chapter 2 organizing and graphing data - …math.uhcl.edu/li/teach/stat3308/ch02_9e.pdf3 worries...

1

Chapter 2 Organizing and Graphing Data

21 Organizing and Graphing Qualitative Data

22 Organizing and Graphing Quantitative Data

23 Stem-and-leaf Displays

24 Dotplots

21 Organizing and Graphing Qualitative Data

Data recorded in the sequence in which they are collected and before they are processed or ranked are called raw data

Examples Ages of 50 students

Status of 50 Students

Dr Yingfu (Frank) Li111STAT 3308

2

New Table of Data for Previous Example

Dr Yingfu (Frank) Li2

Name Age StatusJohn 21 Junior

Mary 19 Freshman

STAT 3308

Organizing and Graphing Qualitative Data

Easy job for this type of data

Frequency Distributions (tables) A frequency distribution for qualitative data lists all categories and

the number of elements that belong to each of the categories

Relative Frequency and Percentage Distributions Relative frequency = frequency sum of all frequency

Percentage = (Relative frequency) 100

Graphical Presentation of Qualitative Data Bar graph

Pie chart

hellip


3

Worries About Not Having Enough Money to Pay Normal Monthly Bills

MATH 3038 - 01 Dr Yingfu (Frank) Li4

Frequency Distribution Example 21


A sample of 30 persons who often consume donuts were asked what variety of donuts is their favorite The responses from these 30 persons are as follows

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 (relative amp percentage) frequency distribution table for these data

STAT 3308

4

Frequency Distribution of Favorite Donut Variety


Relative Frequency and Percentage Distributions

STAT 3308

Graphical Presentation of Qualitative Data

Bar graph Height of each bar represents the

frequency of respective category

A Pareto chart A bar graph with bars arranged by

their heights in descending order

To make a Pareto chart arrange the bars according to their heights such that the bar with the largest height appears first on the left side and then subsequent bars are arranged in descending order with the bar with the smallest height appearing last on the right side


5

Pie Chart of Favorite Donut Variety


Pie chart Each portion represent the relative frequencies or percentages of a population or a sample belonging to a category

Case Studies


6


Frequency Distributions Group class etc

Class width class limit class boundary etc

Frequency of each group or class

Constructing Frequency Distribution Tables

Relative and Percentage Distributions

Graphing Grouped Data Histogram ndash similar to bar graph

polygons


Weekly Earnings of 100 Employees of a Company


7

Frequency Distributions for Quantitative Data

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

The class boundary is given by the midpoint of the upper limit of one class and the lower limit of the next class

Class width = Lower limit of the next class ndash Lower limit of the current class

Class midpoint = (upper limit + lower limit)2

Approximate class width = (largest value ndash smallest value) number of classes


Class Boundaries Widths and Midpoints


8

Example 2-3


The following table gives the value (in million dollars) of each of the 30 baseball teams as estimated by Forbes magazine Construct a frequency distribution table

STAT 3308

Example 2-3 Solution


Now we round this approximate width to a convenient number say 450 The lower limit of the first class can be taken as 605 or any number less than 605 Suppose we take 601 as the lower limit of the first class Then our classes will be

601ndash1050 1051ndash1500 1501ndash1950 1951ndash2400 and 2851ndash3300

The minimum value is 605 and the maximum value is 3200 Suppose we decide to group these data using six classes of equal width Then

Approximatewithofeachclass 3200 605

6 4325

9

Freq Distribution for the Data of Baseball Teams


Example 2-4 Relative Frequency and Percentage Distributions

STAT 3308

Constructing Frequency Table Histogram for Large Data


1 Range = largest value ndash smallest value

2 Pick the number of classes usually 5 ~ 20

3 Range of classes asymp round up =gt approx width

4 Lower boundary of the first class

= smallest ndash half of smallest unit of data or place value

5 Obtain all boundaries and this defined classes

6 Construct (relative) frequency distribution table

7 Construct (relative) Histogram

Suitable for using computer to obtain frequency table of large data set

STAT 3308

10

Graphing Grouped Data

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 Bar graph of frequency table

One class =gt one bar

Height = frequency relative frequency percentage

A graph formed by joining the midpoints of the tops of successive bars in a histogram with straight lines is called apolygon Plot (midpoint frequency)




Polygon is a graph formed by joining the midpoints of the tops of successive bars in a histogram with straight lines

It starts and ends from the horizontal line

STAT 3308

11

Frequency Distribution Curve


For large data set the number of classes is big Then the frequency polygon becomes a smooth curve

