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0580/21 May/Jun 2026, Question 14: Finding the Median and Quartiles

Cambridge IGCSE Mathematics 0580 · Paper 21 (Extended) · Non-calculator · 5 marks

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The question, in short

Using a cumulative frequency curve for 60 students' television watching times, estimate the median and interquartile range, then complete a grouped frequency table.

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

Part (ai) · 1 mark

Estimate the median time from the cumulative frequency curve.

  1. 1Median at cumulative frequency 60 ÷ 2 = 30
  2. 2Read across to the curve and down: t = 2.5 hours

Answer2.5

Part (aii) · 2 marks

Estimate the interquartile range from the cumulative frequency curve.

  1. 1LQ at cf 15: t = 1.8
  2. 2UQ at cf 45: t = 3
  3. 3IQR = 3 − 1.8 = 1.2 hours

Answer1.2

Part (b) · 2 marks

Use the curve to fill in the missing frequencies for the 1 < t ≤ 2 and 2 < t ≤ 3 groups.

  1. 1cf at t = 1 is 7, at t = 2 is 18, at t = 3 is 45
  2. 21 < t ≤ 2: 18 − 7 = 11
  3. 32 < t ≤ 3: 45 − 18 = 27

Answer11, 27

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