Lemmara logoLemmaraWorked solution

4MA1/1HR Jun 2025, Question 12: Drawing Cumulative Frequency Diagrams

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 6 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

From a grouped frequency table of 80 people's ages, complete a cumulative frequency table, draw its graph, then use it to estimate the percentage aged over 46.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 1 mark

Fill in the cumulative frequency column for the six age intervals, accumulating the given frequencies.

  1. 112
  2. 212 + 15 = 27
  3. 327 + 20 = 47
  4. 447 + 18 = 65
  5. 565 + 9 = 74
  6. 674 + 6 = 80

Answer12, 27, 47, 65, 74, 80

Part (b) · 2 marks

Plot the cumulative frequency graph on the grid with age from 10 to 70 and cumulative frequency from 0 to 80.

  1. 1Plot each cumulative frequency at the upper end of its class
  2. 2(20, 12), (30, 27), (40, 47), (50, 65), (60, 74), (70, 80)
  3. 3Join the points with a smooth curve or line segments

AnswerPoints plotted at (20, 12), (30, 27), (40, 47), (50, 65), (60, 74), (70, 80), joined with a smooth curve or straight line segments (may start at (10, 0))

Part (c) · 3 marks

Use the cumulative frequency graph to estimate the percentage of the 80 people older than 46, to the nearest whole number.

  1. 1Read up from age 46 to the curve: about 58 people are 46 or under
  2. 280 − 58 = 22 people are over 46
  3. 322/80 × 100 = 27.5%
  4. 4≈ 28%

Answer28 (accept 26 to 29)

Stuck on a step? Read the free lesson: Drawing Cumulative Frequency Diagrams

Practise more drawing cumulative frequency diagrams questions

Real 4MA1 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on drawing cumulative frequency diagrams

Also searched as: 4MA1 1HR June 2025 · 4MA1/1HR · 4ma1 jun25 1hr · question 12.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.