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4024/11 Oct/Nov 2024, Question 18: Finding the Median and Quartiles

Cambridge O Level Mathematics 4024 · Paper 11 (Non-calculator) · Non-calculator · 6 marks

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The question, in short

From a cumulative frequency graph of 50 adults' quiz scores, estimate the interquartile range, find the minimum score for the top 20%, and complete a grouped frequency table.

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

Part (a) · 2 marks

Use the cumulative frequency curve to estimate the interquartile range of the scores.

  1. 1LQ at CF 50 ÷ 4 = 12.5: score ≈ 17
  2. 2UQ at CF 37.5: score ≈ 68
  3. 3IQR ≈ 68 − 17 = 51

Answer49 to 53

Part (b) · 2 marks

Using the graph, work out the lowest score needed for the top 20% to win a prize.

  1. 120% of 50 = 10 adults win, so read at CF 50 − 10 = 40
  2. 2Minimum score ≈ 75

Answer74 to 76

Part (c) · 2 marks

Use the graph to fill in the missing frequencies for the five score intervals, given 8 in the last.

  1. 1Read CF at 20, 40, 60, 80: 14, 27, 35, 42
  2. 2Frequencies: 14, 27 − 14 = 13, 35 − 27 = 8, 42 − 35 = 7
  3. 3Check: 50 − 42 = 8 for 80 < s ≤ 100
  4. 414, 13, 8, 7

Answer14, 13, 8, 7

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