Box Plots
A box plot, or box-and-whisker diagram, summarises a set of data using five key values: the minimum, the lower quartile, the median, the upper quartile and the maximum. In GCSE Statistics, box plots are drawn on a scaled number line and are especially useful for comparing the spread and average of two or more data sets at a glance.
Before you start
Make sure you're comfortable with these topics first:
Method
- Find or read off the five key values needed: the minimum, lower quartile, median, upper quartile and maximum.
- Draw a scaled horizontal number line that covers the full range of the data, with a suitable scale.
- Draw a box from the lower quartile to the upper quartile, with a vertical line inside the box marking the median.
- Draw a whisker (a straight line) from each end of the box out to the minimum and maximum values.
- Label the box plot clearly, including a title and the units of the scale.
- To compare two box plots, look at where the medians sit, a measure of average, and how wide each box and whisker span is, a measure of spread.
Worked example
A data set has minimum 12, lower quartile 18, median 25, upper quartile 31 and maximum 40. Draw a box plot and state the interquartile range.
- Draw a scaled number line running from at least 12 to at least 40.
- Draw a box from 18 (lower quartile) to 31 (upper quartile).
- Draw a vertical line inside the box at 25 to mark the median.
- Draw a whisker from 18 down to 12 (the minimum) and a whisker from 31 up to 40 (the maximum).
- Find the interquartile range by subtracting the lower quartile from the upper quartile: 31 - 18 = 13.
- Final answer: the interquartile range is 13.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1Name the five values needed to draw a box plot.Show answer
Answer: Minimum, lower quartile, median, upper quartile and maximum.
Q2A box plot has lower quartile 10 and upper quartile 22. Find the interquartile range.Show answer
Answer: 12 (22 - 10 = 12).
Q3A box plot shows minimum 4 and maximum 36, with median 20. State the range of the data.Show answer
Answer: 32 (36 - 4 = 32).
Q4Box plot A has a median of 50 and box plot B has a median of 42, for the same type of data. What does this tell you about the two data sets?Show answer
Answer: Data set A typically has higher values than data set B, since its median is higher.
Q5Box plot A has an interquartile range of 8 and box plot B has an interquartile range of 15. What does this tell you about the spread of the middle 50 percent of each data set?Show answer
Answer: Data set A's middle 50 percent of values is less spread out (more consistent) than data set B's.
Q6A box plot for 40 values has lower quartile 15 and upper quartile 25. Roughly how many of the 40 values lie between 15 and 25?Show answer
Answer: About 20 values (the box always contains the middle 50 percent of the data, so 50 percent of 40 = 20).
Exam-style questions
Written in the style of a GCSE Statistics exam paper, with a full mark scheme.
A box plot for the heights, in cm, of a rugby team has minimum 165, lower quartile 172, median 178, upper quartile 184 and maximum 195. Find the interquartile range and the range of the heights.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 3 available
Box plots are drawn for the times, in minutes, taken to complete a race by Team A and Team B. Team A: minimum 30, lower quartile 34, median 38, upper quartile 44, maximum 52. Team B: minimum 28, lower quartile 32, median 46, upper quartile 50, maximum 58. Compare the two teams' race times, giving two comparisons.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 4 available
Explain one limitation of a box plot compared to looking at the original raw data.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 2 available
See real GCSE Statistics past-paper questions, with official mark schemes →
Free printable worksheet
Want more practice on paper? Download the box plots worksheet pack - 18 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 22 of GCSE Statistics Foundation Workbook 1 and chapter 26 of GCSE Statistics Higher Workbook 1, the whole course as one free printable PDF.
Next topics
Not quite what you needed?
Tell us what is missing on box plots, or which topic to write up next. Every request is read, and we reply to every one.
Build a full practice pack.
This topic is one of hundreds in the library - pick the ones a student needs and generate a printable PDF in minutes.