A histogram is a special type of bar chart, used predominantly for continuous variables. The key difference between a histogram and a bar chart, is that the frequency in a bar chart is represented by the height of the bar, whereas for a histogram, the frequency is represented by the area of the bar. The example below will demonstrate why this should be a benefit.

A distribution of heights

The heights of a class of 30 students were recorded, and a bar chart plotted. As you would expect, most heights were concentrated around the average, so in order to make the process easier a larger range of heights were grouped at the extremes

A normal bar graph of these results would look like

Does this give a fair impression of the distribution of the heights?

No! Looking at this chart, you would not know that the students were spread more thinly at the extreme heights. If anything, your eye would be more drawn to these bars, on account of their greater area. 

To get around this problem, we draw a chart were the frequency is represented by the area of a bar. This means that we need to rescale the y-axis, to the frequency density. To calculate this, you just divide the frequency by the width of the group.

The resulting histogram looks like

It is now clear that the heights were bunched around the average value.

A Second Example

The results of a maths test, conducted throughout a whole school, are given below.

To draw a histogram of this data, we must first add the frequency density to the table. To make this clearer, I will also add the group width.

The histogram will therefore be

Again, the graph clearly shows that the results are clustered around the average.

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