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0580/41 Oct/Nov 2024, Question 3: Estimating the Mean for Grouped Data

Cambridge IGCSE Mathematics 0580 · Paper 41 (Extended) · Calculator · 8 marks

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The question, in short

From grouped waiting-time data for 120 patients, work out an estimated mean, then use a histogram for 90 patients to finish the missing bars.

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

Part (a) · 4 marks

Using the grouped frequencies and class intervals, find an estimated value for the mean waiting time.

  1. 1Midpoints: 5, 15, 30, 45, 65
  2. 2Σfx = 2 × 5 + 46 × 15 + 33 × 30 + 26 × 45 + 13 × 65
  3. 3Σfx = 10 + 690 + 990 + 1170 + 845 = 3705
  4. 4Mean = 3705 ÷ 120 = 30.875 minutes

Answer30.875

Part (b) · 4 marks

Given 90 patients total and none over 80 minutes, work out the missing frequencies and draw the bars for 10 to 30 minutes.

  1. 1Frequencies of drawn bars: 10 × 1.3 = 13, 20 × 1.5 = 30, 30 × 0.4 = 12
  2. 2Frequency for 10 < t ≤ 30 = 90 − (13 + 30 + 12) = 35
  3. 3Frequency density = 35 ÷ 20 = 1.75
  4. 4Draw a bar from t = 10 to t = 30 with height 1.75

AnswerDraws correct bar to height 1.75

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