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4024/22 May/Jun 2025, Question 18: Estimating the Mean for Grouped Data

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 7 marks

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The question, in short

From a grouped frequency table of 300 students' competition scores, estimate the mean score and complete a histogram using the given grid and one drawn bar.

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

Part (a) · 4 marks

Calculate an estimate of the mean score from the grouped frequency table.

  1. 1Midpoints: 15, 35, 50, 65, 85
  2. 2Σfx = 24 × 15 + 70 × 35 + 88 × 50 + 76 × 65 + 42 × 85
  3. 3= 360 + 2450 + 4400 + 4940 + 3570 = 15720
  4. 4Mean = 15720 ÷ 300 = 52.4

Answer52.4 or 52 2/5

Part (b) · 3 marks

Complete the histogram on the grid to represent all the table's data, using the bar already drawn for 30 < s ≤ 40.

  1. 1Frequency density = frequency ÷ class width
  2. 20−30: 24 ÷ 30 = 0.8; 40−60: 88 ÷ 20 = 4.4
  3. 360−70: 76 ÷ 10 = 7.6; 70−100: 42 ÷ 30 = 1.4
  4. 4Draw bars with no gaps on bases 0−30, 40−60, 60−70, 70−100 at these heights

AnswerCorrect histogram drawn

Stuck on a step? Read the free lesson: Estimating the Mean for Grouped Data

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Also searched as: 4024/22/M/J/25 · 4024_s25_qp_22 · 4024 s25 22 · question 18.
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