Numeracy, Maths and Statistics - Academic Skills Kit

Histograms

ContentsToggle Main Menu 1 Definition 2 Worked Example 3 Video Example 4 Workbook 5 Test Yourself 6 External Resources

Definition

A histogram is a graphical representation of discrete or continuous data. The area of a bar in a histogram is equal to the frequency. The $y$ -axis is plotted by frequency density (which is proportional to the frequency) and the $x$ -axis is plotted with the range of values divided into intervals.

A histogram can only be used to plot numerical values and it is usually used for large data sets. It is useful for detecting outliers and/or gaps in the data set.

Worked Example

Construct a histogram of the following marks in a maths test where the maximum possible mark is 20. $2,\ 4,\ 14,\ 14,\ 16,\ 17,\ 13,\ 16,\ 7,$ $8,\ 9,\ 10,\ 11,\ 19,\ 18,\ 15,\ 15,\ 16,$ $13,\ 12,\ 7,\ 8,\ 9,\ 12,\ 11,\ 18.$

Solution

Firstly order your data so it will make it easier to group.

$2,\ 4,\ 7,\ 7,\ 8,\ 8,\ 9,\ 9,\ 10,\ 11,$ $11,\ 12,\ 12,\ 13,\ 13,\ 14,\ 14,\ 15,\ 15,\ 16,$ $16,\ 16,\ 17,\ 18,\ 18,\ 19.$

Next, look at your data and find the minimum and maximum values and choose a sensible class width. The minimum value is $2$ and the maximum value is $19$ , a sensible class width would be anywhere between $3$ and $5$ ; for this example you might choose $4$ . Your class intervals will be $0-4$ , $5-8$ , $9-12$ , $13-16$ and $17-20$ .