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0580/41 May/Jun 2025, Question 15: Estimating the Mean for Grouped Data

Cambridge IGCSE Mathematics 0580 · Paper 41 (Extended) · Calculator · 9 marks

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The question, in short

From a grouped frequency table of 140 basketball players' heights, estimate the mean, find a probability for two randomly chosen players, and complete a histogram.

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

Part (a) · 4 marks

Calculate an estimated mean height from the grouped frequency table.

  1. 1Midpoints: 170, 182.5, 187.5, 195, 205
  2. 2Σfm = 7 × 170 + 12 × 182.5 + 31 × 187.5 + 70 × 195 + 20 × 205
  3. 3= 1190 + 2190 + 5812.5 + 13 650 + 4100 = 26 942.5
  4. 4Mean = 26 942.5 ÷ 140 = 192.4… ≈ 192 cm

Answer192 or 192.4…

Part (b) · 2 marks

Find the probability that two randomly chosen players both have heights in the 190 < h ≤ 200 class.

  1. 170 players have 190 < h ≤ 200
  2. 2P = 70/140 × 69/139 = 4830/19 460
  3. 3= 69/278

Answer69/278

Part (c) · 3 marks

Complete the histogram using the frequency table, given one bar already drawn.

  1. 1Frequency density = frequency ÷ class width
  2. 2160−180: 7 ÷ 20 = 0.35; 180−185: 12 ÷ 5 = 2.4
  3. 3185−190: 31 ÷ 5 = 6.2; 190−200: 70 ÷ 10 = 7
  4. 4Draw bars of these heights across each class

AnswerCorrect histogram

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