Histograms

The following table shows the ages of 25 children on a school bus:

 

Age	Frequency
5-10	6
11-15	15
16-17	4
> 17	0

If we are going to draw a histogram to represent the data, we first need to find the class boundaries. In this case they are 5, 11, 16 and 18. The class widths are therefore 6, 5 and 2.

The area of a histogram represents the frequency.

The areas of our bars should therefore be 6, 15 and 4.

Remember that in a bar chart the height of the bar represents the frequency. It is therefore correct to label the vertical axis 'frequency'.

However, as in a histogram, it is the area which represents the frequency.

It would therefore be incorrect to label the vertical axis 'frequency' and the label should be 'frequency density'.

So we know that Area = frequency = Frequency density x class width hence:

Frequency density = frequency ÷ class width