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4MA1/1H Jan 2020, Question 12: Finding the Median and Quartiles

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 runners' race times in minutes, estimate the interquartile range, then use the 50-minute information to estimate how many men raced.

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Part (a) · 2 marks

Use the cumulative frequency graph to estimate the interquartile range of the race times.

  1. 180 people took part, so the lower quartile is the 20th value
  2. 2Read across from cumulative frequency 20: time = 38 minutes
  3. 3The upper quartile is the 60th value, since 3/4 of 80 = 60
  4. 4Read across from cumulative frequency 60: time = 56 minutes
  5. 5Interquartile range = 56 − 38 = 18 minutes

Answer18

Part (b) · 3 marks

Given 60% of men and no women finished in 50 minutes or less, estimate the number of men in the race.

  1. 1Estimate number of people who took 50 minutes or less: read from graph at 50 minutes ≈ 42
  2. 260% of men = 42
  3. 3So total number of men = 42 ÷ 0.6
  4. 442 ÷ 0.6 = 70

Answer70

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