Question 1Warm-upHigher
Four classes have frequencies 3, 7, 12 and 8. Write the cumulative frequencies.
Keep a running total.
Worked solution
- , , ,
Answer:
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Cumulative frequency questions and answers
Cumulative frequency is a running total of the frequencies. On a cumulative frequency graph, plot each running total at the upper bound of its class and join the points with a smooth curve. To estimate the median, read across from half the total; the quartiles are at a quarter and three quarters.
8 questions · Higher tier · Every answer is checked as you type it, with a full worked solution. Updated .
Where cumulative frequency comes up
| GCSE (AQA, Edexcel, OCR) | Higher only: construct and interpret cumulative frequency graphs, including quartiles and the interquartile range. |
|---|---|
| Cambridge IGCSE (0580) | Extended only: draw and interpret cumulative frequency tables and diagrams, and estimate the median, percentiles, quartiles and interquartile range. |
The method
- Running total: add each frequency to the total so far.
- Plot at the upper class bound.
- Median at n ÷ 2; lower quartile at n ÷ 4; upper quartile at 3n ÷ 4.
- IQR = upper quartile − lower quartile.
Cumulative frequency questions
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Warm-up
Question 2Warm-upHigher
A cumulative frequency graph shows 80 people. At what cumulative frequency do you read off the median?
Half the total.
Worked solution
Answer:
Exam-style
Question 3Exam-styleHigher
For the same 80 people, at what cumulative frequency do you read off the lower quartile?
A quarter of the total.
Worked solution
Answer:
Question 4Exam-styleHigher
From a cumulative frequency graph, the lower quartile is 23 and the upper quartile is 41. Find the interquartile range.
UQ − LQ.
Worked solution
Answer:
Question 5Exam-styleHigher
How many people took between 20 and 30 minutes?
| Time, t (minutes) | Cumulative frequency |
|---|---|
| t ≤ 10 | 6 |
| t ≤ 20 | 20 |
| t ≤ 30 | 41 |
| t ≤ 40 | 50 |
Subtract the running totals.
Worked solution
Answer:
Question 6Exam-styleHigher
Using the same table, how many people took more than 30 minutes?
| Time, t (minutes) | Cumulative frequency |
|---|---|
| t ≤ 10 | 6 |
| t ≤ 20 | 20 |
| t ≤ 30 | 41 |
| t ≤ 40 | 50 |
Total minus those up to 30.
Worked solution
Answer:
Challenge
Question 7ChallengeHigher
Using the same table, what percentage of people took 20 minutes or less?
| Time, t (minutes) | Cumulative frequency |
|---|---|
| t ≤ 10 | 6 |
| t ≤ 20 | 20 |
| t ≤ 30 | 41 |
| t ≤ 40 | 50 |
20 out of 50.
Worked solution
Answer:
Question 8ChallengeHigher
The class has cumulative frequency 20. Which point do you plot?
Cumulative frequency goes at the upper bound.
Worked solution
- By , 20 people have finished.
Answer:
Common mistakes
- Plotting at the midpoint instead of the upper bound.
- Reading the median from the horizontal axis at n ÷ 2.
- Giving the frequency of a class instead of the cumulative frequency.
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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