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 width may not be equal.
The frequency density gives the ratio of the frequency of a class to its width. Frequency density is used to plot a frequency density histogram; here, you plot frequency density instead of frequency on the y-axis. Frequency density gives you the total area of bars and tells you about the frequency in the histogram (rather than the height).
You can calculate frequency density when you have a set of grouped data that consists of unequal widths of class intervals. For example, see the following Excel worksheet in Figure 22, which shows information about the ages of a group of people playing football.
To calculate the frequency densities:
- In Column C, find the class 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.
In the activity below, you will test your knowledge of the difference between a frequency density histogram and a frequency histogram.
Activity 7 The difference between frequency histograms and frequency density histograms
Timing: Allow approximately 15 minutes to complete this activity
Watch the video below and note down in the box the difference between frequency histograms and frequency density histograms.
Download this video clip.Video player: Video 3
Transcript: Video 3
NARRATOR
Difference between histograms. In this video, we will discuss the following topics-- what we mean by frequency density, how we calculate frequency density and construct the frequency density histogram, what is the difference between the frequency histogram and the frequency density histogram.
Let's first have a look at what frequency density is. Frequency density is defined as the frequency per unit of the data in each class. Frequency density gives us the ratio of the frequency of a class to its width. Frequency density is used to plot the histogram. And it allows for a meaningful comparison of different classes where the class width may not be equal.
So how is frequency density calculated? Frequency density is calculated by dividing the frequency with the class width. We calculate frequency density when we have a set of group data that consists of an unequal width of class intervals.
Let's have a look at this worksheet for an example. This Excel sheet consists of information relating to the age of people playing football. The spreadsheet consists of four columns. Column A shows the age range of the people playing football in distinct groups. Column B shows the frequency. Column C is labeled as class width. And column D is labeled as frequency density.
To calculate the frequency density of each class interval or group, first, you should determine the class width of each group. In column C, we can find the class width of the class intervals or groups by determining the difference of upper and lower bounds, also called limits. For example, in column C on the first row, type equals 10 minus 0 equals 10, equals 15 minus 10 equals 5, and so on.
Then in column D, you will calculate the frequency density by using the formula for frequency density, which is the frequency of each class interval or group divided by its width. For example, on the first row of column D, we divide the frequency of the first class interval or group, which is 10 by its class width, which is also 10, so equals 10 divided by 10 equals 1, which is the frequency density of the first class interval or group.
You can calculate the frequency density of the rest of the groups in the same way. And we get nine divided by five equals 1.8. 18 divided by 35 equals 0.5. 7 divided by 10 equals 0.7. And 5 divided by 10 equals 0.5.
Once you calculate the frequency density of each group, you will be able to construct the frequency density histogram. As we said earlier, frequency density is used to plot the histogram and allows for a meaningful comparison of different classes where the class width may not be equal.
Here you can see that we plot the frequency density on the vertical y-axis and the class interval or group, which in this case is the age range of the people playing football, on the horizontal x-axis.
The height of each bar shows the frequency density of each group. You will also see that the bar of range 15 to 50 is wider than the bar of range 0 to 10. In the frequency density histogram, the frequency of each group is equal to the area of each class. And it can be calculated by multiplying the class width by the frequency density.
So the frequency is equal to the area of the class, which is equal to the class width multiplied by the frequency density.
Let's now have a look at what the difference between the frequency histogram and frequency density histogram is.
Here, we have a frequency histogram and frequency density histogram and their corresponding frequency tables. In each case, we are measuring quantitative data that is continuous. This here is the frequency histogram. And you will notice that the bars or groups consist of a range of quantitative data values that are equally spaced out, whereas in the case of the frequency density histogram, which is this histogram here, the bars or groups of each range of quantitative data values are not equally spaced out.
This is not always the case as you can have a frequency density histogram which has equally spaced out bars or columns. In both the cases of the frequency histogram and the frequency density histogram, the bars are connected with each other. And there are no spaces between the bars.
Another distinction between the frequency histogram and the frequency density histogram is that in the case of the frequency histogram, the height of the bars corresponds to the frequencies, whereas in the case of the frequency density histogram, the height of the bars corresponds to the frequency density. The order or sequence of the bars cannot be changed again. For example, once you determine the class intervals or groups, then you cannot change their orders.
Video 3
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Interactive feature not available in single page view (see it in standard view).