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4MA1/1H Nov 2021, Question 11: Drawing Cumulative Frequency Diagrams

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 5 marks

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The question, in short

Using a grouped frequency table for 90 runners' 10 km times, complete a cumulative frequency table, plot the cumulative frequency graph, and estimate how many runners finished between 42 and 52 minutes.

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

Part (a) · 1 mark

Fill in the missing cumulative frequency values for the intervals ending at 45, 55, 65, 75 and 85 minutes.

  1. 1Keep a running total of the frequencies
  2. 212, 12 + 24 = 36, 36 + 28 = 64
  3. 364 + 12 = 76, 76 + 10 = 86, 86 + 4 = 90

Answer12, 36, 64, 76, 86, 90

Part (b) · 2 marks

Draw a cumulative frequency curve on the grid using the completed table, plotting cumulative frequency against time.

  1. 1Plot at the upper class boundaries: 35, 45, 55, 65, 75, 85
  2. 2Points: (35, 12), (45, 36), (55, 64), (65, 76), (75, 86), (85, 90)
  3. 3Join the points with a smooth curve or straight lines

AnswerCorrect cumulative frequency graph plotted using upper class boundaries and cumulative frequencies

Part (c) · 2 marks

Read from your graph to estimate the number of runners with times T where 42 < T ≤ 52 minutes.

  1. 1Find cumulative frequency at t = 42 minutes by reading from graph.
  2. 2Draw vertical line from 42 to the curve, then horizontal to cumulative frequency axis.
  3. 3Read off value ≈ 28 (cumulative frequency at 42 min).
  4. 4Find cumulative frequency at t = 52 minutes similarly.
  5. 5Read off value ≈ 55 (cumulative frequency at 52 min).
  6. 6Number who took between 42 and 52 minutes is 55 − 28 = 27.

Answer27 (accept 25 to 29)

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