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Chapter 2: Q21 (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 5 (Age of Best Actress When Oscar Was Won)

Short Answer

Expert verified

The cumulative frequency distribution is constructed as follows:

Age (in years)

Cumulative Frequency

Less than 30

29

Less than 40

63

Less than 50

77

Less than 60

80

Less than 70

85

Less than 80

86

Less than 90

87

Step by step solution

01

Given information

Thegrouped frequency distribution of the ages (in years) of the best actress when the Oscar was won is given.

02

Cumulative frequency

The cumulative 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 actress when Oscar was won:

Age (in years)

Frequency

20-29

29

30-39

34

40-49

14

50-59

3

60-69

5

70-79

1

80-89

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.

The cumulative frequencies corresponding to the classes are obtained as shown below:

Age (in years)

Frequency

Cumulative Frequency

Less than 30

29

29

Less than 40

34

34 + 29 = 63

Less than 50

14

14 + 63 = 77

Less than 60

3

3 + 77 = 80

Less than 70

5

5 + 80 = 85

Less than 80

1

1 + 85 = 86

Less than 90

1

1 + 86 = 87

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