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4024/12 May/Jun 2021, Question 24: Histograms (Unequal Class Intervals)

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 4 marks

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The question, in short

Using a histogram of distances travelled to work, complete the missing bar and find the percentage of workers travelling more than 20 km.

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

Part (a) · 1 mark

Given 20 workers in the 0 < d ≤ 5 group and 12 in the 20 < d ≤ 40 group, complete the histogram by drawing the missing bar.

  1. 1Frequency density = 12 ÷ (40 − 20) = 0.6
  2. 2Draw a bar from 20 to 40 at height 0.6

AnswerBar for 20 < d ≤ 40 drawn at height 0.6

Part (b) · 3 marks

Using 20 workers in 0 < d ≤ 5 and 12 workers in 20 < d ≤ 40, calculate the percentage travelling more than 20 km.

  1. 1Frequency = frequency density × class width
  2. 25 < d ≤ 10: 6 × 5 = 30; 10 < d ≤ 20: 1.8 × 10 = 18
  3. 320 < d ≤ 40 has 12 workers (part a), so total = 20 + 30 + 18 + 12 = 80
  4. 4Percentage = 12/80 × 100 = 15%

Answer15

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Also searched as: 4024/12/M/J/21 · 4024_s21_qp_12 · 4024 s21 12 · question 24.
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