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0580/22 May/Jun 2025, Question 13: Estimating the Mean for Grouped Data

Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Non-calculator · 11 marks

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The question, in short

From grouped time data for 100 students and cumulative frequency data for 80 adults solving a puzzle, estimate mean, complete a histogram, draw a cumulative frequency diagram, and estimate median and lower quartile.

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

Part (ai) · 4 marks

Calculate an estimated mean time from the grouped frequency table for the 100 students.

  1. 1Midpoints: 30, 50, 80
  2. 2Σfx = 30 × 30 + 40 × 50 + 30 × 80 = 900 + 2000 + 2400 = 5300
  3. 3Mean = 5300 ÷ 100 = 53 s

Answer53

Part (aii) · 2 marks

Complete the histogram by drawing bars for the remaining time intervals using frequency density.

  1. 140 < t ≤ 60: frequency density = 40 ÷ 20 = 2
  2. 260 < t ≤ 100: frequency density = 30 ÷ 40 = 0.75
  3. 3Draw a bar from 40 to 60 of height 2 and a bar from 60 to 100 of height 0.75

AnswerTwo correct bars with correct widths and heights 2 and 0.75

Part (bi) · 3 marks

Plot a cumulative frequency curve for the 80 adults on the given grid.

  1. 1Plot (20, 0), (40, 12), (60, 36), (80, 60), (100, 74), (120, 80) at the upper class boundaries
  2. 2Join the points with a smooth increasing curve

AnswerCorrect diagram

Part (biia) · 1 mark

Use the cumulative frequency diagram to estimate the median time for the adults.

  1. 1Median at cumulative frequency 80 ÷ 2 = 40
  2. 2Between (60, 36) and (80, 60): 60 + 4/24 × 20 ≈ 63
  3. 3Median ≈ 63 s

Answer62 to 64

Part (biib) · 1 mark

Use the cumulative frequency diagram to estimate the lower quartile time for the adults.

  1. 1Lower quartile at cumulative frequency 80 ÷ 4 = 20
  2. 2Between (40, 12) and (60, 36): 40 + 8/24 × 20 ≈ 47
  3. 3Lower quartile ≈ 47 s

Answer46 to 48

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