Box Plots
Box plots are used to summarise and compare distributions. They show the spread of the data and where the middle values are.
A box plot shows five key values:
minimum, lower quartile, median, upper quartile and maximum.
The five-number summary
To draw or read a box plot, you need to understand the five-number summary.
Minimum: smallest value
Lower quartile: one quarter of the data is below this
Median: middle value
Upper quartile: three quarters of the data is below this
Maximum: largest value
Example 1: Identify values from a box plot
A box plot has these values:
Minimum = 8
Lower quartile = 12
Median = 18
Upper quartile = 25
Maximum = 31
These values tell us about the centre and spread of the data.
Range and interquartile range
The range measures the spread of the whole data set. The interquartile range measures the spread of the middle 50% of the data.
Range = maximum − minimum
Interquartile range = upper quartile − lower quartile
Example 2: Find range and interquartile range
Use these values:
Minimum = 8
Lower quartile = 12
Upper quartile = 25
Maximum = 31
Range = 31 − 8 = 23
Interquartile range = 25 − 12 = 13
Drawing a box plot
To draw a box plot, mark the five-number summary on a number line.
Draw a box from the lower quartile to the upper quartile.
Draw a line inside the box for the median.
Draw whiskers from the box to the minimum and maximum.
Example 3: Describe how to draw the box
If the lower quartile is 20 and the upper quartile is 35, the box starts at 20 and ends at 35.
If the median is 28, draw a vertical line inside the box at 28.
Comparing box plots
GCSE questions often ask you to compare two box plots. You should compare both average and spread.
Example 4: Compare two box plots
Class A has median 62 and interquartile range 14.
Class B has median 58 and interquartile range 9.
Class A has a higher median, so its typical score is higher.
Class B has a smaller interquartile range, so its scores are more consistent in the middle 50%.
A common mistake is comparing only the medians. In exam questions, also compare spread using the range or interquartile range.
When comparing box plots, use values from the graph. For example: “Class A has a median of 62, which is 4 marks higher than Class B.”
Video explanation
A short Worthing Maths Tutor video explanation for box plots can be embedded here later to improve student engagement and time on page.
Practice questions
- A box plot has minimum 5 and maximum 27. Find the range.
- A box plot has lower quartile 14 and upper quartile 31. Find the interquartile range.
- A data set has minimum 10, lower quartile 18, median 24, upper quartile 35 and maximum 42. Where does the box start and end?
- Which value represents the middle of the data on a box plot?
- Two classes have medians 68 and 61. Which class has the higher typical score?
Answers
- 22
- 17
- The box starts at 18 and ends at 35.
- The median
- The class with median 68
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