this to a more convenient number say 3 We can take a lower limit of the first class equal to 367 or any number lower than 367 If we start the first class at 36 the classes will be written as 36 to less than 39 39 to less than 42 and so on
119808119849119849119851119848119857119842119846119834119853119838119856119842119837119853119841119848119839 119834119836119845119834119852119852=558minus367
6=318
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Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
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Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
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Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
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Figure 27 Bar graph for Table 213
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Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
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SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
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Figure 28 Symmetric histograms
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Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
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Figure 210 A histogram with uniform distribution
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Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
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Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
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Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
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Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
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Figure 212 Ogive for the cumulative frequency distribution of Table 214
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STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
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Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
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Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
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Figure 213 Stem-and-leaf display
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Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
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Figure 214 Stem-and-leaf display of test scores
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Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
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Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
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Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
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Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
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Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
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Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
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Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
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Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
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DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
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Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
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Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
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Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
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Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
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Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
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Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
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Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
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Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
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TI-84
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TI-84
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Minitab
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Minitab
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Minitab
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Minitab
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Minitab
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Excel
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Excel
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- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Frequency Distributions
Finding Class Width
Class width = Upper boundary ndash Lower boundary
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Frequency Distributions
Calculating Class Midpoint or Mark
2
limit Upper limit Lower markor midpoint Class
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Constructing Frequency Distribution Tables
Calculation of Class Width
classes ofNumber
alueSmallest v - lueLargest va widthclass eApproximat
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Table 28 Class Boundaries Class Widths and Class Midpoints for Table 27
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Example 2-3
The following data give the total number of iPodsreg sold by a mail order company on each of 30 days Construct a frequency distribution table
8 25 11 15 29 22 10 5 17 21
22 13 26 16 18 12 9 26 20 16
23 14 19 23 20 16 27 16 21 14
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Example 2-3 Solution
29 5Approximate width of each class 48
5
Now we round this approximate width to a convenient number say 5 The lower limit of the first class can be taken as 5 or any number less than 5 Suppose we take 5 as the lower limit of the first class Then our classes will be 5 ndash 9 10 ndash 14 15 ndash 19 20 ndash 24 and 25 ndash 29
The minimum value is 5 and the maximum value is 29 Suppose we decide to group these data using five classes of equal width Then
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Table 29 Frequency Distribution for the Data on iPods Sold
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Relative Frequency and Percentage Distributions
Calculating Relative Frequency and Percentage
100 frequency) (Relative Percentage
sfrequencie all of Sum
class that of Frequencyclass a of frequency Relative
f
f
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Example 2-4 Calculate the relative frequencies and percentages for
Table 29
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Example 2-4 SolutionTable 210 Relative Frequency and Percentage Distributions for Table 29
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Graphing Grouped Data Definition A histogram is a graph in which classes are marked on the
horizontal axis and the frequencies relative frequencies or percentages are marked on the vertical axis The frequencies relative frequencies or percentages are represented by the heights of the bars In a histogram the bars are drawn adjacent to each other
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Figure 23 Frequency histogram for Table 29
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Figure 24 Relative frequency histogram for Table 210
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Case Study 2-3 How Long Does Your Typical One-Way Commute Take
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Graphing Grouped Data Definition A graph formed by joining the midpoints of the tops of
successive bars in a histogram with straight lines is called a polygon
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Figure 25 Frequency polygon for Table 29
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Case Study 2-4 How Much Does it Cost to Insure a Car
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Figure 26 Frequency distribution curve
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Example 2-5 The percentage of the population working in the United
States peaked in 2000 but dropped to the lowest level in 30 years in 2010 Table 211 shows the percentage of the population working in each of the 50 states in 2010 These percentages exclude military personnel and self-employed persons (Source USA TODAY April 14 2011 Based on data from the US Census Bureau and US Bureau of Labor Statistics)
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Example 2-5
Construct a frequency distribution table Calculate the relative frequencies and percentages for all classes
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Example 2-5 Solution
The minimum value in the data set of Table 211 is 367 and the maximum value is 558 Suppose we decide to group these data using six classes of equal width Then
We round this to a more convenient number say 3 We can take a lower limit of the first class equal to 367 or any number lower than 367 If we start the first class at 36 the classes will be written as 36 to less than 39 39 to less than 42 and so on
119808119849119849119851119848119857119842119846119834119853119838119856119842119837119853119841119848119839 119834119836119845119834119852119852=558minus367
6=318
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Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
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Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
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Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
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Figure 27 Bar graph for Table 213
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Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
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SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
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Figure 28 Symmetric histograms
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Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
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Figure 210 A histogram with uniform distribution
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Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
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Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
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Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
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Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
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Figure 212 Ogive for the cumulative frequency distribution of Table 214
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STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
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Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
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Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
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Figure 213 Stem-and-leaf display
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Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
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Figure 214 Stem-and-leaf display of test scores
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Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
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Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
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Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
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Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
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Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
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Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
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DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
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Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
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Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
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Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
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Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
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TI-84
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Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Frequency Distributions
Calculating Class Midpoint or Mark
2
