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GROUPED FREQUENCY DISTRIBUTION EXAMPLE PROBLEMS WITH SOLUTIONS

Frequency distribution is a statistical technique used to organize and summarize data into groups or intervals. Grouped frequency distribution is a method of organizing data into intervals or classes, along with the frequency of observations falling into each interval. In this article, we will explore some example problems of grouped frequency distribution along with their solutions.

Example Problem 1:

Consider the following data set:

10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80

We want to create a grouped frequency distribution with intervals of width 10 starting from 10.

Solution:

To create a grouped frequency distribution, we first need to determine the intervals. Since the data starts from 10 and has a range of 70, we can create intervals of width 10 as follows:

10-19
20-29
30-39
40-49
50-59
60-69
70-79

Next, we count the frequency of observations falling into each interval:

10-19: 1
20-29: 2
30-39: 2
40-49: 2
50-59: 3
60-69: 3
70-79: 2

Example Problem 2:

Consider the following data set:

12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60

We want to create a grouped frequency distribution with intervals of width 5 starting from 10.

Solution:

Following the same steps as in Example Problem 1, we can create intervals of width 5 starting from 10:

10-14
15-19
20-24
25-29
30-34
35-39
40-44
45-49
50-54
55-59
60-64

Next, we count the frequency of observations falling into each interval:

10-14: 1
15-19: 2
20-24: 2
25-29: 2
30-34: 2
35-39: 2
40-44: 2
45-49: 2
50-54: 2
55-59: 2
60-64: 1

Conclusion:

Grouped frequency distribution is a useful tool for organizing and summarizing data into intervals. By following the steps outlined in the example problems above, you can create a grouped frequency distribution for your own data sets.