Ch. 4 Describing the Relation between Two Variables
4.1 Scatter Diagrams and Correlation
1 Draw and Interpret Scatter Diagrams
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Construct a scatter diagram for the data.
1) The data below are the final exam scores of 10 randomly selected history students and the number of hours
they studied for the exam.
Hours, x 3 5 2 8 2 4 4 5 6 3
Scores, y 65 80 60 88 66 78 85 90 90 71
y
x
2) The data below are the temperatures on randomly chosen days during a summer class and the number of
absences on those days.
Temperature, x 72 85 91 90 88 98 75 100 80
Number of absences, y 3 7 10 10 8 15 4 15 5
y
x
Page 79
Copyright © 2010 Pearson Education, Inc.
,3) The data below are the ages and systolic blood pressures (measured in millimeters of mercury) of 9 randomly
selected adults.
Age, x 38 41 45 48 51 53 57 61 65
Pressure, y 116 120 123 131 142 145 148 150 152
y
x
4) The data below are the number of absences and the final grades of 9 randomly selected students from a
literature class.
Number of absences, x 0 3 6 4 9 2 15 8 5
Final grade, y 98 86 80 82 71 92 55 76 82
y
x
Page 80
Copyright © 2010 Pearson Education, Inc.
,5) A manager wishes to determine the relationship between the number of miles (in hundreds of miles) the
managerʹs sales representatives travel per month and the amount of sales (in thousands of dollars) per month.
Miles traveled, x 2 3 10 7 8 15 3 1 11
Sales, y 31 33 78 62 65 61 48 55 120
y
x
6) In order for employees of a company to work in a foreign office, they must take a test in the language of the
country where they plan to work. The data below show the relationship between the number of years that
employees have studied a particular language and the grades they received on the proficiency exam.
Number of years, x 3 4 4 5 3 6 2 7 3
Grades on test, y 61 68 75 82 73 90 58 93 72
y
x
Page 81
Copyright © 2010 Pearson Education, Inc.
, 7) In an area of the Great Plains, records were kept on the relationship between the rainfall (in inches) and the
yield of wheat (bushels per acre).
Rainfall (in inches), x 10.5 8.8 13.4 12.5 18.8 10.3 7.0 15.6 16.0
Yield (bushels per acre), y 50.5 46.2 58.8 59.0 82.4 49.2 31.9 76.0 78.8
y
x
8) Five brands of cigarettes were tested for the amounts of tar and nicotine they contained. All measurements are
in milligrams per cigarette.
y
Cigarette Tar Nicotine
Brand A 16 1.2
Brand B 13 1.1
Brand C 16 1.3
Brand D 18 1.4
Brand E 6 0.6
x
9) The scores of nine members of a local community college womenʹs golf team in two rounds of tournament play
are listed below.
Player 1 2 3 4 5 6 7 8 9
Round 1 85 90 87 78 92 85 79 93 86
Round 2 90 87 85 84 86 78 77 91 82
y
x
Page 82
Copyright © 2010 Pearson Education, Inc.
4.1 Scatter Diagrams and Correlation
1 Draw and Interpret Scatter Diagrams
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Construct a scatter diagram for the data.
1) The data below are the final exam scores of 10 randomly selected history students and the number of hours
they studied for the exam.
Hours, x 3 5 2 8 2 4 4 5 6 3
Scores, y 65 80 60 88 66 78 85 90 90 71
y
x
2) The data below are the temperatures on randomly chosen days during a summer class and the number of
absences on those days.
Temperature, x 72 85 91 90 88 98 75 100 80
Number of absences, y 3 7 10 10 8 15 4 15 5
y
x
Page 79
Copyright © 2010 Pearson Education, Inc.
,3) The data below are the ages and systolic blood pressures (measured in millimeters of mercury) of 9 randomly
selected adults.
Age, x 38 41 45 48 51 53 57 61 65
Pressure, y 116 120 123 131 142 145 148 150 152
y
x
4) The data below are the number of absences and the final grades of 9 randomly selected students from a
literature class.
Number of absences, x 0 3 6 4 9 2 15 8 5
Final grade, y 98 86 80 82 71 92 55 76 82
y
x
Page 80
Copyright © 2010 Pearson Education, Inc.
,5) A manager wishes to determine the relationship between the number of miles (in hundreds of miles) the
managerʹs sales representatives travel per month and the amount of sales (in thousands of dollars) per month.
Miles traveled, x 2 3 10 7 8 15 3 1 11
Sales, y 31 33 78 62 65 61 48 55 120
y
x
6) In order for employees of a company to work in a foreign office, they must take a test in the language of the
country where they plan to work. The data below show the relationship between the number of years that
employees have studied a particular language and the grades they received on the proficiency exam.
Number of years, x 3 4 4 5 3 6 2 7 3
Grades on test, y 61 68 75 82 73 90 58 93 72
y
x
Page 81
Copyright © 2010 Pearson Education, Inc.
, 7) In an area of the Great Plains, records were kept on the relationship between the rainfall (in inches) and the
yield of wheat (bushels per acre).
Rainfall (in inches), x 10.5 8.8 13.4 12.5 18.8 10.3 7.0 15.6 16.0
Yield (bushels per acre), y 50.5 46.2 58.8 59.0 82.4 49.2 31.9 76.0 78.8
y
x
8) Five brands of cigarettes were tested for the amounts of tar and nicotine they contained. All measurements are
in milligrams per cigarette.
y
Cigarette Tar Nicotine
Brand A 16 1.2
Brand B 13 1.1
Brand C 16 1.3
Brand D 18 1.4
Brand E 6 0.6
x
9) The scores of nine members of a local community college womenʹs golf team in two rounds of tournament play
are listed below.
Player 1 2 3 4 5 6 7 8 9
Round 1 85 90 87 78 92 85 79 93 86
Round 2 90 87 85 84 86 78 77 91 82
y
x
Page 82
Copyright © 2010 Pearson Education, Inc.
