# Histograms

## What are Histograms?

A histogram is a graph that is made up of vertical lines of equal bases centred at the class midpoints. It is similar to bar charts. However, in bar charts, all bars are the same width in the bar and the height shows the difference. The area of the bases is important in a histogram, as with the vertical bars in the histogram.The histogram is used for continuous group data.

When drawing a histogram, the y-axis is labelled ‘relative frequency’ or ‘frequency density’. You must work out the relative frequency before you can draw a histogram. To do this, first you must choose a standard width of the groups. Some of the heights are grouped into 2s (0-2, 2-4, 6-8) and some into 1s (4-5, 5-6). Most are 2s, so we shall call the standard width 2. To make the areas match, we must double the values for frequency which have a class division of 1 (since 1 is half of 2). Therefore the figures in the 4-5 and the 5-6 columns must be doubled. If any of the class divisions were 4 (for example if there was a 8-12 group), these figures would be halved. This is because the area of this ‘bar’ will be twice the standard width of 2 unless we half the frequency.

How to Make a Histogram
a. Check if the range of the groups or classes is the same.
b. x-axis or the vertical line is the frequency.
c. y-axis or the horizontal line is the lower value of each interval to the lower value of the next interval.
d. The height of each bar corresponds to the interval.
The distribution of the data is shown at the below.
Example:

The distribution of the data is shown below.

Observing the graph, the intervals are the same because the frequency is in the vertical line of the y-axis. The area in a histogram represents frequency.

Unequal Class Interval
Where the class interval is not equal, frequency density is used to get the area of the bar so that it is proportional to the frequency.
Frequency density = frequency ÷ class width
Area = frequency = Frequency density x class width
Example:
The table shows the height of the plant in cm of Steven’s garden.

To represent it by diagram, we have this example. The x-axis is the height of the plants and y-axis is the frequency density.

Note:
In a bar chart, the height of the bar represents the frequency. In a histogram, the area shows the frequencies.