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4024/22 Oct/Nov 2025, Question 24: Histograms (Unequal Class Intervals)

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 6 marks

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The question, in short

From a histogram of masses of 250 onions, show the count of onions at or below 200 g, then estimate the mean mass showing working.

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

Part (a) · 1 mark

Use the histogram bars up to 200 g to show that 28 onions have mass 200 g or less.

  1. 1Frequency = frequency density × class width
  2. 2= 0.7 × (200 − 160) = 28

Answer0.7 × (200 − 160) = 28

Part (b) · 5 marks

Use the histogram to estimate the mean mass of the 250 onions, showing all working.

  1. 1Frequencies: 28, 3.9 × 20 = 78, 4.5 × 20 = 90, 0.9 × 60 = 54 (total 250)
  2. 2Midpoints: 180, 210, 230, 270
  3. 3Σfx = 28 × 180 + 78 × 210 + 90 × 230 + 54 × 270 = 5040 + 16 380 + 20 700 + 14 580 = 56 700
  4. 4Mean = 56 700 ÷ 250 = 226.8 g

Answer226.8

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