2.4 Frequency density

Frequency density is defined as the frequency per unit of the data in each class. Frequency density is calculated by dividing the frequency by the class width (the class width is the difference between the upper limit of the class interval and the lower limit of the class interval). Frequency density allows for a meaningful comparison of different classes where the class widths may not be equal.

The frequency density gives us the ratio of the frequency of a class to its width. Frequency density is used to plot a frequency density histogram; here, we plot frequency density instead of frequency on the y-axis. Frequency density gives us the total area of bars and tells us about the frequency in the histogram (rather than the height).

We calculate frequency density when we have a set of grouped data that consists of unequal widths of class intervals. For example, see the following Excel worksheet, which gives us information about the ages of people playing cricket.

To calculate the frequency densities:

• In Column C, find the width of the class intervals by finding the difference of upper and lower bounds/limits. (For example, and so on.)

• Then, in Column D, divide the frequency of each class interval by its width following the Frequency density formula given above. Even though the frequency in the first age bracket is higher, because the interval is twice as large as in the second age bracket, it could be misleading. From looking at the frequency density column, we can see that cricket is most popular in the 10-15 age category, with a frequency density of 1.8.

In the activity below, you will test your knowledge of the difference between a frequency density histogram and a frequency histogram.