limit Upper limit Lower markor midpoint Class
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Constructing Frequency Distribution Tables
Calculation of Class Width
classes ofNumber
alueSmallest v - lueLargest va widthclass eApproximat
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Table 28 Class Boundaries Class Widths and Class Midpoints for Table 27
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-3
The following data give the total number of iPodsreg sold by a mail order company on each of 30 days Construct a frequency distribution table
8 25 11 15 29 22 10 5 17 21
22 13 26 16 18 12 9 26 20 16
23 14 19 23 20 16 27 16 21 14
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Example 2-3 Solution
29 5Approximate width of each class 48
5
Now we round this approximate width to a convenient number say 5 The lower limit of the first class can be taken as 5 or any number less than 5 Suppose we take 5 as the lower limit of the first class Then our classes will be 5 ndash 9 10 ndash 14 15 ndash 19 20 ndash 24 and 25 ndash 29
The minimum value is 5 and the maximum value is 29 Suppose we decide to group these data using five classes of equal width Then
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Table 29 Frequency Distribution for the Data on iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Relative Frequency and Percentage Distributions
Calculating Relative Frequency and Percentage
100 frequency) (Relative Percentage
sfrequencie all of Sum
class that of Frequencyclass a of frequency Relative
f
f
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Example 2-4 Calculate the relative frequencies and percentages for
Table 29
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Example 2-4 SolutionTable 210 Relative Frequency and Percentage Distributions for Table 29
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Graphing Grouped Data Definition A histogram is a graph in which classes are marked on the
horizontal axis and the frequencies relative frequencies or percentages are marked on the vertical axis The frequencies relative frequencies or percentages are represented by the heights of the bars In a histogram the bars are drawn adjacent to each other
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Figure 23 Frequency histogram for Table 29
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Figure 24 Relative frequency histogram for Table 210
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Case Study 2-3 How Long Does Your Typical One-Way Commute Take
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Graphing Grouped Data Definition A graph formed by joining the midpoints of the tops of
successive bars in a histogram with straight lines is called a polygon
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Figure 25 Frequency polygon for Table 29
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Case Study 2-4 How Much Does it Cost to Insure a Car
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Figure 26 Frequency distribution curve
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Example 2-5 The percentage of the population working in the United
States peaked in 2000 but dropped to the lowest level in 30 years in 2010 Table 211 shows the percentage of the population working in each of the 50 states in 2010 These percentages exclude military personnel and self-employed persons (Source USA TODAY April 14 2011 Based on data from the US Census Bureau and US Bureau of Labor Statistics)
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5
Construct a frequency distribution table Calculate the relative frequencies and percentages for all classes
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Example 2-5 Solution
The minimum value in the data set of Table 211 is 367 and the maximum value is 558 Suppose we decide to group these data using six classes of equal width Then
We round this to a more convenient number say 3 We can take a lower limit of the first class equal to 367 or any number lower than 367 If we start the first class at 36 the classes will be written as 36 to less than 39 39 to less than 42 and so on
119808119849119849119851119848119857119842119846119834119853119838119856119842119837119853119841119848119839 119834119836119845119834119852119852=558minus367
6=318
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Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
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Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
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Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
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Figure 27 Bar graph for Table 213
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Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
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SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
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Figure 28 Symmetric histograms
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Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
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Figure 210 A histogram with uniform distribution
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Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
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Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
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Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
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Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
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Figure 212 Ogive for the cumulative frequency distribution of Table 214
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STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
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Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
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Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
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Figure 213 Stem-and-leaf display
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Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
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Figure 214 Stem-and-leaf display of test scores
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Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
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Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
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Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
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Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
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Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
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Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
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DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
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Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
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Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
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TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Constructing Frequency Distribution Tables
Calculation of Class Width
classes ofNumber
alueSmallest v - lueLargest va widthclass eApproximat
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 28 Class Boundaries Class Widths and Class Midpoints for Table 27
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-3
The following data give the total number of iPodsreg sold by a mail order company on each of 30 days Construct a frequency distribution table
8 25 11 15 29 22 10 5 17 21
22 13 26 16 18 12 9 26 20 16
23 14 19 23 20 16 27 16 21 14
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-3 Solution
29 5Approximate width of each class 48
5
Now we round this approximate width to a convenient number say 5 The lower limit of the first class can be taken as 5 or any number less than 5 Suppose we take 5 as the lower limit of the first class Then our classes will be 5 ndash 9 10 ndash 14 15 ndash 19 20 ndash 24 and 25 ndash 29
The minimum value is 5 and the maximum value is 29 Suppose we decide to group these data using five classes of equal width Then
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 29 Frequency Distribution for the Data on iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Relative Frequency and Percentage Distributions
Calculating Relative Frequency and Percentage
100 frequency) (Relative Percentage
sfrequencie all of Sum
class that of Frequencyclass a of frequency Relative
f
f
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-4 Calculate the relative frequencies and percentages for
Table 29
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Example 2-4 SolutionTable 210 Relative Frequency and Percentage Distributions for Table 29
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Graphing Grouped Data Definition A histogram is a graph in which classes are marked on the
horizontal axis and the frequencies relative frequencies or percentages are marked on the vertical axis The frequencies relative frequencies or percentages are represented by the heights of the bars In a histogram the bars are drawn adjacent to each other
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 23 Frequency histogram for Table 29
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Figure 24 Relative frequency histogram for Table 210
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Case Study 2-3 How Long Does Your Typical One-Way Commute Take
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Graphing Grouped Data Definition A graph formed by joining the midpoints of the tops of
successive bars in a histogram with straight lines is called a polygon
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 25 Frequency polygon for Table 29
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Case Study 2-4 How Much Does it Cost to Insure a Car
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Figure 26 Frequency distribution curve
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Example 2-5 The percentage of the population working in the United
States peaked in 2000 but dropped to the lowest level in 30 years in 2010 Table 211 shows the percentage of the population working in each of the 50 states in 2010 These percentages exclude military personnel and self-employed persons (Source USA TODAY April 14 2011 Based on data from the US Census Bureau and US Bureau of Labor Statistics)
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5
Construct a frequency distribution table Calculate the relative frequencies and percentages for all classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5 Solution
The minimum value in the data set of Table 211 is 367 and the maximum value is 558 Suppose we decide to group these data using six classes of equal width Then
We round this to a more convenient number say 3 We can take a lower limit of the first class equal to 367 or any number lower than 367 If we start the first class at 36 the classes will be written as 36 to less than 39 39 to less than 42 and so on
119808119849119849119851119848119857119842119846119834119853119838119856119842119837119853119841119848119839 119834119836119845119834119852119852=558minus367
6=318
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Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
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Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
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Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
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Figure 27 Bar graph for Table 213
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Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
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SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
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Figure 28 Symmetric histograms
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Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
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Figure 210 A histogram with uniform distribution
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Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
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Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
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Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
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Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
