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0580/43 Oct/Nov 2024, Question 8: Estimating the Mean for Grouped Data

Cambridge IGCSE Mathematics 0580 · Paper 43 (Extended) · Calculator · 9 marks

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The question, in short

From a table of 100 cars' speeds in four intervals, find a pie chart angle, estimate the mean speed, and complete a histogram with one bar already drawn.

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

Part (a) · 2 marks

Calculate the pie chart angle for the 45 < v ≤ 50 interval using its frequency of 35 out of 100 cars.

  1. 1Angle = 35/100 × 360°
  2. 2= 126°

Answer126

Part (b) · 4 marks

Estimate the mean speed from the grouped frequency table, using midpoints of the four speed intervals.

  1. 1Mid-values: 35, 42.5, 47.5, 60
  2. 2Σfx = 15 × 35 + 20 × 42.5 + 35 × 47.5 + 30 × 60 = 4837.5
  3. 3Mean = 4837.5 ÷ 100 = 48.375 km/h

Answer48.375

Part (c) · 3 marks

Complete the histogram: use frequency density, with the 40 < v ≤ 45 bar of height 4 already drawn.

  1. 1Frequency density = frequency ÷ class width
  2. 230 to 40: 15 ÷ 10 = 1.5; 45 to 50: 35 ÷ 5 = 7; 50 to 70: 30 ÷ 20 = 1.5
  3. 3Draw bars of these heights across each class width

AnswerCorrect histogram with correct widths and heights 1.5 (30 to 40), 7 (45 to 50), 1.5 (50 to 70)

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Also searched as: 0580/43/O/N/24 · 0580_w24_qp_43 · 0580 w24 43 · question 8.
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