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4MA1/1HR Jan 2021, Question 11: Drawing Cumulative Frequency Diagrams

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

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The question, in short

From a grouped frequency table of 120 callers' waiting times, complete a cumulative frequency table, draw its graph, then estimate the median and the percentage waiting over 23 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 band up to 30 minutes.

  1. 18 = 8
  2. 28 + 15 = 23
  3. 323 + 17 = 40
  4. 440 + 28 = 68
  5. 568 + 33 = 101
  6. 6101 + 19 = 120

Answer8, 23, 40, 68, 101, 120

Part (b) · 2 marks

Plot the cumulative frequency graph on the given grid of cumulative frequency against time waited.

  1. 1Plot each cumulative frequency at the upper end of its interval
  2. 2Points: (5, 8), (10, 23), (15, 40), (20, 68), (25, 101), (30, 120)
  3. 3Join the points with a smooth cumulative frequency curve

AnswerA cumulative frequency curve through (5, 8), (10, 23), (15, 40), (20, 68), (25, 101), (30, 120)

Part (c) · 1 mark

Read the median waiting time from your cumulative frequency graph.

  1. 1Find 60 on cumulative frequency axis (half of 120)
  2. 2Draw horizontal line from 60 to the curve
  3. 3Draw vertical line down to time axis
  4. 4Read value: 17 to 20 minutes

Answer17 to 20

Part (d) · 2 marks

Use the graph to estimate the percentage of the 120 people who waited longer than 23 minutes, showing working.

  1. 1Draw vertical line up from 23 minutes to the curve
  2. 2Draw horizontal line to cumulative frequency axis
  3. 3Read off value at 23 minutes (≈ 85 to 90)
  4. 4(120 − 88) ÷ 120 × 100 = 26.7%
  5. 5Answer is 25% to 29%

Answer27 (accept 25 to 29)

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