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Figure 212 Ogive for the cumulative frequency distribution of Table 214
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STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
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Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
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Figure 213 Stem-and-leaf display
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Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
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Figure 214 Stem-and-leaf display of test scores
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
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Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
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Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
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DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
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Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
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Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
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TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Table 28 Class Boundaries Class Widths and Class Midpoints for Table 27
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-3
The following data give the total number of iPodsreg sold by a mail order company on each of 30 days Construct a frequency distribution table
8 25 11 15 29 22 10 5 17 21
22 13 26 16 18 12 9 26 20 16
23 14 19 23 20 16 27 16 21 14
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-3 Solution
29 5Approximate width of each class 48
5
Now we round this approximate width to a convenient number say 5 The lower limit of the first class can be taken as 5 or any number less than 5 Suppose we take 5 as the lower limit of the first class Then our classes will be 5 ndash 9 10 ndash 14 15 ndash 19 20 ndash 24 and 25 ndash 29
The minimum value is 5 and the maximum value is 29 Suppose we decide to group these data using five classes of equal width Then
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Table 29 Frequency Distribution for the Data on iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Relative Frequency and Percentage Distributions
Calculating Relative Frequency and Percentage
100 frequency) (Relative Percentage
sfrequencie all of Sum
class that of Frequencyclass a of frequency Relative
f
f
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-4 Calculate the relative frequencies and percentages for
Table 29
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Example 2-4 SolutionTable 210 Relative Frequency and Percentage Distributions for Table 29
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Graphing Grouped Data Definition A histogram is a graph in which classes are marked on the
horizontal axis and the frequencies relative frequencies or percentages are marked on the vertical axis The frequencies relative frequencies or percentages are represented by the heights of the bars In a histogram the bars are drawn adjacent to each other
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Figure 23 Frequency histogram for Table 29
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Figure 24 Relative frequency histogram for Table 210
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Case Study 2-3 How Long Does Your Typical One-Way Commute Take
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Graphing Grouped Data Definition A graph formed by joining the midpoints of the tops of
successive bars in a histogram with straight lines is called a polygon
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Figure 25 Frequency polygon for Table 29
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Case Study 2-4 How Much Does it Cost to Insure a Car
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Figure 26 Frequency distribution curve
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Example 2-5 The percentage of the population working in the United
States peaked in 2000 but dropped to the lowest level in 30 years in 2010 Table 211 shows the percentage of the population working in each of the 50 states in 2010 These percentages exclude military personnel and self-employed persons (Source USA TODAY April 14 2011 Based on data from the US Census Bureau and US Bureau of Labor Statistics)
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5
Construct a frequency distribution table Calculate the relative frequencies and percentages for all classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5 Solution
The minimum value in the data set of Table 211 is 367 and the maximum value is 558 Suppose we decide to group these data using six classes of equal width Then
We round this to a more convenient number say 3 We can take a lower limit of the first class equal to 367 or any number lower than 367 If we start the first class at 36 the classes will be written as 36 to less than 39 39 to less than 42 and so on
119808119849119849119851119848119857119842119846119834119853119838119856119842119837119853119841119848119839 119834119836119845119834119852119852=558minus367
6=318
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Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
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Figure 27 Bar graph for Table 213
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Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
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SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
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Figure 28 Symmetric histograms
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Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 210 A histogram with uniform distribution
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Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
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Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
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Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 212 Ogive for the cumulative frequency distribution of Table 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 213 Stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
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Figure 214 Stem-and-leaf display of test scores
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Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
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Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
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Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
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DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
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Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
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Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
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Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
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Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
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Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Example 2-3
The following data give the total number of iPodsreg sold by a mail order company on each of 30 days Construct a frequency distribution table
8 25 11 15 29 22 10 5 17 21
22 13 26 16 18 12 9 26 20 16
23 14 19 23 20 16 27 16 21 14
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Example 2-3 Solution
29 5Approximate width of each class 48
5
Now we round this approximate width to a convenient number say 5 The lower limit of the first class can be taken as 5 or any number less than 5 Suppose we take 5 as the lower limit of the first class Then our classes will be 5 ndash 9 10 ndash 14 15 ndash 19 20 ndash 24 and 25 ndash 29
The minimum value is 5 and the maximum value is 29 Suppose we decide to group these data using five classes of equal width Then
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 29 Frequency Distribution for the Data on iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Relative Frequency and Percentage Distributions
Calculating Relative Frequency and Percentage
100 frequency) (Relative Percentage
sfrequencie all of Sum
class that of Frequencyclass a of frequency Relative
f
f
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-4 Calculate the relative frequencies and percentages for
Table 29
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Example 2-4 SolutionTable 210 Relative Frequency and Percentage Distributions for Table 29
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Graphing Grouped Data Definition A histogram is a graph in which classes are marked on the
horizontal axis and the frequencies relative frequencies or percentages are marked on the vertical axis The frequencies relative frequencies or percentages are represented by the heights of the bars In a histogram the bars are drawn adjacent to each other
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Figure 23 Frequency histogram for Table 29
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Figure 24 Relative frequency histogram for Table 210
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Case Study 2-3 How Long Does Your Typical One-Way Commute Take
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Graphing Grouped Data Definition A graph formed by joining the midpoints of the tops of
successive bars in a histogram with straight lines is called a polygon
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Figure 25 Frequency polygon for Table 29
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Case Study 2-4 How Much Does it Cost to Insure a Car
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Figure 26 Frequency distribution curve
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Example 2-5 The percentage of the population working in the United
States peaked in 2000 but dropped to the lowest level in 30 years in 2010 Table 211 shows the percentage of the population working in each of the 50 states in 2010 These percentages exclude military personnel and self-employed persons (Source USA TODAY April 14 2011 Based on data from the US Census Bureau and US Bureau of Labor Statistics)
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5
Construct a frequency distribution table Calculate the relative frequencies and percentages for all classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5 Solution
The minimum value in the data set of Table 211 is 367 and the maximum value is 558 Suppose we decide to group these data using six classes of equal width Then
We round this to a more convenient number say 3 We can take a lower limit of the first class equal to 367 or any number lower than 367 If we start the first class at 36 the classes will be written as 36 to less than 39 39 to less than 42 and so on
119808119849119849119851119848119857119842119846119834119853119838119856119842119837119853119841119848119839 119834119836119845119834119852119852=558minus367
6=318
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Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
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Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
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Figure 27 Bar graph for Table 213
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Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
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SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
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Figure 28 Symmetric histograms
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Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
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Figure 210 A histogram with uniform distribution
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Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
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Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
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Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
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Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
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Figure 212 Ogive for the cumulative frequency distribution of Table 214
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STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
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Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
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Figure 213 Stem-and-leaf display
