1. 1
   The cumulative frequency table for the times (in minutes) taken by 60 runners to finish a race is: t ≤ 20: 5; t ≤ 30: 18; t ≤ 40: 40; t ≤ 50: 54; t ≤ 60: 60.

   (a)

   How many runners took between 30 and 40 minutes to finish?

   [1 mark]

   • A22
   • B18
   • C40
   • D14

   (b)

   Which class interval contains the median (the 30th value)?

   [1 mark]

   • At ≤ 20
   • B20 < t ≤ 30
   • C40 < t ≤ 50
   • D30 < t ≤ 40

   (c)

   How many runners took more than 50 minutes to finish?

   [1 mark]

   • A14
   • B54
   • C6
   • D20

   Total for question 1: 3 marks

2. 2
   The cumulative frequency table for the masses (in kg) of 80 parcels is: m ≤ 5: 8; m ≤ 10: 26; m ≤ 15: 58; m ≤ 20: 74; m ≤ 25: 80.

   (a)

   Estimate the median mass, using linear interpolation.

   [2 marks]

   (b)

   Estimate the lower quartile mass, using linear interpolation.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   The cumulative frequency table for the heights (in cm) of 100 plants is: h ≤ 10: 6; h ≤ 20: 28; h ≤ 30: 64; h ≤ 40: 88; h ≤ 50: 100. It is given that the lower quartile height is 18.6 cm.

   (a)

   Estimate the upper quartile height, using linear interpolation.

   [3 marks]

   (b)

   Using your answer to part (a) and the given lower quartile of 18.6 cm, find the interquartile range.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A box plot summarises the delivery times, in minutes, for company X: minimum = 10, lower quartile = 22, median = 30, upper quartile = 38, maximum = 55. For company Y: minimum = 15, lower quartile = 25, median = 32, upper quartile = 40, maximum = 48.

   (a)

   Find the interquartile range of delivery times for each company.

   [4 marks]

   (b)

   Find the range of delivery times for each company.

   [4 marks]

   (c)

   Using the median and the interquartile range, compare the delivery times of the two companies. Which company tends to deliver faster, and which company is more consistent?

   [5 marks]

   Total for question 4: 13 marks

End of questions