data & graphs

11CONFIDENTIALCONFIDENTIAL

Data & GraphsData & Graphs

ReviewReview

CONFIDENTIALCONFIDENTIAL 22

Frequency TablesFrequency Tables

• Statistics involves collecting, organizing, analyzing, and presenting data.

• Data are pieces of information that are often numerical.• A frequency table shows the number of pieces of data

that fall within given intervals.


Make a Frequency TableMake a Frequency Table

• Example: The number of points scored by major league soccer teams in a recent season is shown.

Major League Soccer Points Scored

53 26 35 45

42 53 14 36

27 45 47 23



• Step 1: Choose an appropriate scale and interval for the data• Scale: 1 to 60

• Interval:15 The scale includes all of the data, the least number and the greatest

The interval separates the scale into equal parts.



• Step 2: Draw a table with three columns and label the columns Points, Tally, and Frequency

• Step 3: In the first column, list the intervals. In the second column, tally the data. In the third column, add the tallies.

Major League Soccer Points Scored, 2001 season

Points Tally Frequency

1-15 I 1

16-30 III 3

31-45 IIII 5

46-60 III 3

Some frequency tables may not have scales and intervals



• Make a frequency table of the data shown in the table.

Surprise Quiz Scores

99 83 92 52 75

100100 65 80 85

101 80 75 85 85

70 75 90 95 75

Your Turn


Line GraphsLine Graphs• A line graph is used to show how a set of data changes over a

period of time.

U.S.Wooden Roller Coasters

0102030405060708090

1925 1950 1975 2000

Year

Num

ber

of C

oast

ers

The scale and interval are also shown on the vertical axis.

A line graph also has titles and labels

The categories are written on the horizontal axis.

Each frequency is shown using a point.


Make & Interpret a Line GraphMake & Interpret a Line Graph

• Example: Make a line graph of the data at the left. Then describe the change in the number of tornadoes from 2001 to 2003.

• Step 1; Decide on the scale and the interval. The data includes numbers from 941 to 1,424. The scale is 900 to 1,500 and the interval is 100.

U.S.Tornadoes

Year Tornadoes

1998 1,424

1999 1,343

2000 1,071

2001 1,216

2002 941

2003 1,246



• Step 2: Label the horizontal and vertical axes.

• Step 3: Draw and connect the points for each year. Each point shows the number of tornadoes in that year.

• Step 4: Label the graph with a title.

The number of tornadoes decreased from 2001 to 2002 and then increased from 2002 to 2003.

U.S. Tornadoes, 1998-2003

0200400600800

1,0001,2001,4001,600

Year

Tor

nado

es



Your Turn

• Make a line graph of the data. Then describe the change from 1960 to 1995.

U.S. Water Consumption

Year Water consumed per day (billion gallons)

1960 61

1965 77

1970 87

1975 96

1980 100

1985 92

1990 94

1995 100


Bar GraphsBar Graphs• A bar graph is used to compare data.

0

50

100

1st Qtr 2nd Qtr 3rd Qtr 4th QtrRev

enue

$ m

illio

ns

Time

Sales of toysThe scale is written on the vertical axis

On this scale, the interval is 50

The categories are written on the horizontal axis.

The height of each bar represents the frequency

The title and label describe the data


Make & Interpret a Bar GraphMake & Interpret a Bar Graph

• Example: Make a vertical bar graph of the data. Compare the number of students who scored a B to the number who scored a C.

• Step 1: Decide on the scale and interval. The data includes numbers from 2 to 13. So, a scale from 0 to 14 and an interval of 2 is reasonable.

Math Scores

Grade Frequency

A 10

B 13

C 7

D 2



• Step 2: Label the horizontal and vertical axes.

• Step 3: Draw bars for each grade. The height of each bar shows the number of students earning that grade.

• Step 4: Label the graph with a title.

About twice as many students scored a B than a C.

Student's Math Scores

0

2

4

6

8

10

12

14

A B C D

Grade

Stu

den

ts



• Make a vertical bar graph of the data. Compare the time it takes for a rabbit to be born to the time it takes for a camel to be born.