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Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
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Figure 214 Stem-and-leaf display of test scores
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Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
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Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
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Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
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Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
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Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
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Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
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DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
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Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
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Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
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Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
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Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
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Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
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Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
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Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
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Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
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TI-84
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TI-84
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Minitab
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Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
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Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Example 2-3 Solution
29 5Approximate width of each class 48
5
Now we round this approximate width to a convenient number say 5 The lower limit of the first class can be taken as 5 or any number less than 5 Suppose we take 5 as the lower limit of the first class Then our classes will be 5 ndash 9 10 ndash 14 15 ndash 19 20 ndash 24 and 25 ndash 29
The minimum value is 5 and the maximum value is 29 Suppose we decide to group these data using five classes of equal width Then
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 29 Frequency Distribution for the Data on iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Relative Frequency and Percentage Distributions
Calculating Relative Frequency and Percentage
100 frequency) (Relative Percentage
sfrequencie all of Sum
class that of Frequencyclass a of frequency Relative
f
f
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-4 Calculate the relative frequencies and percentages for
Table 29
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-4 SolutionTable 210 Relative Frequency and Percentage Distributions for Table 29
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Graphing Grouped Data Definition A histogram is a graph in which classes are marked on the
horizontal axis and the frequencies relative frequencies or percentages are marked on the vertical axis The frequencies relative frequencies or percentages are represented by the heights of the bars In a histogram the bars are drawn adjacent to each other
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 23 Frequency histogram for Table 29
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Figure 24 Relative frequency histogram for Table 210
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Case Study 2-3 How Long Does Your Typical One-Way Commute Take
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Graphing Grouped Data Definition A graph formed by joining the midpoints of the tops of
successive bars in a histogram with straight lines is called a polygon
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Figure 25 Frequency polygon for Table 29
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Case Study 2-4 How Much Does it Cost to Insure a Car
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Figure 26 Frequency distribution curve
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5 The percentage of the population working in the United
States peaked in 2000 but dropped to the lowest level in 30 years in 2010 Table 211 shows the percentage of the population working in each of the 50 states in 2010 These percentages exclude military personnel and self-employed persons (Source USA TODAY April 14 2011 Based on data from the US Census Bureau and US Bureau of Labor Statistics)
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5
Construct a frequency distribution table Calculate the relative frequencies and percentages for all classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5 Solution
The minimum value in the data set of Table 211 is 367 and the maximum value is 558 Suppose we decide to group these data using six classes of equal width Then
We round this to a more convenient number say 3 We can take a lower limit of the first class equal to 367 or any number lower than 367 If we start the first class at 36 the classes will be written as 36 to less than 39 39 to less than 42 and so on
119808119849119849119851119848119857119842119846119834119853119838119856119842119837119853119841119848119839 119834119836119845119834119852119852=558minus367
6=318
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Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
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Figure 27 Bar graph for Table 213
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Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
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SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
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Figure 28 Symmetric histograms
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Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
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Figure 210 A histogram with uniform distribution
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Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 212 Ogive for the cumulative frequency distribution of Table 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 213 Stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 214 Stem-and-leaf display of test scores
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
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Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
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Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Table 29 Frequency Distribution for the Data on iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Relative Frequency and Percentage Distributions
Calculating Relative Frequency and Percentage
100 frequency) (Relative Percentage
sfrequencie all of Sum
class that of Frequencyclass a of frequency Relative
f
f
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-4 Calculate the relative frequencies and percentages for
Table 29
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-4 SolutionTable 210 Relative Frequency and Percentage Distributions for Table 29
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Graphing Grouped Data Definition A histogram is a graph in which classes are marked on the
horizontal axis and the frequencies relative frequencies or percentages are marked on the vertical axis The frequencies relative frequencies or percentages are represented by the heights of the bars In a histogram the bars are drawn adjacent to each other
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 23 Frequency histogram for Table 29
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Figure 24 Relative frequency histogram for Table 210
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Case Study 2-3 How Long Does Your Typical One-Way Commute Take
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Graphing Grouped Data Definition A graph formed by joining the midpoints of the tops of
successive bars in a histogram with straight lines is called a polygon
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 25 Frequency polygon for Table 29
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Case Study 2-4 How Much Does it Cost to Insure a Car
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Figure 26 Frequency distribution curve
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5 The percentage of the population working in the United
States peaked in 2000 but dropped to the lowest level in 30 years in 2010 Table 211 shows the percentage of the population working in each of the 50 states in 2010 These percentages exclude military personnel and self-employed persons (Source USA TODAY April 14 2011 Based on data from the US Census Bureau and US Bureau of Labor Statistics)
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5
Construct a frequency distribution table Calculate the relative frequencies and percentages for all classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5 Solution
The minimum value in the data set of Table 211 is 367 and the maximum value is 558 Suppose we decide to group these data using six classes of equal width Then
We round this to a more convenient number say 3 We can take a lower limit of the first class equal to 367 or any number lower than 367 If we start the first class at 36 the classes will be written as 36 to less than 39 39 to less than 42 and so on
119808119849119849119851119848119857119842119846119834119853119838119856119842119837119853119841119848119839 119834119836119845119834119852119852=558minus367
6=318
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 27 Bar graph for Table 213
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Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 28 Symmetric histograms
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Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 210 A histogram with uniform distribution
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 212 Ogive for the cumulative frequency distribution of Table 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
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Figure 213 Stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
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Figure 214 Stem-and-leaf display of test scores
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
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Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
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Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
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DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
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Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Relative Frequency and Percentage Distributions
Calculating Relative Frequency and Percentage
100 frequency) (Relative Percentage
sfrequencie all of Sum
class that of Frequencyclass a of frequency Relative
f
f
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-4 Calculate the relative frequencies and percentages for
Table 29
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-4 SolutionTable 210 Relative Frequency and Percentage Distributions for Table 29
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Graphing Grouped Data Definition A histogram is a graph in which classes are marked on the
horizontal axis and the frequencies relative frequencies or percentages are marked on the vertical axis The frequencies relative frequencies or percentages are represented by the heights of the bars In a histogram the bars are drawn adjacent to each other
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 23 Frequency histogram for Table 29
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 24 Relative frequency histogram for Table 210
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Case Study 2-3 How Long Does Your Typical One-Way Commute Take
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Graphing Grouped Data Definition A graph formed by joining the midpoints of the tops of
successive bars in a histogram with straight lines is called a polygon
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 25 Frequency polygon for Table 29
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Case Study 2-4 How Much Does it Cost to Insure a Car
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 26 Frequency distribution curve
