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0580/43 Oct/Nov 2022, Question 3: Estimating the Mean for Grouped Data

Cambridge IGCSE Mathematics 0580 · Paper 43 (Extended) · Calculator · 7 marks

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The question, in short

From a grouped frequency table of 100 plant heights, complete a partly drawn histogram and estimate the mean height.

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

Part (a) · 3 marks

Complete the histogram for the remaining height intervals using frequency density, with the first two blocks already drawn.

  1. 1Frequency density = frequency ÷ class width
  2. 225 < h ≤ 40: 28 ÷ 15 = 1.87 (1.866…)
  3. 340 < h ≤ 60: 33 ÷ 20 = 1.65
  4. 460 < h ≤ 70: 13 ÷ 10 = 1.3
  5. 5Draw each block across its class with these heights

AnswerCorrect histogram

Part (b) · 4 marks

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

  1. 1Mid-points: 12.5, 20, 32.5, 50, 65
  2. 2Σfx = 8×12.5 + 18×20 + 28×32.5 + 33×50 + 13×65 = 3865
  3. 3Mean = 3865 ÷ 100 = 38.65 cm

Answer38.65

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

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Also searched as: 0580/43/O/N/22 · 0580_w22_qp_43 · 0580 w22 43 · question 3.
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