Skip to content

Paper Together: sit a paper in a room with your friends.See how it works

Cumulative frequency practice questions with answers

Higher · Grade 6

A second set of cumulative frequency questions for GCSE Maths. They are different from the ones on the topic page, so work through both. Try each question, then open the answer to check your working.

More questions

Question 1 Easy

The total frequency is 30. The curve reads 22 at cumulative frequency 15. Find the median.

Show answer

Answer: 22

  1. Half of 30 is 15.
  2. The curve reads 22 at cumulative frequency 15.
  • Method (1): Half of 30 is 15.
  • Accuracy (1): The curve reads 22 at cumulative frequency 15.

Question 2 Easy

The total frequency is 16. The curve reads 9 at cumulative frequency 8. Find the median.

Show answer

Answer: 9

  1. Half of 16 is 8.
  2. The curve reads 9 at cumulative frequency 8.
  • Method (1): Half of 16 is 8.
  • Accuracy (1): The curve reads 9 at cumulative frequency 8.

Question 3 Medium

The total frequency is 24. The curve reads 26 at cumulative frequency 18. Find the upper quartile.

Show answer

Answer: 26

  1. Three quarters of 24 is 18.
  2. The curve reads 26 at cumulative frequency 18.
  • Method (1): Three quarters of 24 is 18.
  • Accuracy (1): The curve reads 26 at cumulative frequency 18.

Question 4 Medium

The total frequency is 40. The curve reads 30 at cumulative frequency 30. Find the upper quartile.

Show answer

Answer: 30

  1. Three quarters of 40 is 30.
  2. The curve reads 30 at cumulative frequency 30.
  • Method (1): Three quarters of 40 is 30.
  • Accuracy (1): The curve reads 30 at cumulative frequency 30.

Question 5 Hard

Which set has the higher median? Set A has median 12 and set B has median 18.

Show answer

Answer: B

  1. Compare medians 12 and 18.
  2. 18 is greater than 12, so set B is higher.
  • Method (1): Compare medians 12 and 18.
  • Accuracy (1): 18 is greater than 12, so set B is higher.

Question 6 Hard

Which set has the higher median? Set A has median 27 and set B has median 21.

Show answer

Answer: A

  1. Compare medians 27 and 21.
  2. 27 is greater than 21, so set A is higher.
  • Method (1): Compare medians 27 and 21.
  • Accuracy (1): 27 is greater than 21, so set A is higher.

Exam-style question

A longer question with marks, in the style of a written paper. This is a Yumio practice question, not a past paper question.

Exam-style question 12 marks

The total frequency is 60. The curve reads 28 at cumulative frequency 30. Find the median.

Show answer

Answer: 28

  1. Half the total frequency is 60 ÷ 2 = 30.
  2. Read across from 30 on the vertical axis to the curve, then down to the horizontal axis: the median is 28.
  • Method (1): Half the total: 60 ÷ 2 = 30
  • Accuracy (1): Median 28 read from the data axis

Quick checks

Short one-step questions. Pick an option before you open the answer.

Check 1

The median is read at what fraction of the total frequency?

Show answer

Median is at 50% or one half of total frequency. Median is at 50% or one half of total frequency.

Check 2

Total 24, curve reads 20 at cumulative frequency 12. The median is

  1. 12
  2. 20
  3. 40
Show answer

20 At half total 12, the curve value is 20.

Check 3

Total 40, curve reads 18 at cumulative frequency 20. The median is

  1. 20
  2. 18
  3. 40
Show answer

18 At half total 20, the curve value is 18.

Check 4

The lower quartile is read at what fraction of the total?

Show answer

Lower quartile is at 25% or one quarter. Lower quartile is at 25% or one quarter.

Check 5

Total 24, curve reads 14 at cumulative frequency 6. The lower quartile is

  1. 13
  2. 28
  3. 14
Show answer

14 At one quarter total 6, the value is 14.

Check 6

The upper quartile is read at what fraction of the total?

Show answer

Upper quartile is at 75% or three quarters. Upper quartile is at 75% or three quarters.

Check 7

Total 24, curve reads 26 at cumulative frequency 18. The upper quartile is

  1. 24
  2. 26
  3. 18
Show answer

26 At three quarters total 18, the value is 26.

Check 8

Set A has median 20 and set B has median 28. The higher set is

  1. A with median 32
  2. B with median 28
  3. higher on average
Show answer

B with median 28 28 is greater than 20, so set B is higher.

Check 9

Set A has median 32 and set B has median 25. The higher set is

  1. A with median 32
  2. B with median 28
  3. higher on average
Show answer

A with median 32 32 is greater than 25, so set A is higher.

Check 10

Why is 12 not the median when the total is 24?

Show answer

12 is where you look on the vertical axis, not the value. 12 is where you look on the vertical axis, not the value.

Check 11

The value you write down comes from which axis?

Show answer

The measured data values sit on the horizontal axis. The measured data values sit on the horizontal axis.

Check 12

Half of a total of 40 is the cumulative frequency

Show answer

Half of 40 is 20 where the median is read. Half of 40 is 20 where the median is read.

Check 13

A quarter of a total of 24 is the cumulative frequency

Show answer

One quarter of 24 is 6 where LQ is read. One quarter of 24 is 6 where LQ is read.

Check 14

Comparing medians tells you which set is

  1. higher on average
  2. A with median 32
  3. B with median 28
Show answer

higher on average Medians compare average or typical level, not spread.

Check 15

Can a cumulative frequency curve ever decrease as you move right?

Show answer

Because frequencies are added on, a cumulative frequency curve always rises or stays level. Because frequencies are added on, a cumulative frequency curve always rises or stays level.

Keep going with Cumulative frequency

Practise free

Start free

AQA-style and Edexcel-style questions. Yumio is not affiliated with, endorsed by or connected to AQA, Pearson Edexcel or any other exam board.

Next topicPractise free