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5 The percentage of the population working in the United
States peaked in 2000 but dropped to the lowest level in 30 years in 2010 Table 211 shows the percentage of the population working in each of the 50 states in 2010 These percentages exclude military personnel and self-employed persons (Source USA TODAY April 14 2011 Based on data from the US Census Bureau and US Bureau of Labor Statistics)
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5
Construct a frequency distribution table Calculate the relative frequencies and percentages for all classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5 Solution
The minimum value in the data set of Table 211 is 367 and the maximum value is 558 Suppose we decide to group these data using six classes of equal width Then
We round this to a more convenient number say 3 We can take a lower limit of the first class equal to 367 or any number lower than 367 If we start the first class at 36 the classes will be written as 36 to less than 39 39 to less than 42 and so on
119808119849119849119851119848119857119842119846119834119853119838119856119842119837119853119841119848119839 119834119836119845119834119852119852=558minus367
6=318
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 27 Bar graph for Table 213
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 28 Symmetric histograms
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 210 A histogram with uniform distribution
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 212 Ogive for the cumulative frequency distribution of Table 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 213 Stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 214 Stem-and-leaf display of test scores
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
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TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Example 2-4 Calculate the relative frequencies and percentages for
Table 29
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-4 SolutionTable 210 Relative Frequency and Percentage Distributions for Table 29
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Graphing Grouped Data Definition A histogram is a graph in which classes are marked on the
horizontal axis and the frequencies relative frequencies or percentages are marked on the vertical axis The frequencies relative frequencies or percentages are represented by the heights of the bars In a histogram the bars are drawn adjacent to each other
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 23 Frequency histogram for Table 29
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Figure 24 Relative frequency histogram for Table 210
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Case Study 2-3 How Long Does Your Typical One-Way Commute Take
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Graphing Grouped Data Definition A graph formed by joining the midpoints of the tops of
successive bars in a histogram with straight lines is called a polygon
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Figure 25 Frequency polygon for Table 29
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Case Study 2-4 How Much Does it Cost to Insure a Car
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Figure 26 Frequency distribution curve
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5 The percentage of the population working in the United
States peaked in 2000 but dropped to the lowest level in 30 years in 2010 Table 211 shows the percentage of the population working in each of the 50 states in 2010 These percentages exclude military personnel and self-employed persons (Source USA TODAY April 14 2011 Based on data from the US Census Bureau and US Bureau of Labor Statistics)
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5
Construct a frequency distribution table Calculate the relative frequencies and percentages for all classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5 Solution
The minimum value in the data set of Table 211 is 367 and the maximum value is 558 Suppose we decide to group these data using six classes of equal width Then
We round this to a more convenient number say 3 We can take a lower limit of the first class equal to 367 or any number lower than 367 If we start the first class at 36 the classes will be written as 36 to less than 39 39 to less than 42 and so on
119808119849119849119851119848119857119842119846119834119853119838119856119842119837119853119841119848119839 119834119836119845119834119852119852=558minus367
6=318
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Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
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Figure 27 Bar graph for Table 213
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Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
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SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
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Figure 28 Symmetric histograms
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Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 210 A histogram with uniform distribution
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Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
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Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
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Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
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Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 212 Ogive for the cumulative frequency distribution of Table 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 213 Stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 214 Stem-and-leaf display of test scores
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
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Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
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DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
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TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Example 2-4 SolutionTable 210 Relative Frequency and Percentage Distributions for Table 29
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Graphing Grouped Data Definition A histogram is a graph in which classes are marked on the
horizontal axis and the frequencies relative frequencies or percentages are marked on the vertical axis The frequencies relative frequencies or percentages are represented by the heights of the bars In a histogram the bars are drawn adjacent to each other
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 23 Frequency histogram for Table 29
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 24 Relative frequency histogram for Table 210
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Case Study 2-3 How Long Does Your Typical One-Way Commute Take
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Graphing Grouped Data Definition A graph formed by joining the midpoints of the tops of
successive bars in a histogram with straight lines is called a polygon
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 25 Frequency polygon for Table 29
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Case Study 2-4 How Much Does it Cost to Insure a Car
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 26 Frequency distribution curve
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5 The percentage of the population working in the United
States peaked in 2000 but dropped to the lowest level in 30 years in 2010 Table 211 shows the percentage of the population working in each of the 50 states in 2010 These percentages exclude military personnel and self-employed persons (Source USA TODAY April 14 2011 Based on data from the US Census Bureau and US Bureau of Labor Statistics)
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5
Construct a frequency distribution table Calculate the relative frequencies and percentages for all classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5 Solution
The minimum value in the data set of Table 211 is 367 and the maximum value is 558 Suppose we decide to group these data using six classes of equal width Then
We round this to a more convenient number say 3 We can take a lower limit of the first class equal to 367 or any number lower than 367 If we start the first class at 36 the classes will be written as 36 to less than 39 39 to less than 42 and so on
119808119849119849119851119848119857119842119846119834119853119838119856119842119837119853119841119848119839 119834119836119845119834119852119852=558minus367
6=318
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 27 Bar graph for Table 213
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 28 Symmetric histograms
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 210 A histogram with uniform distribution
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 212 Ogive for the cumulative frequency distribution of Table 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 213 Stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 214 Stem-and-leaf display of test scores
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Graphing Grouped Data Definition A histogram is a graph in which classes are marked on the
horizontal axis and the frequencies relative frequencies or percentages are marked on the vertical axis The frequencies relative frequencies or percentages are represented by the heights of the bars In a histogram the bars are drawn adjacent to each other
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 23 Frequency histogram for Table 29
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Figure 24 Relative frequency histogram for Table 210
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Case Study 2-3 How Long Does Your Typical One-Way Commute Take
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Graphing Grouped Data Definition A graph formed by joining the midpoints of the tops of
successive bars in a histogram with straight lines is called a polygon
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 25 Frequency polygon for Table 29
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Case Study 2-4 How Much Does it Cost to Insure a Car
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Figure 26 Frequency distribution curve
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5 The percentage of the population working in the United
States peaked in 2000 but dropped to the lowest level in 30 years in 2010 Table 211 shows the percentage of the population working in each of the 50 states in 2010 These percentages exclude military personnel and self-employed persons (Source USA TODAY April 14 2011 Based on data from the US Census Bureau and US Bureau of Labor Statistics)
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5
Construct a frequency distribution table Calculate the relative frequencies and percentages for all classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5 Solution
The minimum value in the data set of Table 211 is 367 and the maximum value is 558 Suppose we decide to group these data using six classes of equal width Then
We round this to a more convenient number say 3 We can take a lower limit of the first class equal to 367 or any number lower than 367 If we start the first class at 36 the classes will be written as 36 to less than 39 39 to less than 42 and so on
119808119849119849119851119848119857119842119846119834119853119838119856119842119837119853119841119848119839 119834119836119845119834119852119852=558minus367
6=318
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Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
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Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
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Figure 27 Bar graph for Table 213
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Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
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SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
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Figure 28 Symmetric histograms
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Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 210 A histogram with uniform distribution
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 212 Ogive for the cumulative frequency distribution of Table 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 213 Stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 214 Stem-and-leaf display of test scores
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Figure 23 Frequency histogram for Table 29
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 24 Relative frequency histogram for Table 210
