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Box plots – GCSE Maths Higher · Grade 6
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On this page Objectives Key points Examples Questions Mistakes Tips Worksheet Draw a box plot from the five key values and compare two data sets using the median and interquartile range. It is Higher only, aimed at grade 6. Free questions with answers are on this page. Worked examples show each line before you try the questions.
A box plot shows lowest, LQ, median, UQ, highest (and sometimes outliers). The box is the IQR; the line in the box is the median; the whiskers run to the extremes. Compare two box plots with a typical-value sentence (medians) and a spread sentence (IQR or range), in context: 'the girls generally scored higher and more consistently'.
To draw one you need those five numbers, from a list, a cf graph, or a table. Do not put the mean on a box plot. A longer whisker is skew, not 'more people' — the whisker is values, not frequency.
Five-number summary: min, LQ, median, UQ, max. IQR = UQ − LQ
Objectives Find the quartiles from a list of ordered data. Find an interquartile range from the two quartiles. Find a range from the lowest and highest values. Compare two interquartile ranges. Key points Identify the five values: minimum, lower quartile, median, upper quartile, maximum. Draw a box plot to scale from those five values or from a cumulative frequency curve. Find the quartiles of a small ordered list. Read range and IQR from a box plot. Worked examples Example 1 Lower quartile 9 and upper quartile 20. Find the interquartile range.
2 marks
Identify lower quartile LQ = 9 and upper quartile UQ = 20. Subtract lower quartile from upper quartile: 20 - 9 = 11. State the interquartile range is 11. Answer: 11
Common slips Slip: Read the ends of the whiskers. The box boundaries represent the quartiles. Slip: Add the two quartiles: 20 + 9 = 29. Interquartile range is the difference UQ - LQ. Slip: Write 20. The IQR measures the spread of the middle 50%. Example 2 Lowest value 4 and highest value 28. Find the range.
2 marks
Identify the minimum value 4 and maximum value 28. Subtract lowest from highest: 28 - 4 = 24. State the range is 24. Answer: 24
Common slips Slip: Use the box quartiles. Full range uses the extreme values. Slip: Divide highest by lowest: 28 ÷ 4 = 7. Range is highest minus lowest. Slip: Write 4. The total range is 24. Example 3 Which set has the larger interquartile range? Set A has interquartile range 12 and set B has interquartile range 7.
3 marks
Compare IQR of Set A (12) and Set B (7). Identify that 12 > 7. Conclude Set A has the larger interquartile range. Answer: A
Common slips Slip: Compare the ranges instead. The question specifies interquartile range. Slip: Select Set B because 7 is smaller. Larger IQR means greater spread. Slip: Choose Set B. Set A has the larger IQR. Questions and answers GCSE Maths box plots questions and answers. Try each one, then open the answer. Easy questions come first.
Question 1 Easy 2 marks Lower quartile 8 and upper quartile 20. Find the interquartile range.
Show answer Answer: 12
Subtract lower from upper quartile. 20 − 8 = 12. M1 — Subtract lower from upper quartile. A1 — 20 − 8 = 12. Question 2 Easy 2 marks Ordered data: 2, 5, 7, 9, 12, 14, 20. Find the median.
Show answer Answer: 9
There are 7 values, so the median is the 4th. The 4th value is 9. M1 — There are 7 values, so the median is the 4th. A1 — The 4th value is 9. Question 3 Medium 2 marks Lowest value 3 and highest value 19. Find the range.
Show answer Answer: 16
Subtract lowest from highest value. 19 − 3 = 16. M1 — Subtract lowest from highest value. A1 — 19 − 3 = 16. Question 4 Medium 2 marks Lowest value 5 and highest value 22. Find the range.
Show answer Answer: 17
Subtract lowest from highest value. 22 − 5 = 17. M1 — Subtract lowest from highest value. A1 — 22 − 5 = 17. Question 5 Hard 2 marks Which set has the larger interquartile range? Set A has interquartile range 5 and set B has interquartile range 9.
Show answer Answer: B
Compare IQRs: 9 is greater than 5. Set B has the larger interquartile range. M1 — Compare IQRs: 9 is greater than 5. A1 — Set B has the larger interquartile range. Question 6 Hard 2 marks Which set has the larger interquartile range? Set A has interquartile range 14 and set B has interquartile range 8.
Show answer Answer: A
Compare IQRs: 14 is greater than 8. Set A has the larger interquartile range. M1 — Compare IQRs: 14 is greater than 8. A1 — Set A has the larger interquartile range. Question 7 Exam-style 4 marks A box plot has minimum 6, lower quartile 14, median 19, upper quartile 27 and maximum 41. How much larger is the range than the interquartile range?
Show answer Answer: 22
Range = 41 - 6 = 35. Interquartile range = 27 - 14 = 13. Difference = 35 - 13 = 22. M1 — Range 41 - 6 = 35 M1 — Interquartile range 27 - 14 = 13 M1 — 35 - 13 A1 — 22 Common mistakes Most lost marks on this topic are one slip.
Writing a quartile instead of the difference
Subtract lower from upper
Using the ends for an interquartile range
Use the two quartiles
Choosing the smaller interquartile range as the bigger spread
The larger difference is more spread
Spot the slip A box has lower quartile 9 and upper quartile 20. What is the interquartile range?
11 9 20 Show the slip 11 Upper quartile minus lower quartile is 20 − 9 = 11.
Exam tips This topic can appear on a calculator or a non-calculator paper. Show enough working for a method mark. If the question says “show that”, the result is given. The marks are for the steps that reach it. The method is the same on AQA-style and Edexcel-style papers. For a 'compare' question, two sentences (average + spread, in context) is the standard way to collect all the marks. When drawing from a cumulative frequency curve, read the LQ, median and UQ first and then draw the box directly under the curve using the same scale. Printable worksheet The same questions are in a PDF you can print. Answers start on a later page.
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Questions students ask Is Box plots Foundation or Higher? Box plots is Higher only, aimed at grade 6.
What is a common slip on Box plots? Writing a quartile instead of the difference. Subtract lower from upper.
Where can I get Box plots questions and answers? The questions on this page are free. Open Show answer under each one, or download the worksheet PDF. Start free to practise this topic in the app.
Related topics More on Box plots Previous topic Cumulative frequency Next topic Capture recapture AQA-style and Edexcel-style questions. Yumio is not affiliated with, endorsed by or connected to AQA, Pearson Edexcel or any other exam board.
Last updated 9 November 2026.