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4024/23 May/Jun 2026, Question 16: Estimating the Mean for Grouped Data

Cambridge O Level Mathematics 4024 · Paper 23 (Calculator) · Calculator · 6 marks

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The question, in short

From a grouped frequency table of 50 children's homework times, find the modal class, estimate the mean time, and find a probability for a randomly chosen child.

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

Part (a) · 1 mark

State the class interval with the highest frequency from the table.

  1. 1The highest frequency is 18
  2. 2Modal class 30 < t ≤ 50

Answer30 < t ≤ 50

Part (b) · 4 marks

Use class midpoints and frequencies to calculate an estimated mean time in minutes.

  1. 1Midpoints: 20, 40, 60, 80
  2. 2Σfx = 20 × 12 + 40 × 18 + 60 × 14 + 80 × 6
  3. 3= 240 + 720 + 840 + 480 = 2280
  4. 4Mean = 2280 ÷ 50 = 45.6 minutes

Answer45.6

Part (c) · 1 mark

Find the probability that a randomly chosen child took 30 minutes or less.

  1. 112 children took 30 minutes or less
  2. 2Probability = 12/50

Answer12/50 or 0.24 or 24%

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