Question 1Warm-upHigher
Find the median of 3, 5, 7, 8, 9, 12, 14.
7 values: the 4th.
Worked solution
- th value
Answer:
GCSE & IGCSE maths practice
Box plots questions and answers
A box plot (box-and-whisker diagram) shows five values: the minimum, lower quartile, median, upper quartile and maximum. The box covers the middle 50% of the data, so its length is the interquartile range (IQR). To compare two box plots, compare the medians (which is higher on average) and the IQRs (which is more consistent).
8 questions · Higher tier · Every answer is checked as you type it, with a full worked solution. Updated .
Where box plots comes up
| GCSE (AQA, Edexcel, OCR) | Higher only: box plots, quartiles and the interquartile range, to interpret and compare distributions. |
|---|---|
| Cambridge IGCSE (0580) | Not in the 0580 syllabus: box-and-whisker plots were removed from 2025 (quartiles and the IQR are still in Extended). |
The method
- Order the data.
- Median: the (n + 1) ÷ 2th value. Quartiles: the (n + 1) ÷ 4th and 3(n + 1) ÷ 4th values.
- IQR = UQ − LQ; range = max − min.
- Compare: the median (average) and the IQR (spread), in context.
Box plots questions
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Warm-up
Question 2Warm-upHigher
Find the lower and upper quartiles of 3, 5, 7, 8, 9, 12, 14.
The 2nd and 6th values.
Worked solution
- nd value
- th value
Answer: LQ , UQ
Exam-style
Question 3Exam-styleHigher
Find the interquartile range of 3, 5, 7, 8, 9, 12, 14.
UQ − LQ.
Worked solution
Answer:
Question 4Exam-styleHigher
A box plot shows: minimum 10, lower quartile 18, median 25, upper quartile 31, maximum 40. Find the range.
Max − min.
Worked solution
Answer:
Question 5Exam-styleHigher
For the same box plot, find the interquartile range.
UQ − LQ.
Worked solution
Answer:
Question 6Exam-styleHigher
Group A has median 25 and IQR 13. Group B has median 28 and IQR 6. Which group's results are more consistent?
Consistency is about spread.
Worked solution
- B's IQR (6) is smaller than A's (13), so B's middle 50% are closer together.
Answer: Group B: its IQR is smaller
Challenge
Question 7ChallengeHigher
What percentage of the data is above the upper quartile?
The quartiles split the data into four equal parts.
Worked solution
- Each quarter holds of the data.
Answer:
Question 8ChallengeHigher
For data with LQ 18 and UQ 31, an outlier is any value more than 1.5 × IQR above the upper quartile. Is 52 an outlier?
Find 1.5 × IQR first.
Worked solution
- IQR ;
- , so it's an outlier.
Answer: Yes: the limit is , and
Common mistakes
- Forgetting to order the data first.
- Comparing ranges instead of IQRs.
- Comparing without saying what it means in context.
Stuck on one of these?
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Sources
The questions are our own. The “where it comes up” notes are from each board's published specification, checked on 26 October 2026:
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