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0580/42 Oct/Nov 2025, Question 16: Estimating the Mean for Grouped Data

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 8 marks

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The question, in short

Using a histogram of coconut masses split into categories A to D, work out counts, a probability and an estimated mean mass.

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

Part (a) · 1 mark

Demonstrate that category D contains 10 coconuts, using the histogram's frequency density and class width.

  1. 1Frequency = class width × frequency density
  2. 2D: (1.6 − 1.35) × 40 = 0.25 × 40 = 10

Answer(1.6 − 1.35) × 40 = 10

Part (b) · 3 marks

Pick two coconuts at random from categories C and D combined; find the probability both come from D.

  1. 1C: (1.35 − 1.25) × 170 = 17, so C and D have 17 + 10 = 27 coconuts
  2. 2P(both D) = 10/27 × 9/26
  3. 3= 90/702 = 5/39

Answer5/39

Part (c) · 4 marks

Use the histogram to work out an estimated value for the mean mass of all the coconuts.

  1. 1Frequencies: A = 0.2 × 30 = 6, B = 0.15 × 100 = 15, C = 17, D = 10; total 48
  2. 2Midpoints: 1, 1.175, 1.3, 1.475
  3. 3Σfm = 6 × 1 + 15 × 1.175 + 17 × 1.3 + 10 × 1.475 = 60.475
  4. 4Mean = 60.475 ÷ 48 = 1.259… ≈ 1.26 kg

Answer1.26 or 1.259…

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