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0580/32 Oct/Nov 2023, Question 5: Averages from Frequency Tables

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 11 marks

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The question, in short

From data on 500 cars crossing a bridge, use a pie chart and given counts to find red cars, verify a grey sector angle, complete the chart, find a probability, predict white cars in 320, and compute a mean.

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

Part (a) · 1 mark

Using the pie chart's right angle for red and the total of 500 cars, work out how many cars are red.

  1. 1Red sector = 90°
  2. 290/360 × 500 = 125

Answer125

Part (b) · 1 mark

Given 35 grey cars out of 500, show by calculation that the grey sector angle is 25.2°.

  1. 135/500 × 360 = 25.2°

Answer35/500 × 360

Part (c) · 2 marks

With 175 white and 150 black cars, complete the pie chart showing all the information.

  1. 1White = 175/500 × 360 = 126°, black = 150/500 × 360 = 108°
  2. 2Draw these sectors in the blank part with a protractor and label them

AnswerCorrect pie chart

Part (d) · 2 marks

Find the probability that a randomly chosen car is not grey, giving a fraction in simplest form.

  1. 1The grey sector is 25.2°, so grey = 25.2/360 × 500 = 35 cars.
  2. 2Not grey = 500 − 35 = 465 cars
  3. 3P(not grey) = 465/500 = 93/100

Answer93/100

Part (e) · 2 marks

For another 320 cars, calculate how many are expected to be white.

  1. 1P(white) = 175/500
  2. 2175/500 × 320 = 112

Answer112

Part (f) · 3 marks

From the frequency table of people per car, calculate the mean number of people.

  1. 1Σfx = 1 × 20 + 2 × 6 + 3 × 0 + 4 × 15 + 5 × 8 + 6 × 12 = 204
  2. 2Σf = 20 + 6 + 0 + 15 + 8 + 12 = 61
  3. 3Mean = 204 ÷ 61 = 3.344… ≈ 3.34

Answer3.34 or 3.344… or 3 21/61

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