7-9 Scatter Plots

Course 2

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Warm UpWhich of the following pairs do you think have a cause-and-effect relationship?

1. height and age2. hand span and address3. grade average and shoe size4. temperature and date

Course 2

7-9 Scatter Plots

yesno

noyes

Problem of the Day

From the pizza shop, James walks 12 blocks south, 22 blocks east, 18 blocks north, and 30 blocks west. What is the least number of blocks that he must travel if he returns to the pizza shop?

Course 2

7-9 Scatter Plots

14

Learn to display and analyze data in scatter plots.

Course 2

7-9 Scatter Plots

Vocabularyscatter plotpositive correlationnegative correlationno correlation

Course 2

7-9 Scatter Plots

To find out if two sets of data may be related, you can make a scatter plot of the data values in each set.

A scatter plot has two number lines, called axes—one for each set of data values.

Each point on the scatter plot represents a pair of data values. These points may appear to be scattered or may cluster in the shape of a line or a curve.

Course 2

7-9 Scatter Plots

Use the data to make a scatter plot. Describe the relationship between the data sets.

Additional Example 1: Making a Scatter Plot

Course 2

7-9 Scatter Plots

Type U.S. Only Rest of World

Mammals 63 251

Birds 78 175

Reptiles 14 64

Amphibians 10 8

Fishes 70 11

Clams 61 2

Number of Endangered Species

Step 1: Determine the scale and interval for each axis. Place the number of animals endangered in the U.S. on the horizontal axis and the number of animals endangered in the rest of the world on the vertical axis.

0 20 40 60 80

300 240

180

120 60 0

Additional Example 1 Continued

Course 2

7-9 Scatter Plots

Type U.S. Only Rest of World

Mammals 63 251

Birds 78 175

Reptiles 14 64

Amphibians 10 8

Fishes 70 11

Clams 61 2

Number of Endangered Species

Step 2: Plot a point for each pair of values.

0 20 40 60 80

300 240

180

120 60 0

Use the data to make a scatter plot. Describe the relationship between the data sets.

Additional Example 1 Continued

Course 2

7-9 Scatter Plots

Type U.S. Only Rest of World

Mammals 63 251

Birds 78 175

Reptiles 14 64

Amphibians 10 8

Fishes 70 11

Clams 61 2

Number of Endangered Species

Step 3: Label the axes and give the graph a title.

0 20 40 60 80

300 240

180

120 60 0

U.S.

Rest

of

Worl

d

Number of Endangered Species

Use the data to make a scatter plot. Describe the relationship between the data sets.

Additional Example 1 Continued

Course 2

7-9 Scatter Plots

Type U.S. Only Rest of World

Mammals 63 251

Birds 78 175

Reptiles 14 64

Amphibians 10 8

Fishes 70 11

Clams 61 2

Number of Endangered Species

There appears to be no relationship between the data sets.

0 20 40 60 80

300 240

180

120 60 0

U.S.

Rest

of

Worl

d

Number of Endangered Species

Check It Out: Example 1

Course 2

7-9 Scatter Plots

Step 1: Determine the scale and interval for each axis. Place the year on the horizontal axis and the number of farm workers on the vertical axis.

1940 1960 1980 2000

10,000

8,000

6,000

4,000

2,000

1940 8,9951950 6,8581960 4,1321970 2,8811980 2,8181990 2,864

Number of farm workers in thousands

Year

Use the data to make a scatter plot. Describe the relationship between the data sets.

Check It Out: Example 1 Continued

Course 2

7-9 Scatter Plots

Step 2: Plot a point from each pair of values.

1940 8,9951950 6,8581960 4,1321970 2,8811980 2,8181990 2,864

Number of farm workers in thousands

Year

1940 1960 1980 2000

10,000

8,000

6,000

4,000

2,000

Check It Out: Example 1 Continued

Course 2

7-9 Scatter Plots

Step 3: Label the axes and give the graph a title.Year

Num

ber

(in t

housa

nds)

Number of Farm Workers

1940 8,9951950 6,8581960 4,1321970 2,8811980 2,8181990 2,864

Number of farm workers in thousands

Year

1940 1960 1980 2000

10,000

8,000

6,000

4,000

2,000

Check It Out: Example 1 Continued

Course 2

7-9 Scatter Plots

The number of farm workers decreased from 1940 to 1970.

1940 8,9951950 6,8581960 4,1321970 2,8811980 2,8181990 2,864

Number of farm workers in thousands

Year

Year

Num

ber

(in t

housa

nds)

Number of Farm Workers

1940 1960 1980 2000

10,000

8,000

6,000

4,000

2,000

There are three ways to describe data displayed in a scatter plot.

Course 2

7-9 Scatter Plots

Positive Correlation

The values in both data sets increase at the same time.

Negative Correlation

The values in one data set increase as the values in the other set decrease.

No Correlation

The values in both data sets show no pattern.

Write positive correlation, negative correlation, or no correlation to describe each relationship. Explain.

Additional Example 2A: Determining Relationships Between Two Sets of Data

Course 2

7-9 Scatter Plots

The graph shows that as area increases, population increases. So the graph shows a positive correlation between the data sets.

Write positive correlation, negative correlation, or no correlation to describe each relationship. Explain.

Additional Example 2B: Determining Relationships Between Two Sets of Data

Course 2

7-9 Scatter Plots

The number of vacation days is not related to height. So there would not be any correlation between these two variables.

height and number of vacation days

Write positive correlation, negative correlation, or no correlation to describe each relationship. Explain.

outdoor temperature and coat sales

Additional Example 2C: Determining Relationships Between Two Sets of Data

Course 2

7-9 Scatter Plots

As the outdoor temperature increases, the number of coat sales will decrease. So there would be a negative correlation between the data sets.

Write positive correlation, negative correlation, or no correlation to describe each relationship.

Check It Out: Example 2A

Course 2

7-9 Scatter Plots

Tornado Frequency

0

200

400

600

800

1000

1200

1940 1960 1980 2000

Year

Nu

mb

er

of

To

rna

do

s

The graph shows that as the year increases, number of tornados increases. So the graph shows a positive correlation between the data sets.

Write positive correlation, negative correlation, or no correlation to describe each relationship.

Check It Out: Example 2B

Course 2

7-9 Scatter Plots

Guitar String Frequency

200

300

400

500

600

700

40 60 80 100 120

Length of string (cm)

Fre

qu

en

cy

(vp

s)

The graph shows that as the length of string increases, frequency decreases. So the graph shows a negative correlation between the data sets.

vps = vibrations per second

Write positive correlation, negative correlation, or no correlation to describe each relationship.

Check It Out: Example 2C

Course 2

7-9 Scatter Plots

There would not be any correlation between these two variables.

eye color and age

Lesson Quiz: Part I

1. Use the data to make a scatter plot. Describe the relationship.

Course 2

7-9 Scatter Plots

Temperature Attendance

70 100

80 350

75 250

85 400

74 200

82 375

72 260

Beach Attendance

0

100

200

300

400

500

70 75 80 85

Temperature

Att

en

da

nc

e

The graph shows a positive correlation.

Lesson Quiz: Part II

2. Write positive, negative, or no correlation to describe each relationship. Explain

Course 2

7-9 Scatter Plots

negative correlation; as age increases, attendance decreases.