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4MA1/2H Jun 2024, Question 13: Finding the Median and Quartiles

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 5 marks

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The question, in short

From a grouped frequency table of 70 teachers' distances, complete a cumulative frequency table and use cumulative frequency graphs to estimate an interquartile range and a count above 46 km.

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 distance class up to 60 km.

  1. 1Cumulative frequency adds each frequency step by step.
  2. 20 < d ≤ 10: 7
  3. 30 < d ≤ 20: 7 + 17 = 24
  4. 40 < d ≤ 30: 24 + 18 = 42
  5. 50 < d ≤ 40: 42 + 14 = 56
  6. 60 < d ≤ 50: 56 + 10 = 66
  7. 70 < d ≤ 60: 66 + 4 = 70

Answer7, 24, 42, 56, 66, 70

Part (c) · 2 marks

Draw a cumulative frequency graph and use it to estimate the interquartile range of the distances.

  1. 1Interquartile range = upper quartile − lower quartile.
  2. 2Lower quartile at cumulative frequency 70 ÷ 4 = 17.5
  3. 3Upper quartile at cumulative frequency 3 × 70 ÷ 4 = 52.5
  4. 4Reading from graph: at cf = 17.5, distance ≈ 18 km
  5. 5At cf = 52.5, distance ≈ 38 km
  6. 6Interquartile range = 38 − 18 = 20

Answer20 (accept 18 to 22)

Part (d) · 2 marks

Use a cumulative frequency graph to estimate how many teachers travel more than 46 km.

  1. 1Total teachers = 70
  2. 2From graph, at d = 46 km, cumulative frequency ≈ 62
  3. 3So 70 − 62 = 8 teachers travel more than 46 km.

Answer8 (accept 6 to 9)

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