Statistics practice problems GCSE Maths, Topic 6
Averages and range, frequency tables and grouped data, box plots and comparing distributions, and histograms. Try each question before you look: use the hint if you are stuck, then reveal the worked solution one step at a time.
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Key equations for statistics
| mean = Σfx ÷ Σf | mean from a frequency table |
|---|---|
| IQR = upper quartile − lower quartile | interquartile range |
| frequency = frequency density × class width | histograms (Higher) |
A formulae sheet is provided in the 2025, 2026 and 2027 GCSE Maths exams. Answers within 2.5% are marked correct, and you can type fractions such as 23/20. Every topic, Foundation and Higher, is in our GCSE Maths topic list.
Warm-up questions
Quick checks on the core ideas. If these feel easy, go straight to the exam-style questions.
Hint
Put the numbers in order first.
Worked solution
- In order: 3, 4, 5, 8, 10.
- The middle value is 5.
Hint
Largest minus smallest.
Worked solution
- 19 − 3 = 16.
Hint
Which average is not pulled towards an extreme value?
Worked solution
- The mean is affected by the extreme value; the median is not.
- So the median is best: B.
Exam-style questions
Questions at the level of the GCSE Maths exam. The ones marked Challenge combine more than one idea.
Hint
Multiply each score by its frequency, add, then divide by the total frequency.
Worked solution
- Σfx = 3 + 10 + 24 + 16 = 53, and Σf = 20.
- Mean = 53 ÷ 20 = 2.65.
Hint
Find the total of all five first.
Worked solution
- Total = 5 × 12 = 60.
- Fifth = 60 − (10 + 11 + 13 + 15) = 11.
Hint
IQR = UQ − LQ.
Worked solution
- 26 − 14 = 12.
Hint
Use the midpoint of each class.
Worked solution
- Midpoints 5, 15, 25: Σfx = 20 + 90 + 250 = 360.
- Estimated mean = 360 ÷ 20 = 18.
Hint
Frequency = frequency density × class width.
Worked solution
- Class width = 25 − 10 = 15.
- Frequency = 2.4 × 15 = 36.
Exam question practice
One original exam-style question in the style of a GCSE paper. Answer it in full, with working, before you open the mark scheme: most marks are for method, so show every step.
Exam-style question style · 5 points · about 5 minutes
Two classes sat the same test. Class A had median 64 and interquartile range 12. Class B had median 58 and interquartile range 20.
- (a) Compare the scores of the two classes.
- (b) Why is the IQR a better measure of spread than the range here?
Write your full answer on paper first, then open the scoring guide and tick each point you earned.
Scoring guide and model answer
Part (a)
Class A scored higher on average, since its median (64) is greater than Class B's (58). Class A's scores were more consistent, since its IQR (12) is smaller than Class B's (20).
Part (b)
The IQR is not affected by extreme scores, because it uses only the middle 50% of the data.
Your mark: 0 of 5
Common mistakes in statistics
- Forgetting to order the data before finding the median.
- Dividing Σfx by the number of rows instead of Σf.
- Reading frequency straight off a histogram's vertical axis.
- Comparing two data sets without referring to both an average and a measure of spread.
Keep going
Revise the ideas behind these questions:
Then try real exam questions: GCSE Maths past papers, with official scoring guidelines. · All GCSE Maths units