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4MA1/1H Jun 2018, Question 10: 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

From a cumulative frequency graph of 80 film lengths in minutes, estimate the interquartile range and judge whether Clare's claim that over 35% of films exceed 120 minutes is correct, giving a reason.

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

Part (a) · 2 marks

Use the cumulative frequency graph to estimate the interquartile range of the film lengths.

  1. 1There are 80 films, so the lower quartile is the length at cumulative frequency 20.
  2. 2Reading across from 20 gives a length of 103.5 minutes.
  3. 3The upper quartile is the length at cumulative frequency 60.
  4. 4Reading across from 60 gives a length of 124 minutes.
  5. 5Interquartile range = 124 − 103.5 = 20.5 minutes

Answer20.5

Part (b) · 3 marks

Decide whether Clare's statement that more than 35% of the films are over 120 minutes is correct, justifying your decision.

  1. 1Read across at 120 minutes: cumulative frequency is 55
  2. 2Films over 120 minutes = 80 − 55 = 25
  3. 335% of 80 = 0.35 × 80 = 28
  4. 4No, 35% of 80 is 28 but only 25 films are over 120 minutes

AnswerNo, 35% of 80 is 28 but only 25 films are over 120 minutes

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