STAT 3308

Example 2-5


Based on the information collected by American Petroleum Institute Table 210 lists the total of federal and state taxes (in cents per gallon) on gasoline for each of the 50 states as of April 1 2015 (wwwapiorg)

Construct a frequency distribution table Calculate the relative frequencies and percentages for all classes

STAT 3308

12

Example 25 Solution


The minimum value in the data set of Table 210 is 297 and the maximum value is 70 Suppose we decide to group these data using five classes of equal width Then

We round this to a more convenient number say 9 and take 9 as the width of each class We can take the lower limit of the first class equal to 297 or any number lower than 297 If we start the first class at 27 the classes will be written as 27 to less than 36 36 to less than 45 etc

70 297

5806

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 and draw a bar graph

STAT 3308

13

Example 26 Solution


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

STAT 3308

Cumulative Frequency Distribution

A cumulative frequency distribution gives the total number of values that fall below the upper boundary of each class


100 frequency) relative e(Cumulativ percentage Cumulative

set data in the nsobservatio Total

class a offrequency Cumulativefrequency relative Cumulative

14



Hands-on Example

Data set Road race

Tool Microsoft Excel Add-ins

Statistical Analysis Tool Package

Cell reference

Bin upper boundary (limit)

Method follow the guideline of slide 17 How to find max and min values


15

Shapes of Histograms


Frequency Curves

Symmetric frequency curves - (a) and (b)

Frequency curve skewed to the right ndash (c) and frequency curve skewed to the left (d)


16

Truncating Axes

Changing the scale either on one or on both axesmdashthat is shortening or stretching one or both of the axes

Truncating the frequency axismdashthat is starting the frequency axis at a number greater than zero


23 Stem-and-Leaf Displays

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

Example 28 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

STAT 3308

17

Construct a Stem-and-Leaf Display

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



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 The leaves for each stem of the stem-and-leaf display of Figure 214

are ranked (in increasing order) and presented in Figure 215


Key5|2 = 52

STAT 3308

18

Example 2-9

The following data are monthly rents paid by a sample of 30 households selected from a small city

Construct a stem-and-leaf display for these data


88012101151

1081985630

72112311175

1075932952

1023850

1100

775825

1140

12351000750

750915

1140

96511911370

96010351280

Key6|30 = 630

STAT 3308

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


19

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


24 Dotplots

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

Dotplot can help us detect outliers ndash extremely small or large values

Example 2-12 A statistics class that meets once a week at night from 700 PM to

945 PM has 33 students The following data give the ages (in years) of these students Create a dotplot for these data

34 21 49 37 23 22 33 23 21 20 19

33 23 38 32 31 22 20 24 27 33 19

23 21 31 31 22 20 34 21 33 27 21


20

Example 212 Ages of Students


Step1 Draw a horizontal line with numbers that cover the given data as shown in Figure 222

Step 2 Place a dot above the value on the numbers line that represents each of the ages listed above After all the dots are placed Figure 223 gives the complete dotplot

As we examine the dotplot of Figure 223 we notice that there are two clusters (groups) of data Eighteen of the 33 students (which is almost 55) are 19 to 24 years old and 10 of the 33 students (which is about 30) are 31 to 34 years old There is one student who is 49 years old and is an outlier

2

New Table of Data for Previous Example


Name Age StatusJohn 21 Junior

Mary 19 Freshman

STAT 3308

Organizing and Graphing Qualitative Data

Easy job for this type of data

Frequency Distributions (tables) A frequency distribution for qualitative data lists all categories and

the number of elements that belong to each of the categories

Relative Frequency and Percentage Distributions Relative frequency = frequency sum of all frequency

