Frequency density
A histogram is drawn like a bar chart, but often has bars of unequal width. It is the area of the bar that tells us the frequency in a histogram, not its height.
Example
Look at the following table:
In order to draw a histogram to represent this data, we need to find the frequency density for each group.
If we look at the first group, we can see it has a frequency of 4 and a width of 20, because 20 - 0 = 20.
\(\text{Frequency density = frequency ÷ group width}\)
= 4 ÷ 20
= 0.2
So we need to draw a bar which goes from 0 to 20 on the \(\text{x}\)-axis and up to 0.2 on the \(\text{y}\)–axis.
Looking at the second group, we have a frequency of 9 and a width of 15.
\(\text{Frequency density = frequency ÷ group width}\)
= 9 ÷ 15
= 0.6
So we need to draw a bar which goes from 20 to 35 on the \(\text{x}\)-axis and up to 0.6 on the \(\text{y}\)–axis.
Calculating similarly for the remaining groups we get:
Plotting this data, our histogram will look like this:
Question
Draw a histogram for the following data:
First we must calculate the frequency density for each group by dividing the frequency by the group width.
We can now draw our histogram: