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0580/42 Feb/Mar 2025, Question 15: Estimating the Mean for Grouped Data

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 7 marks

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The question, in short

From a grouped frequency table of 80 sunflower heights, estimate the mean height and draw a histogram on the given grid of frequency density against height.

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

Part (a) · 4 marks

Use the table's class intervals and frequencies to calculate an estimated mean height, showing the working.

  1. 1Mid-points: 1.35, 1.55, 1.65, 1.8
  2. 2Σfm = 12 × 1.35 + 20 × 1.55 + 34 × 1.65 + 14 × 1.8
  3. 3= 16.2 + 31 + 56.1 + 25.2 = 128.5
  4. 4Mean = 128.5 ÷ 80 = 1.60625 m

Answer1.60625

Part (b) · 3 marks

Draw a histogram of the data on the grid, plotting frequency density against height h in metres.

  1. 1Frequency density = frequency ÷ class width
  2. 212 ÷ 0.3 = 40, 20 ÷ 0.1 = 200, 34 ÷ 0.1 = 340, 14 ÷ 0.2 = 70
  3. 3Draw bars 1.2−1.5 height 40, 1.5−1.6 height 200, 1.6−1.7 height 340, 1.7−1.9 height 70

AnswerCorrect histogram: frequency densities 40, 200, 340, 70

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