Percentage = (Relative frequency) 100

Graphical Presentation of Qualitative Data Bar graph

Pie chart

hellip


3












STAT 3308

4




STAT 3308








5




Case Studies


6








polygons




7










8

Example 2-3



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6 4325

9




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10











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11




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Example 2-5




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12

Example 25 Solution




70 297

5806

Example 2-6



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


STAT 3308

13

Example 26 Solution



STAT 3308







14



Hands-on Example

Data set Road race



Cell reference




15



Frequency Curves




16

Truncating Axes







test



756983

527284

808177

966164

657671

798687

717972

876892

935057

959298

STAT 3308

17








Key5|2 = 52

STAT 3308

18

Example 2-9




88012101151

1081985630

72112311175

1075932952

1023850

1100

775825

1140

12351000750

750915

1140

96511911370

96010351280

Key6|30 = 630

STAT 3308

Example 2-10





19

Example 2-11



24 Dotplots





34 21 49 37 23 22 33 23 21 20 19

33 23 38 32 31 22 20 24 27 33 19

23 21 31 31 22 20 34 21 33 27 21


20






3












STAT 3308

4




STAT 3308








5




Case Studies


6








polygons




7










8

Example 2-3



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6 4325

9




STAT 3308












STAT 3308

10











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11




STAT 3308

Example 2-5




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12

Example 25 Solution




70 297

5806

Example 2-6



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


STAT 3308

13

Example 26 Solution



STAT 3308







14



Hands-on Example

Data set Road race



Cell reference




15



Frequency Curves




16

Truncating Axes







test



756983

527284

808177

966164

657671

798687

717972

876892

935057

959298

STAT 3308

17








Key5|2 = 52

STAT 3308

18

Example 2-9




88012101151

1081985630

72112311175

1075932952

1023850

1100

775825

1140

12351000750

750915

1140

96511911370

96010351280

Key6|30 = 630

STAT 3308

Example 2-10





19

Example 2-11



24 Dotplots





34 21 49 37 23 22 33 23 21 20 19

33 23 38 32 31 22 20 24 27 33 19

23 21 31 31 22 20 34 21 33 27 21


20






4




STAT 3308








5




Case Studies


6








polygons




7










8

Example 2-3



STAT 3308







6 4325

9




STAT 3308












STAT 3308

10











STAT 3308

11




STAT 3308

Example 2-5




STAT 3308

12

Example 25 Solution




70 297

5806

Example 2-6



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


STAT 3308

13

Example 26 Solution



STAT 3308







14



Hands-on Example

Data set Road race



Cell reference




15



Frequency Curves




16

Truncating Axes







test



756983

527284

808177

966164

657671

798687

717972

876892

935057

959298

STAT 3308

17








Key5|2 = 52

STAT 3308

18

Example 2-9




88012101151

1081985630

72112311175

1075932952

1023850

1100

775825

1140

12351000750

750915

1140

96511911370

96010351280

Key6|30 = 630

STAT 3308

Example 2-10





19

Example 2-11



24 Dotplots





34 21 49 37 23 22 33 23 21 20 19

33 23 38 32 31 22 20 24 27 33 19

23 21 31 31 22 20 34 21 33 27 21


20






5




Case Studies


6








polygons




7










8

Example 2-3



STAT 3308







6 4325

9




STAT 3308












STAT 3308

10











STAT 3308

11




STAT 3308

Example 2-5




STAT 3308

12

Example 25 Solution




70 297

5806

Example 2-6



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


STAT 3308

13

Example 26 Solution



STAT 3308







14



Hands-on Example

Data set Road race



Cell reference




15



Frequency Curves




16

Truncating Axes







test



756983

527284

808177

966164

657671

798687

717972

876892

935057

959298

STAT 3308

17








Key5|2 = 52

STAT 3308

18

Example 2-9




88012101151

1081985630

72112311175

1075932952

1023850

1100

775825

1140

12351000750

750915

1140

96511911370

96010351280

Key6|30 = 630

STAT 3308

Example 2-10





19

Example 2-11



24 Dotplots





34 21 49 37 23 22 33 23 21 20 19

33 23 38 32 31 22 20 24 27 33 19

23 21 31 31 22 20 34 21 33 27 21


20






6








polygons




7










8

Example 2-3



STAT 3308







6 4325

9




STAT 3308












STAT 3308

10











STAT 3308

11




STAT 3308

Example 2-5




