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4MA1/1H Jan 2022, Question 12: Drawing Cumulative Frequency Diagrams

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

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The question, in short

From a grouped frequency table of 80 customers' shopping times, complete a cumulative frequency table, draw its graph, and use the graph to estimate the median and a probability.

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 of the six time intervals up to 60 minutes.

  1. 17
  2. 27 + 26 = 33
  3. 333 + 24 = 57
  4. 457 + 14 = 71
  5. 571 + 7 = 78
  6. 678 + 2 = 80

Answer7, 33, 57, 71, 78, 80

Part (b) · 2 marks

Plot the cumulative frequency against time on the given grid and join the points with a smooth curve.

  1. 1Plot point (10, 7)
  2. 2Plot point (20, 33)
  3. 3Plot point (30, 57)
  4. 4Plot point (40, 71)
  5. 5Plot point (50, 78)
  6. 6Plot point (60, 80)
  7. 7Join points with smooth curve or line segments

AnswerA cumulative frequency graph through (10, 7), (20, 33), (30, 57), (40, 71), (50, 78), (60, 80)

Part (c) · 1 mark

Read off the median time from your cumulative frequency graph at cumulative frequency 40.

  1. 1Find 40 on cumulative frequency axis (half of 80)
  2. 2Draw horizontal line from 40 to the curve
  3. 3Draw vertical line down to time axis
  4. 4Read off value between 21 and 24

Answer21 to 24

Part (d) · 2 marks

Use the graph to estimate the number above 42 minutes, then find the probability for a randomly chosen customer.

  1. 1Draw vertical line up from 42 minutes to the curve
  2. 2Draw horizontal line from curve to cumulative frequency axis
  3. 3Read off cumulative frequency between 72 and 74
  4. 4Subtract from 80: 80 − 72 = 8
  5. 5Write probability as 8/80

Answer0.1 (accept 0.075 to 0.1)

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