Histogram

In histograms, the frequency of the data is shown by the area of the bars and not just the height.

Histograms are most commonly used for continuous data.

Histograms often have bars of varying width, i.e. unequal class intervals. This is not a problem as we are dealing with area, not just the height.

The vertical axis of a histogram is labelled frequency density and is calculated by the following formula:

Example:

The ages of people sunbathing on a beach somewhere on a Greek island were recorded and organised into the frequency table below. Draw a histogram of this data.

Ages (x): Frequency (f): Class width: Frequency density:

0 ≤ x < 15 15 15 15/15 = 1

15 ≤ x < 25 28 10 28/10 = 2.8

25 ≤ x < 40 30 15 2

40 ≤ x < 60 42 20 2.1

60 ≤ x < 100 20 40 0.5

All we now need to do is draw this onto graph paper and we have our histogram.

The ages will be on the x-axis (from 0 to 100 on a continuous scale).

Frequency density will be on the y-axis (from 0 to 3).

Cumulative frequency

Cumulative frequency is kind oflike a running total. We add each frequency to the ones before to get an 'at least' total.

These cumulative frequencies ('at least' totals) are plotted against theupper class boundaries to give us a cumulative frequency curve.

The cumulative frequency column is the column you will be expected to add for yourself.

To draw the cumulative frequency curve we simply plot the cumulative frequencies against the upper end of each class interval.