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4024/21 Oct/Nov 2023, Question 5: Finding the Median and Quartiles

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 11 marks

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The question, in short

Bus timetable and journey-time data: find a bus journey duration, an arrival time, and use a cumulative frequency graph plus bounds to estimate values and a speed.

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

Part (ai) · 1 mark

Using the timetable, calculate the minutes the bus needs to travel from the town square stop to the business park stop.

  1. 106 30 to 07 16 = 30 + 16 minutes
  2. 2= 46 minutes

Answer46

Part (aii) · 1 mark

Tom reaches the railway station at 07 12; determine when the following bus reaches the airport.

  1. 1Next bus from the railway station after 07 12 leaves at 07 28
  2. 2It arrives at the airport at 08 15

Answer08 15

Part (bi) · 1 mark

From the cumulative frequency curve, estimate how many workers had journeys shorter than 30 minutes.

  1. 1Read up from 30 minutes to the curve and across
  2. 2About 56 workers

Answer55 to 57

Part (bii) · 2 marks

Read the curve to estimate the interquartile range of the journey times.

  1. 1LQ at CF 160 ÷ 4 = 40: 24 minutes
  2. 2UQ at CF 120: 54 minutes
  3. 3IQR = 54 − 24 = 30 minutes

Answer30

Part (biii) · 3 marks

Estimate what percentage of workers had journeys exceeding 1 hour.

  1. 1At 60 minutes, cumulative frequency = 132
  2. 2Longer than 1 hour = 160 − 132 = 28
  3. 328/160 × 100 = 17.5%

Answer17.5

Part (c) · 3 marks

With 37 km and 43 minutes each rounded, work out the lowest possible average speed in km/h.

  1. 1Lower bound of distance = 36.5 km, upper bound of time = 43.5 min
  2. 2Lower bound of speed = 36.5 ÷ (43.5/60)
  3. 3= 50.34… ≈ 50.3 km/h

Answer50.3 or 50.34…

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