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Case Study 2-3 How Long Does Your Typical One-Way Commute Take
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Graphing Grouped Data Definition A graph formed by joining the midpoints of the tops of
successive bars in a histogram with straight lines is called a polygon
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 25 Frequency polygon for Table 29
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Case Study 2-4 How Much Does it Cost to Insure a Car
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 26 Frequency distribution curve
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5 The percentage of the population working in the United
States peaked in 2000 but dropped to the lowest level in 30 years in 2010 Table 211 shows the percentage of the population working in each of the 50 states in 2010 These percentages exclude military personnel and self-employed persons (Source USA TODAY April 14 2011 Based on data from the US Census Bureau and US Bureau of Labor Statistics)
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5
Construct a frequency distribution table Calculate the relative frequencies and percentages for all classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5 Solution
The minimum value in the data set of Table 211 is 367 and the maximum value is 558 Suppose we decide to group these data using six classes of equal width Then
We round this to a more convenient number say 3 We can take a lower limit of the first class equal to 367 or any number lower than 367 If we start the first class at 36 the classes will be written as 36 to less than 39 39 to less than 42 and so on
119808119849119849119851119848119857119842119846119834119853119838119856119842119837119853119841119848119839 119834119836119845119834119852119852=558minus367
6=318
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 27 Bar graph for Table 213
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Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 28 Symmetric histograms
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Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
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Figure 210 A histogram with uniform distribution
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Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 212 Ogive for the cumulative frequency distribution of Table 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 213 Stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 214 Stem-and-leaf display of test scores
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Figure 24 Relative frequency histogram for Table 210
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Case Study 2-3 How Long Does Your Typical One-Way Commute Take
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Graphing Grouped Data Definition A graph formed by joining the midpoints of the tops of
successive bars in a histogram with straight lines is called a polygon
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 25 Frequency polygon for Table 29
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Case Study 2-4 How Much Does it Cost to Insure a Car
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 26 Frequency distribution curve
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5 The percentage of the population working in the United
States peaked in 2000 but dropped to the lowest level in 30 years in 2010 Table 211 shows the percentage of the population working in each of the 50 states in 2010 These percentages exclude military personnel and self-employed persons (Source USA TODAY April 14 2011 Based on data from the US Census Bureau and US Bureau of Labor Statistics)
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5
Construct a frequency distribution table Calculate the relative frequencies and percentages for all classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5 Solution
The minimum value in the data set of Table 211 is 367 and the maximum value is 558 Suppose we decide to group these data using six classes of equal width Then
We round this to a more convenient number say 3 We can take a lower limit of the first class equal to 367 or any number lower than 367 If we start the first class at 36 the classes will be written as 36 to less than 39 39 to less than 42 and so on
119808119849119849119851119848119857119842119846119834119853119838119856119842119837119853119841119848119839 119834119836119845119834119852119852=558minus367
6=318
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 27 Bar graph for Table 213
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 28 Symmetric histograms
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 210 A histogram with uniform distribution
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 212 Ogive for the cumulative frequency distribution of Table 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 213 Stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 214 Stem-and-leaf display of test scores
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Case Study 2-3 How Long Does Your Typical One-Way Commute Take
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Graphing Grouped Data Definition A graph formed by joining the midpoints of the tops of
successive bars in a histogram with straight lines is called a polygon
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 25 Frequency polygon for Table 29
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Case Study 2-4 How Much Does it Cost to Insure a Car
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 26 Frequency distribution curve
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5 The percentage of the population working in the United
States peaked in 2000 but dropped to the lowest level in 30 years in 2010 Table 211 shows the percentage of the population working in each of the 50 states in 2010 These percentages exclude military personnel and self-employed persons (Source USA TODAY April 14 2011 Based on data from the US Census Bureau and US Bureau of Labor Statistics)
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5
Construct a frequency distribution table Calculate the relative frequencies and percentages for all classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5 Solution
The minimum value in the data set of Table 211 is 367 and the maximum value is 558 Suppose we decide to group these data using six classes of equal width Then
We round this to a more convenient number say 3 We can take a lower limit of the first class equal to 367 or any number lower than 367 If we start the first class at 36 the classes will be written as 36 to less than 39 39 to less than 42 and so on
119808119849119849119851119848119857119842119846119834119853119838119856119842119837119853119841119848119839 119834119836119845119834119852119852=558minus367
6=318
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 27 Bar graph for Table 213
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Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
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SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 28 Symmetric histograms
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Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
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Figure 210 A histogram with uniform distribution
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Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
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CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 212 Ogive for the cumulative frequency distribution of Table 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 213 Stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 214 Stem-and-leaf display of test scores
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
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TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Graphing Grouped Data Definition A graph formed by joining the midpoints of the tops of
successive bars in a histogram with straight lines is called a polygon
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 25 Frequency polygon for Table 29
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Case Study 2-4 How Much Does it Cost to Insure a Car
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 26 Frequency distribution curve
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5 The percentage of the population working in the United
States peaked in 2000 but dropped to the lowest level in 30 years in 2010 Table 211 shows the percentage of the population working in each of the 50 states in 2010 These percentages exclude military personnel and self-employed persons (Source USA TODAY April 14 2011 Based on data from the US Census Bureau and US Bureau of Labor Statistics)
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5
Construct a frequency distribution table Calculate the relative frequencies and percentages for all classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5 Solution
The minimum value in the data set of Table 211 is 367 and the maximum value is 558 Suppose we decide to group these data using six classes of equal width Then
We round this to a more convenient number say 3 We can take a lower limit of the first class equal to 367 or any number lower than 367 If we start the first class at 36 the classes will be written as 36 to less than 39 39 to less than 42 and so on
119808119849119849119851119848119857119842119846119834119853119838119856119842119837119853119841119848119839 119834119836119845119834119852119852=558minus367
6=318
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 27 Bar graph for Table 213
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 28 Symmetric histograms
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 210 A histogram with uniform distribution
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 212 Ogive for the cumulative frequency distribution of Table 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 213 Stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 214 Stem-and-leaf display of test scores
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Figure 25 Frequency polygon for Table 29
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Case Study 2-4 How Much Does it Cost to Insure a Car
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 26 Frequency distribution curve
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5 The percentage of the population working in the United
States peaked in 2000 but dropped to the lowest level in 30 years in 2010 Table 211 shows the percentage of the population working in each of the 50 states in 2010 These percentages exclude military personnel and self-employed persons (Source USA TODAY April 14 2011 Based on data from the US Census Bureau and US Bureau of Labor Statistics)
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5
Construct a frequency distribution table Calculate the relative frequencies and percentages for all classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5 Solution
The minimum value in the data set of Table 211 is 367 and the maximum value is 558 Suppose we decide to group these data using six classes of equal width Then
We round this to a more convenient number say 3 We can take a lower limit of the first class equal to 367 or any number lower than 367 If we start the first class at 36 the classes will be written as 36 to less than 39 39 to less than 42 and so on
119808119849119849119851119848119857119842119846119834119853119838119856119842119837119853119841119848119839 119834119836119845119834119852119852=558minus367
6=318
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
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Figure 27 Bar graph for Table 213
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Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
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SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 28 Symmetric histograms
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Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
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Figure 210 A histogram with uniform distribution
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Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 212 Ogive for the cumulative frequency distribution of Table 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 213 Stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 214 Stem-and-leaf display of test scores
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Case Study 2-4 How Much Does it Cost to Insure a Car
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 26 Frequency distribution curve
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5 The percentage of the population working in the United
