Box plots
A A box plot is used to display information about the range, the median and the quartiles. is used to display information about the Range is the difference between the highest and lowest values in a set of data., the median and the The collective term for the lower quartile and upper quartile of a set of data..
The information required to be able to draw a box plot is called the 'five-figure summary'.
The five-figure summary includes:
- Lowest Value (L)
- Lower Quartile (Q1)
- Median (Q2)
- Upper Quartile (Q3)
- Highest Value (H)
A box plot is usually drawn alongside a number line, as shown:
Example
The oldest person in Mathsminster is 90. The youngest person is 15.
The median age of the residents is 44, the lower quartile is 25, and the upper quartile is 67.
Represent this information with a box-and-whisker plot.
Solution
Now try the example question below.
Question
The percentages of Mrs Galbraith's English class test results are shown below:
16, 76, 100, 27, 48, 89, 92, 74, 53, 44, 36
Make a five figure summary and use this to draw a box plot for the results shown above.
We need to put the results in order first:
Five-Figure Summary:
- L = 16
- Q1 = 36
- Q2 = 53
- Q3 = 89
- H = 100
The box plot looks like this:
Comparing distributions
We have already drawn a box plot for Mrs Galbraith's English test results.
Shown below is a box plot displaying the results of Mr Wilson鈥檚 Maths test results.
Question
Make two comparisons.
The median for Mr Wilson's results is higher than the median for Mrs Galbraith's results. This tells us that, on average, Mr Wilson's class performed better in the test in Maths than Mrs Galbraith's class in English.
The pupils in Mrs Galbraith's class must be more varied in levels of ability since the results are more spread out than Mr Wilson's results.