Box plots – Higher

A box plot shows a visual representation of the median and quartiles of a set of data.

To draw a box plot, the following information is needed:

A box plot is a visual representation of the median and quartiles of a set of data.

Drawing a box plot from a list of numbers

Box plots can be created from a list of numbers by ordering the numbers and finding the median and lower and upper quartiles.

Example

Draw a box plot for these numbers:

9, 10, 10, 12, 13, 14, 17, 18, 19, 21, 21

The numbers are already in order so the minimum and maximum numbers can be easily read off as 9 and 21, and the middle number can be read as 14.

9, 10, 10, 12, 13, 14, 17, 18, 19, 21, 21

To find the lower quartile, there are 11 numbers, so \frac{11 + 1}{4} = 3rd number. The lower quartile will be the 3rd number and the upper quartile is the 9th number.

9, 10, 10, 12, 13, 14, 17, 18, 19, 21, 21

Drawing these points onto a number line will give the following box plot.

Box plot from 10 to 19

Drawing a box plot from a cumulative frequency graph

Drawing a box plot from a cumulative frequency graph is straightforward as long as the median and quartiles have been found.

The guideline for median, lower quartile and upper quartile can be used to plot the sections of the box plot. The minimum and maximum values of the box plot are where the cumulative frequency begins and ends.

Box plot and line graph