States peaked in 2000 but dropped to the lowest level in 30 years in 2010 Table 211 shows the percentage of the population working in each of the 50 states in 2010 These percentages exclude military personnel and self-employed persons (Source USA TODAY April 14 2011 Based on data from the US Census Bureau and US Bureau of Labor Statistics)
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5
Construct a frequency distribution table Calculate the relative frequencies and percentages for all classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5 Solution
The minimum value in the data set of Table 211 is 367 and the maximum value is 558 Suppose we decide to group these data using six classes of equal width Then
We round this to a more convenient number say 3 We can take a lower limit of the first class equal to 367 or any number lower than 367 If we start the first class at 36 the classes will be written as 36 to less than 39 39 to less than 42 and so on
119808119849119849119851119848119857119842119846119834119853119838119856119842119837119853119841119848119839 119834119836119845119834119852119852=558minus367
6=318
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 27 Bar graph for Table 213
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 28 Symmetric histograms
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 210 A histogram with uniform distribution
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 212 Ogive for the cumulative frequency distribution of Table 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 213 Stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 214 Stem-and-leaf display of test scores
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Figure 26 Frequency distribution curve
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5 The percentage of the population working in the United
States peaked in 2000 but dropped to the lowest level in 30 years in 2010 Table 211 shows the percentage of the population working in each of the 50 states in 2010 These percentages exclude military personnel and self-employed persons (Source USA TODAY April 14 2011 Based on data from the US Census Bureau and US Bureau of Labor Statistics)
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5
Construct a frequency distribution table Calculate the relative frequencies and percentages for all classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5 Solution
The minimum value in the data set of Table 211 is 367 and the maximum value is 558 Suppose we decide to group these data using six classes of equal width Then
We round this to a more convenient number say 3 We can take a lower limit of the first class equal to 367 or any number lower than 367 If we start the first class at 36 the classes will be written as 36 to less than 39 39 to less than 42 and so on
119808119849119849119851119848119857119842119846119834119853119838119856119842119837119853119841119848119839 119834119836119845119834119852119852=558minus367
6=318
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 27 Bar graph for Table 213
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 28 Symmetric histograms
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Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 210 A histogram with uniform distribution
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 212 Ogive for the cumulative frequency distribution of Table 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 213 Stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 214 Stem-and-leaf display of test scores
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Example 2-5 The percentage of the population working in the United
States peaked in 2000 but dropped to the lowest level in 30 years in 2010 Table 211 shows the percentage of the population working in each of the 50 states in 2010 These percentages exclude military personnel and self-employed persons (Source USA TODAY April 14 2011 Based on data from the US Census Bureau and US Bureau of Labor Statistics)
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5
Construct a frequency distribution table Calculate the relative frequencies and percentages for all classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5 Solution
The minimum value in the data set of Table 211 is 367 and the maximum value is 558 Suppose we decide to group these data using six classes of equal width Then
We round this to a more convenient number say 3 We can take a lower limit of the first class equal to 367 or any number lower than 367 If we start the first class at 36 the classes will be written as 36 to less than 39 39 to less than 42 and so on
119808119849119849119851119848119857119842119846119834119853119838119856119842119837119853119841119848119839 119834119836119845119834119852119852=558minus367
6=318
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 27 Bar graph for Table 213
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 28 Symmetric histograms
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 210 A histogram with uniform distribution
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 212 Ogive for the cumulative frequency distribution of Table 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 213 Stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 214 Stem-and-leaf display of test scores
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Example 2-5
Construct a frequency distribution table Calculate the relative frequencies and percentages for all classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-5 Solution
The minimum value in the data set of Table 211 is 367 and the maximum value is 558 Suppose we decide to group these data using six classes of equal width Then
We round this to a more convenient number say 3 We can take a lower limit of the first class equal to 367 or any number lower than 367 If we start the first class at 36 the classes will be written as 36 to less than 39 39 to less than 42 and so on
119808119849119849119851119848119857119842119846119834119853119838119856119842119837119853119841119848119839 119834119836119845119834119852119852=558minus367
6=318
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 27 Bar graph for Table 213
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Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 28 Symmetric histograms
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Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
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Figure 210 A histogram with uniform distribution
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Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 212 Ogive for the cumulative frequency distribution of Table 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 213 Stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 214 Stem-and-leaf display of test scores
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Example 2-5 Solution
The minimum value in the data set of Table 211 is 367 and the maximum value is 558 Suppose we decide to group these data using six classes of equal width Then
We round this to a more convenient number say 3 We can take a lower limit of the first class equal to 367 or any number lower than 367 If we start the first class at 36 the classes will be written as 36 to less than 39 39 to less than 42 and so on
119808119849119849119851119848119857119842119846119834119853119838119856119842119837119853119841119848119839 119834119836119845119834119852119852=558minus367
6=318
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 27 Bar graph for Table 213
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 28 Symmetric histograms
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 210 A histogram with uniform distribution
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 212 Ogive for the cumulative frequency distribution of Table 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 213 Stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 214 Stem-and-leaf display of test scores
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Table 212 Frequency Relative Frequency and Percentage Distributions of the Percentage of Population Workings
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 27 Bar graph for Table 213
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 28 Symmetric histograms
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 210 A histogram with uniform distribution
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 212 Ogive for the cumulative frequency distribution of Table 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 213 Stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 214 Stem-and-leaf display of test scores
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Example 2-6 The administration in a large city wanted to know the
distribution of vehicles owned by households in that city A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned
5 1 1 2 0 1 1 2 1 11 3 3 0 2 5 1 2 3 42 1 2 2 1 2 2 1 1 14 2 1 1 2 1 1 4 1 3
Construct a frequency distribution table for these data using
single-valued classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 27 Bar graph for Table 213
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 28 Symmetric histograms
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 210 A histogram with uniform distribution
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 212 Ogive for the cumulative frequency distribution of Table 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 213 Stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 214 Stem-and-leaf display of test scores
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Example 2-6 SolutionTable 213 Frequency Distribution of Vehicles Owned
The observations assume only six distinct values 0 1 2 3 4 and 5 Each of these six values is used as a class in the frequency distribution in Table 213
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 27 Bar graph for Table 213
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 28 Symmetric histograms
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 210 A histogram with uniform distribution
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 212 Ogive for the cumulative frequency distribution of Table 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 213 Stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 214 Stem-and-leaf display of test scores
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Figure 27 Bar graph for Table 213
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 28 Symmetric histograms
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 210 A histogram with uniform distribution
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 212 Ogive for the cumulative frequency distribution of Table 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 213 Stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 214 Stem-and-leaf display of test scores
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 28 Symmetric histograms
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 210 A histogram with uniform distribution
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 212 Ogive for the cumulative frequency distribution of Table 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 213 Stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 214 Stem-and-leaf display of test scores
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
SHAPES OF HISTOGRAMS
1 Symmetric2 Skewed3 Uniform or Rectangular
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 28 Symmetric histograms
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 210 A histogram with uniform distribution
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 212 Ogive for the cumulative frequency distribution of Table 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 213 Stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 214 Stem-and-leaf display of test scores
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Figure 28 Symmetric histograms
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 210 A histogram with uniform distribution
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 212 Ogive for the cumulative frequency distribution of Table 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 213 Stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 214 Stem-and-leaf display of test scores
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Figure 29 (a) A histogram skewed to the right (b) A histogram skewed to the left
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 210 A histogram with uniform distribution
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 212 Ogive for the cumulative frequency distribution of Table 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 213 Stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 214 Stem-and-leaf display of test scores