Your Turn

Gestation of selected animals

Animals Gestation period (days)

Squirrel 44

Rabbit 31

Puma 90

Moose 240

Kangaroo 36

camel 406


Circle GraphsCircle Graphs

Driving Together in One Vehicle to Spring

Break

1-3, 11%

4-5, 35%

6-7, 29%

8-9, 11%

10 or more, 14%

• A circle graph is used to compare parts of a whole.

• Analyze data by comparing the size of the sections of the circle.

• One can compare the percents to analyze the data as well.

The pie-shaped sections show the groups.

The percents add up to 100%

The interior of the circle represents a set of data.


Circle GraphsCircle Graphs

• The circle graph shows which method of transportation students use to get to Martin Luther King, Jr. Middle School.

1. Which method of transportation do most students use?

2. How does the number of students who ride a moped to school compare to the number of students who take the bus?

Your Turn

Method of Transportation used by students to arrive

at school

ride moped,

7%

ride bicycle,

23%

ride in car

pools, 20%

take bus, 36%

walk, 14%


Stem & Leaf PlotsStem & Leaf Plots

• In a stem-and-leaf plot, the data is ordered from least to greatest and is organized by place value.

• Step 1: Order the data from least to greatest

56 60 62 67 68 68 69 70 70 70 71 72 76 76 78 82 83 84 88 93 97

• Step 2: Draw a vertical line and write the tens digits from least to greatest to the left of the line. These digits form the stems. Since the least value is 56 and the greatest value is 97, the stems are 5, 6, 7, 8, and 9.

NCAA Division 1 Women’s Basketball Points Scored by Winning Teams, 1982-2002

76 70 56 70 60 68 71

69 97 76 78 70 93 68

72 67 88 84 83 62 82



• Step 3: Write the units digits in order to the right of the line with the corresponding stem. The units digits form the leaves.

Stem Leaf

5 6

6

7

8

9

0 2 7 8 8 9

0 0 0 1 2 6 6 8

2 3 4 8

3 7

7 6 pointskey

In this data, the tens digit forms the stem.

The ones digit of the data form the leaves.

Always write each leaf even if it repeats.



• Make a stem-and-leaf plot for the data in the table. Average July Highs (oF) for

selected European cities

69 72 71 73 76 60

81 67 78 89 74 75

74 66 79 73 88 77

Your Turn


Making Predictions & Interpreting Making Predictions & Interpreting GraphsGraphs

• Line graphs are often used to predict future events because they show trends over time.

Average Monthly Temperature

60657075808590

Month

Tem

per

atu

re (

F)

Example:You can predict the average temperature for Miami in February by the trend in the line graph.


Making Predictions & Interpreting Making Predictions & Interpreting GraphsGraphs

• The graph shows the number of participants in bowling from 1975 to 2000. What does the graph tell you about the popularity of bowling?

Bowling Participants

0

20

40

60

80

100

'75 '80 '85 '90 '95 '00

Year

Nu

mb

er o

f p

arti

cip

ants

(m

illi

on

s)

Your Turn


MeanMean

• The mean of a set of data is the sum of the data divided by the number of pieces of data.

• Example: data set : 8, 7, 9, 6, 10• Mean = 8 + 7 + 9 + 6 + 10 = 40 = 8

5 5


Determine how Outliers affect MeanDetermine how Outliers affect Mean

• A set of data may contain a value much higher or lower than the other values. This value is called outlier.

• Outliers can significantly affect the mean.• Example: data set : 80, 81, 40, 77, 82• Mean with outlier = 80 + 81 + 40 + 77 + 82 = 360 =

72

5 5

• Mean without outlier = 80 + 81 + 77 + 82 = 320 = 80

4 4


Median, Mode, and RangeMedian, Mode, and Range

• The median of a set of data is the middle number of the ordered data, or the mean of the middle two numbers.

• Examples: – data set: 3, 4, 8, 10, 12 -> median: 8

– data set: 2, 4, 6, 8, 11, 12 -> median: 6 + 8 = 7

2



• The mode of a set of data is the number or numbers that occur most often.

