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4MA1/2HR Jun 2022, Question 11: Drawing Cumulative Frequency Diagrams

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 7 marks

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The question, in short

From a cumulative frequency table of ages for 60 gym users, draw the cumulative frequency graph and use it to estimate median, interquartile range, and count older than 55.

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

Part (a) · 2 marks

Plot cumulative frequency against upper age boundary on the grid and draw the cumulative frequency curve.

  1. 1Plot points at (20,13), (30,36), (40,42), (50,47), (60,52), (70,56), (80,60)
  2. 2Join points with smooth curve or line segments

AnswerA cumulative frequency curve through (20, 13), (30, 36), (40, 42), (50, 47), (60, 52), (70, 56), (80, 60), plotted at the end of each interval

Part (b) · 1 mark

Read the age at cumulative frequency 30 from your graph to estimate the median.

  1. 1Find 30 on the cumulative frequency axis
  2. 2Draw horizontal line to meet the curve
  3. 3Draw vertical line down to age axis
  4. 4Read off value between 26 and 28

Answer27 (accept 26 to 28)

Part (c) · 2 marks

Use the graph to find lower and upper quartiles, then estimate the interquartile range.

  1. 1Find 15 on cumulative frequency axis (lower quartile)
  2. 2Draw across to curve and down to read age ≈ 19−21
  3. 3Find 45 on cumulative frequency axis (upper quartile)
  4. 4Draw across to curve and down to read age ≈ 45−47
  5. 5Interquartile range = upper quartile − lower quartile
  6. 646 − 20 = 26 (within 24−28)

Answer24 to 28

Part (d) · 2 marks

Use the graph to estimate how many people are older than 55 years.

  1. 1Find 55 on age axis
  2. 2Draw vertical line up to meet curve
  3. 3Draw horizontal line across to cumulative frequency axis
  4. 4Read off cumulative frequency ≈ 49 or 50
  5. 5Number older than 55 = total number − cumulative frequency at 55
  6. 660 − 50 = 10

Answer10 or 11

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