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4024/21 May/Jun 2020, Question 1: Estimating the Mean for Grouped Data

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 9 marks

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The question, in short

From a grouped frequency table of 80 vehicle speeds, estimate the mean, draw a cumulative frequency diagram, then use it to estimate the median and interquartile range.

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

Part (a) · 3 marks

Calculate an estimated mean speed from the grouped frequency table of 80 vehicles.

  1. 1Midpoints: 35, 45, 55, 65, 75
  2. 2Σfx = 35 × 10 + 45 × 18 + 55 × 27 + 65 × 19 + 75 × 6 = 350 + 810 + 1485 + 1235 + 450 = 4330
  3. 3Mean = 4330 ÷ 80 = 54.125 ≈ 54.1 km/h

Answer54.1 or 54.12 to 54.13

Part (b) · 3 marks

Plot cumulative frequency against speed on the given axes to draw the cumulative frequency diagram.

  1. 1Cumulative frequencies: 10, 28, 55, 74, 80
  2. 2Plot (30, 0), (40, 10), (50, 28), (60, 55), (70, 74), (80, 80) at the upper class boundaries
  3. 3Join with a smooth curve

AnswerCorrect cumulative frequency curve

Part (ci) · 1 mark

Use your cumulative frequency diagram to estimate the median speed.

  1. 1Median at cumulative frequency 80 ÷ 2 = 40
  2. 2Reading across from 40: 50 + (40 − 28)/27 × 10 ≈ 54.4
  3. 3Median ≈ 54 km/h

Answer53 to 55

Part (cii) · 2 marks

Use your cumulative frequency diagram to estimate the interquartile range of the speeds.

  1. 1LQ at cumulative frequency 20: about 45.6
  2. 2UQ at cumulative frequency 60: about 62.6
  3. 3IQR ≈ 62.6 − 45.6 = 17

Answer14 to 18

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