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0580/42 May/Jun 2024, Question 3: Estimating the Mean for Grouped Data

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 15 marks

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The question, in short

Use a grouped frequency table for 40 students' travel times to estimate the mean, draw a histogram, and find a probability; then use summary statistics for 200 questionnaire times to find the shortest time, draw a box plot, and assess a claim.

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

Part (ai) · 4 marks

Estimate the mean travel time from the grouped frequency table.

  1. 1Mid-points: 5, 17.5, 32.5, 50
  2. 2Σfm = 3×5 + 18×17.5 + 15×32.5 + 4×50 = 15 + 315 + 487.5 + 200 = 1017.5
  3. 3Mean = 1017.5 ÷ 40 = 25.4375 min

Answer25.4375

Part (aii) · 3 marks

Draw a histogram of the grouped times using frequency density on the vertical axis.

  1. 1Frequency densities: 3 ÷ 10 = 0.3, 18 ÷ 15 = 1.2, 15 ÷ 15 = 1, 4 ÷ 20 = 0.2
  2. 2Draw bars 0−10 height 0.3, 10−25 height 1.2, 25−40 height 1, 40−60 height 0.2

Answercorrect histogram

Part (aiii) · 3 marks

Find the probability that, of two students chosen at random, one takes over 25 minutes and the other 10 minutes or less.

  1. 1More than 25 min: 15 + 4 = 19; 10 min or less: 3
  2. 2P = 2 × 19/40 × 3/39 = 114/1560
  3. 3= 19/260

Answer19/260

Part (bi) · 1 mark

Write down the shortest questionnaire completion time from the given range and longest time.

  1. 1Shortest = 30 − 25 = 5 min

Answer5

Part (bii) · 3 marks

Draw a box-and-whisker plot using the median, quartiles, shortest and longest times.

  1. 1Upper quartile = 8 + 19 = 27
  2. 2Plot whiskers from 5 to 30
  3. 3Box from 8 to 27 with median line at 22

AnswerCorrect box plot: lowest 5, lower quartile 8, median 22, upper quartile 27, highest 30

Part (biii) · 1 mark

Explain why George's statement that 101 people took more than 22 minutes is incorrect.

  1. 122 min is the median, so half the people (100) took more than 22 min
  2. 2101 is more than half, so George is wrong

AnswerThe median is 22, which is 50% of the people (100 people), and 101 is more than 50%; or: the median is the 100th (accept 100.5th) value.

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Also searched as: 0580/42/M/J/24 · 0580_s24_qp_42 · 0580 s24 42 · question 3.
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