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4024/22 Oct/Nov 2023, Question 3: Histograms (Unequal Class Intervals)

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 9 marks

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The question, in short

Use a pie chart of preferred exercise types and a grouped frequency table of daily step counts to calculate totals, a fraction, a histogram, and an estimated percentage.

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

Part (ai) · 2 marks

Given 90 people prefer running, use the running sector angle to calculate the total number of people surveyed.

  1. 1135° represents 90 people
  2. 2Total = 90/135 × 360 = 240

Answer240

Part (aii) · 2 marks

Find the fraction preferring yoga from its pie chart sector angle, giving the answer in simplest form.

  1. 1Yoga angle = 360 − 60 − 135 − 90 = 75°
  2. 2Fraction = 75/360 = 5/24

Answer5/24

Part (bi) · 3 marks

Complete a histogram of step counts using the grouped frequencies, with frequency density on the vertical axis.

  1. 1Frequency density = frequency ÷ class width
  2. 28 < n ≤ 10: 16 ÷ 2 = 8; 10 < n ≤ 12: 14 ÷ 2 = 7
  3. 312 < n ≤ 15: 15 ÷ 3 = 5; 15 < n ≤ 20: 6 ÷ 5 = 1.2
  4. 4Draw bars of these heights across each class

AnswerCorrect histogram

Part (bii) · 2 marks

Estimate the percentage of the 60 days with more than 11 000 steps, using the grouped frequency table.

  1. 111 to 12 thousand is half of the 10 < n ≤ 12 class: 14 ÷ 2 = 7 days
  2. 2Days meeting target ≈ 7 + 15 + 6 = 28
  3. 328/60 × 100 = 46.66… ≈ 46.7%

Answer46.7 or 46.66 to 46.67 or 46 2/3

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Also searched as: 4024/22/O/N/23 · 4024_w23_qp_22 · 4024 w23 22 · question 3.
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