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0580/41 Oct/Nov 2023, Question 7: Estimating the Mean for Grouped Data

Cambridge IGCSE Mathematics 0580 · Paper 41 (Extended) · Calculator · 7 marks

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The question, in short

From a grouped frequency table of 42 athletes' race times, estimate the mean time and complete a frequency density histogram, with two bars already drawn.

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

Part (a) · 4 marks

Use the grouped times and frequencies to calculate an estimate of the mean race time in seconds.

  1. 1Mid-points: 217.5, 221.5, 229, 239, 254
  2. 2Σfm = 9 × 217.5 + 14 × 221.5 + 14 × 229 + 2 × 239 + 3 × 254
  3. 3= 1957.5 + 3101 + 3206 + 478 + 762 = 9504.5
  4. 4Mean = 9504.5 ÷ 42 = 226.29… ≈ 226 s

Answer226 or 226.2 to 226.30

Part (b) · 3 marks

Complete the histogram by drawing the missing bars, using frequency density against time t from 210 to 270.

  1. 1Frequency density = frequency ÷ class width
  2. 2219−224: 14 ÷ 5 = 2.8
  3. 3224−234: 14 ÷ 10 = 1.4
  4. 4234−244: 2 ÷ 10 = 0.2 — draw these three blocks

AnswerBlocks with heights 2.8, 1.4, 0.2 and with correct widths

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Also searched as: 0580/41/O/N/23 · 0580_w23_qp_41 · 0580 w23 41 · question 7.
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