Construction of Frequency Distribution

Consider the participants running in a marathon. Suppose one wonders how the number of participants varies with age. In order to find out, the data are summarized using a frequency distribution table, which is constructed using six steps.

First, select the number of classes, anywhere between 5 and 20, depending on the data density. Here, let the number of classes be five.

Subtract the smallest from the largest number to determine the range. Dividing this range by the number of classes yields the class width—the range of values per class, which is rounded up for convenience.

The minimum value of the given data is called the first lower-class limit.

To this value, add the class width to determine the second lower-class limit. Similarly, calculate the subsequent lower-class limits.

Next, subtract one from the second lower-class limit to calculate the first upper-class limit. Likewise, calculate the remaining upper-class limits.

In a second column, place tally marks for the participants under each class. The sum of all tally marks gives the frequency of each class.