STAT 3308

12

Example 25 Solution




70 297

5806

Example 2-6



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


STAT 3308

13

Example 26 Solution



STAT 3308







14



Hands-on Example

Data set Road race



Cell reference




15



Frequency Curves




16

Truncating Axes







test



756983

527284

808177

966164

657671

798687

717972

876892

935057

959298

STAT 3308

17








Key5|2 = 52

STAT 3308

18

Example 2-9




88012101151

1081985630

72112311175

1075932952

1023850

1100

775825

1140

12351000750

750915

1140

96511911370

96010351280

Key6|30 = 630

STAT 3308

Example 2-10





19

Example 2-11



24 Dotplots





34 21 49 37 23 22 33 23 21 20 19

33 23 38 32 31 22 20 24 27 33 19

23 21 31 31 22 20 34 21 33 27 21


20






7










8

Example 2-3



STAT 3308







6 4325

9




STAT 3308












STAT 3308

10











STAT 3308

11




STAT 3308

Example 2-5




STAT 3308

12

Example 25 Solution




70 297

5806

Example 2-6



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


STAT 3308

13

Example 26 Solution



STAT 3308







14



Hands-on Example

Data set Road race



Cell reference




15



Frequency Curves




16

Truncating Axes







test



756983

527284

808177

966164

657671

798687

717972

876892

935057

959298

STAT 3308

17








Key5|2 = 52

STAT 3308

18

Example 2-9




88012101151

1081985630

72112311175

1075932952

1023850

1100

775825

1140

12351000750

750915

1140

96511911370

96010351280

Key6|30 = 630

STAT 3308

Example 2-10





19

Example 2-11



24 Dotplots





34 21 49 37 23 22 33 23 21 20 19

33 23 38 32 31 22 20 24 27 33 19

23 21 31 31 22 20 34 21 33 27 21


20






8

Example 2-3



STAT 3308







6 4325

9




STAT 3308












STAT 3308

10











STAT 3308

11




STAT 3308

Example 2-5




STAT 3308

12

Example 25 Solution




70 297

5806

Example 2-6



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


STAT 3308

13

Example 26 Solution



STAT 3308







14



Hands-on Example

Data set Road race



Cell reference




15



Frequency Curves




16

Truncating Axes







test



756983

527284

808177

966164

657671

798687

717972

876892

935057

959298

STAT 3308

17








Key5|2 = 52

STAT 3308

18

Example 2-9




88012101151

1081985630

72112311175

1075932952

1023850

1100

775825

1140

12351000750

750915

1140

96511911370

96010351280

Key6|30 = 630

STAT 3308

Example 2-10





19

Example 2-11



24 Dotplots





34 21 49 37 23 22 33 23 21 20 19

33 23 38 32 31 22 20 24 27 33 19

23 21 31 31 22 20 34 21 33 27 21


20






9




STAT 3308












STAT 3308

10











STAT 3308

11




STAT 3308

Example 2-5




STAT 3308

12

Example 25 Solution




70 297

5806

Example 2-6



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


STAT 3308

13

Example 26 Solution



STAT 3308







14



Hands-on Example

Data set Road race



Cell reference




15



Frequency Curves




16

Truncating Axes







test



756983

527284

808177

966164

657671

798687

717972

876892

935057

959298

STAT 3308

17








Key5|2 = 52

STAT 3308

18

Example 2-9




88012101151

1081985630

72112311175

1075932952

1023850

1100

775825

1140

12351000750

750915

1140

96511911370

96010351280

Key6|30 = 630

STAT 3308

Example 2-10





19

Example 2-11



24 Dotplots





34 21 49 37 23 22 33 23 21 20 19

33 23 38 32 31 22 20 24 27 33 19

23 21 31 31 22 20 34 21 33 27 21


20






10











STAT 3308

11




STAT 3308

Example 2-5




STAT 3308

12

Example 25 Solution




70 297

5806

Example 2-6



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


STAT 3308

13

Example 26 Solution



STAT 3308







14



Hands-on Example

Data set Road race



Cell reference




15



Frequency Curves




16

Truncating Axes







test



756983

527284

808177

966164

657671

798687

717972

876892

935057

959298

STAT 3308

17








Key5|2 = 52

STAT 3308

18

Example 2-9




88012101151

1081985630

72112311175

1075932952

1023850

1100

775825

1140

12351000750

750915

1140

96511911370

96010351280

Key6|30 = 630

STAT 3308

Example 2-10





19

Example 2-11



24 Dotplots





34 21 49 37 23 22 33 23 21 20 19

33 23 38 32 31 22 20 24 27 33 19

23 21 31 31 22 20 34 21 33 27 21


20






11




STAT 3308

Example 2-5




STAT 3308

12

Example 25 Solution




70 297

5806

Example 2-6



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


STAT 3308

13

Example 26 Solution



STAT 3308







14



Hands-on Example

Data set Road race



Cell reference




