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Chapter 2: Q22 (page 50)

Cumulative Frequency Distributions. In Exercises 21 and 22, construct the cumulative frequency distribution that corresponds to the frequency distribution in the exercise indicated.

Exercise 6 (Age of Best Actor When Oscar Was Won)

Short Answer

Expert verified

The cumulative frequency distribution is constructed as follows:

Age (in years)

Cumulative Frequency

Less than 30

1

Less than 40

29

Less than 50

65

Less than 60

80

Less than 70

86

Less than 80

87

Step by step solution

01

Given information

The grouped frequency distribution of the ages (in years) of the best actors when the Oscar was won is given.

02

Define cumulative frequency

Thecumulative frequency distribution is obtained by adding the frequencies of successive classes. It represents the sum of all frequencies of a class interval equal to and less than it.

03

Calculation

The table below shows the frequencies of ages (in years) of the best actor when Oscar was won:

Age (in years)

Frequency

20-29

1

30-39

28

40-49

36

50-59

15

60-69

6

70-79

1

To construct the cumulative frequency distribution, the first class interval should be changed to less than the lower limit of the second class interval; the second class interval should be changed to less than the lower limit of the third class interval, and so on.

Also, the cumulative frequency for each class is obtained by adding the frequencies of successive classes.

The cumulative frequencies are obtained as shown below:

Age (in years)

Frequency

Cumulative Frequency

Less than 30

1

1

Less than 40

28

28 + 1 = 29

Less than 50

36

36 + 29 = 65

Less than 60

15

15 + 65 = 80

Less than 70

6

6 + 80 = 86

Less than 80

1

1 + 86 = 87

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