# Frequency Density and Histograms. How to Calculate Frequensity Density (F.d)

Learn how to calculate the frequency density by dividing the frequency by the group width.

A histogram is usually drawn when you have continuous data and the groups in the frequency table are of unequal size. To draw a histogram you will need to work out the frequency density. The frequency density can be calculated by using the following formula:

**Frequency density = frequency ÷ class width**

The class width is basically the width of the group.

The frequency density goes up the y-axis, and the area of each bar will represent the frequency.

Let’s look at a couple of examples on working out the frequency densities.

**Example 1**

Here is a frequency table on the weight of 17 people. Calculate the frequency densities needed to draw a histogram.

First, work out the frequency density for the 60kg up to 70kg group. The class width here is 10.

Frequency density = 11 ÷ 10 = 1.1

Next, work out the frequency density for the 70kg up to 75kg group. The class width here is 5.

Frequency density = 1 ÷ 5 = 0.2

Finally, work out the frequency density for the 75kg up to 95kg group. The class width here is 20.

Frequency density = 5 ÷ 20 = 0.25

So the frequency densities are 1.1, 0.2 and 0.25.

**Example 2**

Here is another frequency table this time on the heights of a group of people. Calculate the frequency densities needed to draw a histogram.

First, work out the frequency density for the 140cm up to 160cm group. The class width here is 20.

Frequency density = 60 ÷ 20 = 3

Next, work out the frequency density for the 160cm up to 170cm group. The class width here is 10.

Frequency density = 18 ÷ 10 = 1.8

Finally, work out the frequency density for the 170cm up to 200cm group. The class width here is 30.

Frequency density = 45 ÷ 30 = 1.5

So the frequency densities are 1.1, 0.2 and 0.25.

**Summary**

Frequency density = frequency ÷ class width.

Just make sure that you divide the numbers in the correct order!

Liked it

On April 7, 2011 at 3:40 am

it was really helpfull , was explianed really well.

thanks,

amina

On February 24, 2012 at 10:58 am

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On April 3, 2012 at 11:03 am

tinotenda

On February 4, 2013 at 4:29 am

very useful to me