Question

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

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

Given information

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

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.

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