15



Frequency Curves




16

Truncating Axes







test



756983

527284

808177

966164

657671

798687

717972

876892

935057

959298

STAT 3308

17








Key5|2 = 52

STAT 3308

18

Example 2-9




88012101151

1081985630

72112311175

1075932952

1023850

1100

775825

1140

12351000750

750915

1140

96511911370

96010351280

Key6|30 = 630

STAT 3308

Example 2-10





19

Example 2-11



24 Dotplots





34 21 49 37 23 22 33 23 21 20 19

33 23 38 32 31 22 20 24 27 33 19

23 21 31 31 22 20 34 21 33 27 21


20






12

Example 25 Solution




70 297

5806

Example 2-6



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


STAT 3308

13

Example 26 Solution



STAT 3308







14



Hands-on Example

Data set Road race



Cell reference




15



Frequency Curves




16

Truncating Axes







test



756983

527284

808177

966164

657671

798687

717972

876892

935057

959298

STAT 3308

17








Key5|2 = 52

STAT 3308

18

Example 2-9




88012101151

1081985630

72112311175

1075932952

1023850

1100

775825

1140

12351000750

750915

1140

96511911370

96010351280

Key6|30 = 630

STAT 3308

Example 2-10





19

Example 2-11



24 Dotplots





34 21 49 37 23 22 33 23 21 20 19

33 23 38 32 31 22 20 24 27 33 19

23 21 31 31 22 20 34 21 33 27 21


20






13

Example 26 Solution



STAT 3308







14



Hands-on Example

Data set Road race



Cell reference




15



Frequency Curves




16

Truncating Axes







test



756983

527284

808177

966164

657671

798687

717972

876892

935057

959298

STAT 3308

17








Key5|2 = 52

STAT 3308

18

Example 2-9




88012101151

1081985630

72112311175

1075932952

1023850

1100

775825

1140

12351000750

750915

1140

96511911370

96010351280

Key6|30 = 630

STAT 3308

Example 2-10





19

Example 2-11



24 Dotplots





34 21 49 37 23 22 33 23 21 20 19

33 23 38 32 31 22 20 24 27 33 19

23 21 31 31 22 20 34 21 33 27 21


20






14



Hands-on Example

Data set Road race



Cell reference




15



Frequency Curves




16

Truncating Axes







test



756983

527284

808177

966164

657671

798687

717972

876892

935057

959298

STAT 3308

17








Key5|2 = 52

STAT 3308

18

Example 2-9




88012101151

1081985630

72112311175

1075932952

1023850

1100

775825

1140

12351000750

750915

1140

96511911370

96010351280

Key6|30 = 630

STAT 3308

Example 2-10





19

Example 2-11



24 Dotplots





34 21 49 37 23 22 33 23 21 20 19

33 23 38 32 31 22 20 24 27 33 19

23 21 31 31 22 20 34 21 33 27 21


20






15



Frequency Curves




16

Truncating Axes







test



756983

527284

808177

966164

657671

798687

717972

876892

935057

959298

STAT 3308

17








Key5|2 = 52

STAT 3308

18

Example 2-9




88012101151

1081985630

72112311175

1075932952

1023850

1100

775825

1140

12351000750

750915

1140

96511911370

96010351280

Key6|30 = 630

STAT 3308

Example 2-10





19

Example 2-11



24 Dotplots





34 21 49 37 23 22 33 23 21 20 19

33 23 38 32 31 22 20 24 27 33 19

23 21 31 31 22 20 34 21 33 27 21


20






16

Truncating Axes







test



756983

527284

808177

966164

657671

798687

717972

876892

935057

959298

STAT 3308

17








Key5|2 = 52

STAT 3308

18

Example 2-9




88012101151

1081985630

72112311175

1075932952

1023850

1100

775825

1140

12351000750

750915

1140

96511911370

96010351280

Key6|30 = 630

STAT 3308

Example 2-10





19

Example 2-11



24 Dotplots





34 21 49 37 23 22 33 23 21 20 19

33 23 38 32 31 22 20 24 27 33 19

23 21 31 31 22 20 34 21 33 27 21


20






17








Key5|2 = 52

STAT 3308

18

Example 2-9




88012101151

1081985630

72112311175

1075932952

1023850

1100

775825

1140

12351000750

750915

1140

96511911370

96010351280

Key6|30 = 630

STAT 3308

Example 2-10





19

Example 2-11



24 Dotplots





34 21 49 37 23 22 33 23 21 20 19

33 23 38 32 31 22 20 24 27 33 19

23 21 31 31 22 20 34 21 33 27 21


20






18

Example 2-9




88012101151

1081985630

72112311175

1075932952

1023850

1100

775825

1140

12351000750

750915

1140

96511911370

96010351280

Key6|30 = 630

STAT 3308

Example 2-10





19

Example 2-11



24 Dotplots





34 21 49 37 23 22 33 23 21 20 19

33 23 38 32 31 22 20 24 27 33 19

23 21 31 31 22 20 34 21 33 27 21


20






19

Example 2-11



24 Dotplots





34 21 49 37 23 22 33 23 21 20 19

33 23 38 32 31 22 20 24 27 33 19

23 21 31 31 22 20 34 21 33 27 21


20






20






chapter 2 organizing and graphing data - …math.uhcl.edu/li/teach/stat3308/ch02_9e.pdf3 worries...

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