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4MA1/2H Jun 2025, Question 13: Drawing Cumulative Frequency Diagrams

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 6 marks

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The question, in short

Using a grouped frequency table of puzzle completion times for 60 people, complete a cumulative frequency table, draw its graph, and use the graph to estimate a median and a count above 45 minutes.

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 each time interval up to 60 minutes.

  1. 18
  2. 28 + 13 = 21
  3. 321 + 12 = 33
  4. 433 + 17 = 50
  5. 550 + 7 = 57
  6. 657 + 3 = 60

Answer8, 21, 33, 50, 57, 60

Part (b) · 2 marks

Plot the cumulative frequency graph on the given grid with time and cumulative frequency axes.

  1. 1Plot each cumulative frequency at the upper end of its class
  2. 2(10, 8), (20, 21), (30, 33)
  3. 3(40, 50), (50, 57), (60, 60)
  4. 4Join the points with a smooth curve from (0, 0)

AnswerPoints (10, 8), (20, 21), (30, 33), (40, 50), (50, 57), (60, 60) plotted and joined with a smooth curve or line segments, starting from (0, 0)

Part (c) · 1 mark

Read off an estimate of the median completion time from your graph.

  1. 1Median is at cumulative frequency 60 ÷ 2 = 30
  2. 2Read across at 30 to the curve and down
  3. 3Median ≈ 27.5 minutes (27 to 28 accepted)

Answer27.5 (accept 27 to 28)

Part (d) · 2 marks

Use the graph to estimate how many people took longer than 45 minutes.

  1. 1Read up from 45 minutes to the curve
  2. 2Cumulative frequency ≈ 54
  3. 3More than 45 minutes: 60 − 54 = 6

Answer5 to 7

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