To find out if two sets of data may be related,
you can make a scatter plot of the data
values in each set.
Scatter Plots
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.
Scatter plots shows relationships between two
sets of data.
Additional Example 1: Making a Scatter Plot
Additional Example 1 Continued
Use the data to make a scatter plot. Describe the
relationship between the data sets.
300
300
Number of Endangered Species
240
Type
U.S. Only
Mammals
63
Birds
78
Reptiles
14
Amphibians
10
Fishes
70
Clams
61
180
120
60
0
0
20
40
60
Number of Endangered Species
240
Rest of World
251
175
64
8
11
2
Type
U.S. Only
Mammals
63
Birds
78
Reptiles
14
Amphibians
10
Fishes
70
Clams
61
180
120
60
0
0
20
Number of Endangered Species
Additional Example 1 Continued
Use the data to make a scatter plot. Describe the
relationship between the data sets.
Number of Endangered Species
300
Number of Endangered Species
Type
U.S. Only
Mammals
63
Birds
78
Reptiles
14
Amphibians
10
Fishes
70
Clams
61
240
180
120
60
0
40
60
80
Step 3: Label the axes and give the graph a title.
Rest of World
251
175
64
8
11
2
Rest of World
Rest of World
300
U.S.
80
Step 2: Plot a point for each pair of values.
Additional Example 1 Continued
Use the data to make a scatter plot. Describe the
relationship between the data sets.
20
60
80
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
40
Rest of World
251
175
64
8
11
2
Number of Endangered Species
Type
U.S. Only
Mammals
63
Birds
78
Reptiles
14
Amphibians
10
Fishes
70
Clams
61
240
180
120
60
0
0
20
40
U.S.
60
Rest of World
251
175
64
8
11
2
80
There appears to be no relationship between the data
sets.
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Try This: Example 1
Try This: Example 1 Continued
Use the data to make a scatter plot. Describe the
relationship between the data sets.
Year
10,000
8,000
6,000
2,000
1940 1960
1980
2000
Number of farm
workers in
thousands
1940
1950
1960
1970
1980
1990
8,000
8,995
6,858
4,132
2,881
2,818
2,864
Step 1: Determine the scale and interval for each axis. Place the
year on the horizontal axis and the cost on the vertical axis.
6,000
2,000
1940 1960
10,000
8,000
6,000
2,000
1940 1960
1980
2000
Number of farm
workers in
thousands
1940
1950
1960
1970
1980
1990
8,995
6,858
4,132
2,881
2,818
2,864
1940
1950
1960
1970
1980
1990
8,995
6,858
4,132
2,881
2,818
2,864
1980
2000
Try This: Example 1 Continued
Number of Farm
Workers
Number (in thousands)
Number (in thousands)
Year
Number of farm
workers in
thousands
Step 2: Plot a point from each pair of values.
Try This: Example 1 Continued
Number of Farm
Workers
Year
10,000
Year
Number of farm
workers in
thousands
1940
1950
1960
1970
1980
1990
8,995
6,858
4,132
2,881
2,818
2,864
10,000
8,000
6,000
2,000
1940 1960
Year
1980
2000
Year
Step 3: Label the axes and give the graph a title.
The number of farm workers decreased from 1940 to
1970.
There are three ways to describe data displayed in a scatter plot.
Additional Example 2A: Determining Relationships
Between Two Variables
Positive Correlation Negative Correlation
No Correlation
Write positive correlation, negative correlation, or
no correlation to describe each relationship.
The values in both
data sets increase at
the same time.
The values in one
data set increase as
the values in the
other set decrease.
The values in both
data sets show no
pattern.
Population
(thousands)
Population by County
35
30
25
20
15
10
5
0
0
1000
2000
3000
4000
5000
The graph shows that
as area increases,
population increases.
So the graph shows a
positive correlation
between the data sets.
Are a (square mile s)
2
Try This: Example 2A
Additional Example 2B: Determining Relationships
Between Two Variables
Sales (millions)
Record Sales
25
20
15
10
5
0
1990
1992
1994
1996
1998
2000
Year
2002
The graph shows
that as the year
increases, sales
decrease. So the
graph shows a
negative correlation
between the data
sets.
Try This: Example 2B
Write positive correlation, negative correlation, or no
correlation to describe each relationship.
Guitar String Frequency
Freque ncy (vps)
700
600
500
400
300
200
40
60
80
100
120
The graph shows that
as the length of string
increases, frequency
decreases. So the
graph shows a
negative correlation
between the data sets.
Write positive correlation, negative correlation, or no
correlation to describe each relationship.
Tornado Frequency
Numbe r of Tornados
Write positive correlation, negative correlation, or
no correlation to describe each relationship.
1200
1000
800
600
400
200
0
1940
1960
1980
2000
The graph shows that
as the year increases,
number of tornados
increases. So the
graph shows a
positive correlation
between the data
sets.
Ye ar
Additional Example 2C: Determining Relationships
Between Two Variables
Write positive correlation, negative correlation, or
no correlation to describe each relationship.
height and number of vacation days
The number of vacation days is not related
to height. So there would not be any
correlation between these two variables.
Length of string (cm)
vps = vibrations per second
Try This: Example 2C
Additional Example 2A: Identifying the Correlation of
Data
Write positive correlation, negative correlation, or no
correlation to describe each relationship.
Do the data sets have a positive, a negative,
or no correlation?.
eye color and age
A. The size of a jar of baby food and the
number of jars of baby food a baby will eat.
There would not be any correlation between
these two variables.
Negative correlation: The more food in each jar,
the fewer number of jars of baby food a baby
will eat.
3
Additional Example 2B: Identifying the Correlation of
Data
Additional Example 2C: Identifying the Correlation of
Data
Do the data sets have a positive, a negative,
or no correlation?.
Do the data sets have a positive, a negative,
or no correlation?.
B. The speed of a runner and the number of
races she wins.
C. The size of a person and the number of
fingers he has
Positive correlation: The faster the runner, the
more races she will win.
Try This: Example 2A
No correlation: A person generally has ten
fingers regardless of their size.
Try This: Example 2B
Do the data sets have a positive, a negative,
or no correlation?.
Do the data sets have a positive, a negative,
or no correlation?.
A. The size of a car or truck and the number
of miles per gallon of gasoline it can
travel.
B. Your grade point average and the number
of A’s you receive.
Negative correlation: The larger the car or truck,
the fewer miles per gallon of gasoline it can
travel.
Positive correlation: The more A’s you
receive, the higher your grade point average.
Try This: Example 2C
Do the data sets have a positive, a negative,
or no correlation?.
C. The number of telephones using the same
phone number and the number of calls you
receive.
No correlation: No matter how many telephones
you have using the same telephone number, the
number of telephone calls received will be the
same.
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