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4MA1/1HR Jun 2019, Question 17: Histograms (Unequal Class Intervals)

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 5 marks

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The question, in short

Using a histogram of passenger ages up to 80, with 24 people aged 40 to 60, find the total passenger count and a probability estimate.

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

Part (a) · 3 marks

Use the histogram bars and the 24 passengers in the 40 to 60 group to calculate how many passengers are on the plane altogether.

  1. 140−60 bar: frequency density = 24 ÷ 20 = 1.2, which is 6 small squares
  2. 2So 1 small square = 0.2; densities are 0.4, 1.8, 6.4, 2, 1.2, 0.8
  3. 3Frequency = width × density: 4, 18, 32, 30, 24, 16
  4. 4Total = 4 + 18 + 32 + 30 + 24 + 16 = 124

Answer124

Part (b) · 2 marks

For a randomly chosen passenger, estimate the chance that their age is greater than 55 years.

  1. 15 × 1.2 = 6
  2. 220 × 0.8 = 16
  3. 36 + 16 = 22
  4. 422 / 124

Answer22/124

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