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Figure 210 A histogram with uniform distribution
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 212 Ogive for the cumulative frequency distribution of Table 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 213 Stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 214 Stem-and-leaf display of test scores
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Figure 211 (a) and (b) Symmetric frequency curves (c) Frequency curve skewed to the right (d) Frequency curve skewed to the left
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 212 Ogive for the cumulative frequency distribution of Table 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 213 Stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 214 Stem-and-leaf display of test scores
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition A cumulative frequency distribution gives the total number
of values that fall below the upper boundary of each class
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 212 Ogive for the cumulative frequency distribution of Table 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 213 Stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 214 Stem-and-leaf display of test scores
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Example 2-7 Using the frequency distribution of Table 29 reproduced here
prepare a cumulative frequency distribution for the number of iPods sold by that company
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 212 Ogive for the cumulative frequency distribution of Table 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 213 Stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 214 Stem-and-leaf display of test scores
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Example 2-7 SolutionTable 214 Cumulative Frequency Distribution of iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 212 Ogive for the cumulative frequency distribution of Table 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 213 Stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 214 Stem-and-leaf display of test scores
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
CUMULATIVE FREQUENCY DISTRIBUTIONS
Calculating Cumulative Relative Frequency and Cumulative Percentage
100 frequency) relative e(Cumulativ percentage Cumulative
set data in the nsobservatio Total
class a offrequency Cumulativefrequency relative Cumulative
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 212 Ogive for the cumulative frequency distribution of Table 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 213 Stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 214 Stem-and-leaf display of test scores
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Table 215 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 212 Ogive for the cumulative frequency distribution of Table 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 213 Stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 214 Stem-and-leaf display of test scores
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
CUMULATIVE FREQUENCY DISTRIBUTIONS
Definition An ogive is a curve drawn for the cumulative frequency
distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 212 Ogive for the cumulative frequency distribution of Table 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 213 Stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 214 Stem-and-leaf display of test scores
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Figure 212 Ogive for the cumulative frequency distribution of Table 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 213 Stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 214 Stem-and-leaf display of test scores
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
STEM-AND-LEAF DISPLAYS Definition In a stem-and-leaf display of quantitative data each value
is divided into two portions ndash a stem and a leaf The leaves for each stem are shown separately in a display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 213 Stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 214 Stem-and-leaf display of test scores
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Example 2-8 The following are the scores of 30 college students on a
statistics test
Construct a stem-and-leaf display
756983
527284
808177
966164
657671
798687
717972
876892
935057
959298
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 213 Stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 214 Stem-and-leaf display of test scores
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Example 2-8 Solution To construct a stem-and-leaf display for these scores we split
each score into two parts The first part contains the first digit which is called the stem The second part contains the second digit which is called the leaf We observe from the data that the stems for all scores are 5 6 7 8 and 9 because all the scores lie in the range 50 to 98
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 213 Stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 214 Stem-and-leaf display of test scores
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Figure 213 Stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 214 Stem-and-leaf display of test scores
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Example 2-8 Solution After we have listed the stems we read the leaves for all
scores and record them next to the corresponding stems on the right side of the vertical line The complete stem-and-leaf display for scores is shown in Figure 214
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 214 Stem-and-leaf display of test scores
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Figure 214 Stem-and-leaf display of test scores
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Example 2-8 Solution The leaves for each stem of the stem-and-leaf display of
Figure 214 are ranked (in increasing order) and presented in Figure 215
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Figure 215 Ranked stem-and-leaf display of test scores
One advantage of a stem-and-leaf display is that we do not lose information on individual observations
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Example 2-9 The following data give the monthly rents paid by a sample of
30 households selected from a small town
Construct a stem-and-leaf display for these data
88012101151
1081 985 630
72112311175
1075 932 952
1023 8501100
775 8251140
12351000 750
750 9151140
96511911370
96010351280
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Example 2-9 SolutionFigure 216 Stem-and-leaf display of rents
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Example 2-10 The following stem-and-leaf display is prepared for the number of hours that 25 students spent working on computers during the last month
Prepare a new stem-and-leaf display by grouping the stems
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Example 2-10 SolutionFigure 217 Grouped stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Example 2-11 Consider the following stem-and-leaf display which has
only two stems Using the split stem procedure rewrite the stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Example 2-11 SolutionFigure 218 amp 219 Split stem-and-leaf display
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
DOTPLOTS Definition Values that are very small or very large relative to the
majority of the values in a data set are called outliers or extreme values
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Example 2-12
Table 216 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs Create a dotplot for these data
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Table 216 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Example 2-12 Solution
Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 220
Step 2 Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table After all the dots are placed Figure 221 gives the complete dotplot
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Example 2-12 Solution
As we examine the dotplot of Figure 221 we notice that there are two clusters (groups) of data Sixty percent of the players had 17 or fewer penalty minutes during the playoffs while the other 40 had 24 or more penalty minutes
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Example 2-13
Refer to Table 216 in Example 2-12 which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs Table 217 provides the same information for the Vancouver Canucks who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs Make dotplots for both sets of data and compare them
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Table 217 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Example 2-13 SolutionFigure 222 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Example 2-13 Solution
Looking at the stacked dotplot we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs Both teams have one outlier each at 63 and 66 minutes respectively The two distributions of penalty minutes are almost similar in shape
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
TI-84
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Minitab
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
Excel
Prem Mann Introductory Statistics 8E Copyright copy 2013 John Wiley amp Sons All rights reserved
- CHAPTER 2
- Opening Example
- RAW DATA
- Table 21 Ages of 50 Students
- Table 22 Status of 50 Students
- ORGANIZING AND GRAPHING DATA
- Table 23 Types of Employment Students Intend to Engage In
- Frequency Distributions
- Example 2-1
- Example 2-1 (2)
- Example 2-1 Solution Table 24 Frequency Distribution of Favor
- Relative Frequency and Percentage Distributions
- Relative Frequency and Percentage Distributions (2)
- Example 2-2
- Example 2-2 Solution Table 25 Relative Frequency and Percenta
- Case Study 2-1 Will Todayrsquos Children Be Better Off Than Their P
- Graphical Presentation of Qualitative Data
- Figure 21 Bar graph for the frequency distribution of Table 2
- Case Study 2-2 Employeesrsquo Overall Financial Stress Levels
- Graphical Presentation of Qualitative Data
- Table 26 Calculating Angle Sizes for the Pie Chart
- Figure 22 Pie chart for the percentage distribution of Table 2
- ORGANIZING AND GRAPHING QUANTITATIVE
- Table 27 Weekly Earnings of 100 Employees of a Company
- Frequency Distributions (2)
- Frequency Distributions (3)
- Frequency Distributions (4)
- Frequency Distributions (5)
- Constructing Frequency Distribution Tables
- Table 28 Class Boundaries Class Widths and Class Midpoints f
- Example 2-3
- Example 2-3 Solution
- Table 29 Frequency Distribution for the Data on iPods Sold
- Relative Frequency and Percentage Distributions (3)
- Example 2-4
- Example 2-4 Solution Table 210 Relative Frequency and Percent
- Graphing Grouped Data
- Figure 23 Frequency histogram for Table 29
- Figure 24 Relative frequency histogram for Table 210
- Case Study 2-3 How Long Does Your Typical One-Way Commute Take
- Graphing Grouped Data (2)
- Figure 25 Frequency polygon for Table 29
- Case Study 2-4 How Much Does it Cost to Insure a Car
- Figure 26 Frequency distribution curve
- Example 2-5
- Example 2-5 (2)
- Example 2-5 Solution
- Table 212 Frequency Relative Frequency and Percentage Distri
- Example 2-6
- Example 2-6 Solution Table 213 Frequency Distribution of Vehi
- Figure 27 Bar graph for Table 213
- Case Study 2-5 How Many Cups of Coffee Do You Drink a Day
- SHAPES OF HISTOGRAMS
- Figure 28 Symmetric histograms
- Figure 29 (a) A histogram skewed to the right (b) A histogra
- Figure 210 A histogram with uniform distribution
- Figure 211 (a) and (b) Symmetric frequency curves (c) Frequen
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Example 2-7
- Example 2-7 Solution Table 214 Cumulative Frequency Distribut
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- Table 215 Cumulative Relative Frequency and Cumulative Percent
- CUMULATIVE FREQUENCY DISTRIBUTIONS (2)
- Figure 212 Ogive for the cumulative frequency distribution
- STEM-AND-LEAF DISPLAYS
- Example 2-8
- Example 2-8 Solution
- Figure 213 Stem-and-leaf display
- Example 2-8 Solution (2)
- Figure 214 Stem-and-leaf display of test scores
- Example 2-8 Solution (3)
- Figure 215 Ranked stem-and-leaf display of test scores
- Example 2-9
- Example 2-9 Solution Figure 216 Stem-and-leaf display of rent
- Example 2-10
- Example 2-10 Solution Figure 217 Grouped stem-and-leaf displa
- Example 2-11
- Example 2-11 Solution Figure 218 amp 219 Split stem-and-leaf d
- DOTPLOTS
- Example 2-12
- Table 216 Number of Penalty Minutes for Players of the Boston
- Example 2-12 Solution
- Example 2-12 Solution (2)
- Example 2-13
- Table 217 Number of Penalty Minutes for Players of the Vancouv
- Example 2-13 Solution Figure 222 Stacked dotplot of penalty m
- Example 2-13 Solution
- TI-84
- TI-84 (2)
- Minitab
- Minitab (2)
- Minitab (3)
- Minitab (4)
- Minitab (5)
- Excel
- Excel (2)
-
top related