• Examples: – data set: 12, 23, 28, 28, 32, 46, 46 -> modes: 28 and 46



• The range of a set of data is the difference between the greatest and the least values of the set.

• Examples: – data set: 125, 45, 67, 150, 32, 12– The greatest value is 150.– The least value is 12.– So, the range is 150 – 12 or 138.



• Concept Summary

Measure Best Used to describe the data when…

Mean •The data set has no very high or low numbers.

Median •The data set has some high or low numbers and most of the data in the middle are close in value.

Mode •The data set has many identical numbers.



• What are the mean, median, mode, and range of the temperature data 640, 700, 560, 580, 600, and 700 .

Your Turn


Let us take a break!Let us take a break!


Jig-saw puzzleJig-saw puzzle

• http://www.thekidzpage.com/onlinejigsawpuzzles/jigsaw-puzzles/12-piece-jigsaw/05-04-06-kitten.html


Box & Whisker PlotsBox & Whisker Plots• A Box-and-whisker plot is a way to show how data are clustered or spread

out.• Example: The monthly mean temperatures for Burlington, Vermont, are

shown.

Monthly Normal Temperatures for Burlington, VT

Month J F M A M J J A S O N D

Temp (0F)

16 18 31 44 56 65 71 68 59 48 37 23


Box & Whisker PlotsBox & Whisker Plots

• Step 1: Write the data from least to greatest.

16 18 23 31 37 44 48 56 59 65 68 71• Step 2: Draw a number line that includes all of the data.

15 20 25 30 35 40 45 50 55 60 65 70 75

• Step 3: Mark the least and greatest as the lower extreme and upper extreme. Find and label the median.

15 20 25 30 35 40 45 50 55 60 65 70 75

Lower Extreme Upper ExtremeMedian


Box & Whisker PlotsBox & Whisker Plots• Step 4: The median of a data set separates the set in half. Find the medians of the lower

and upper halves.

16 18 23 31 37 44 48 56 59 65 68 71

15 20 25 30 35 40 45 50 55 60 65 70 75

Lower ExtremeUpper ExtremeMedian

23 + 31 = 27 2

Median59 + 65 = 62 2

• Label these values as lower quartile and upper quartile. Draw a box around the quartile values, and whiskers that extend from each quartile to the extreme data points.

Upper Quartile

Lower Quartile


Box & Whisker PlotsBox & Whisker Plots

• Draw a Box-and-whisker plot for the set of data below.

Baseball Games won by Teams in National League, 2002

95 94 79 67 65 95 85 73 72 69 65 97 86 85 82 76

Your Turn


AssessmentAssessment

1) Make a frequency table for the set of data.

Number of siblings

3 1 2 1 3 1

0 4 1 0 2 1

2 1 0 3 1 0



2) Make a line graph for the set of data.

Zoo Visitors

Year Visitors

2000 12,300

2001 13,400

2002 15,900

2003 15,100

2004 16,200



3) Name two muffins that together are preferred by half the people surveyed.

Favorite kind of Muffins

Oat Barn, 5%

Cinnamon, 10%

Banana, 40%Chocolate,

15%

Blueberry, 30%



4) Describe the trend in the winning times. Predict the winning time in 2006.

Winning Times100-m Run

01020

'98 '00 '02 '04

Year

Tim

e (

s)



5) Make a stem-and-leaf plot for the set of data.

83, 72, 95, 64, 90, 88, 78, 84, 61, 73



6) Find the mean for the set of data.

23, 34, 29, 36, 18, 22, 27



7) Find the median, mode, and range for the set of data.

21, 23, 27, 30



8) Which graph would you show to a telephone customer? Explain.

Graph ACall to Port Arthur

0

1

2

3

4

1 2 3 4 5

Length of call (min)

Co

st (

$)

Graph BCall to Port Arthur

0

0.5

1

1.5

2

2.5

3

3.5

1 2 3 4 5

Length of call (min)

Co

st (

$)


Great Job!Great Job!

See you in the Session!

data & graphs

Documents

vertical bar graph

presenting data

number of coastersthe

number of points

number of students

number of tornadoes

number of pieces

set of data changes