1. 1
   A cumulative frequency table shows the times, in minutes, taken by 60 students to complete a puzzle: fewer than 10 minutes - 5 students; fewer than 20 minutes - 18 students; fewer than 30 minutes - 38 students; fewer than 40 minutes - 52 students; fewer than 50 minutes - 60 students.

   (a)

   How many students took less than 30 minutes?

   [1 mark]

   • A38
   • B20
   • C18
   • D52

   (b)

   How many students took between 20 and 30 minutes?

   [1 mark]

   • A38
   • B20
   • C18
   • D14

   (c)

   Estimate the median time, in minutes, using linear interpolation.

   [1 mark]

   • A22
   • B24
   • C28
   • D26

   Total for question 1: 3 marks

2. 2
   A cumulative frequency table shows the masses, in kg, of 50 parcels: fewer than 10 kg - 8 parcels; fewer than 20 kg - 22 parcels; fewer than 30 kg - 38 parcels; fewer than 40 kg - 46 parcels; fewer than 50 kg - 50 parcels.

   (a)

   Find the position of the lower quartile (as the $\frac{n}{4}$th value) and state which class interval contains it.

   [2 marks]

   (b)

   Using linear interpolation, estimate the lower quartile mass, correct to 1 decimal place.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A cumulative frequency table shows the exam scores of 80 students: fewer than 20 marks - 6 students; fewer than 40 marks - 24 students; fewer than 60 marks - 52 students; fewer than 80 marks - 72 students; fewer than 100 marks - 80 students.

   (a)

   Using linear interpolation, estimate the median score, correct to 1 decimal place.

   [3 marks]

   (b)

   Using linear interpolation, estimate the upper quartile score, correct to 1 decimal place.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   Two cumulative frequency tables show the times, in minutes, taken by 100 runners in Race A and Race B of a 5 km event. Race A: fewer than 20 min - 5; fewer than 30 min - 25; fewer than 40 min - 65; fewer than 50 min - 90; fewer than 60 min - 100. Race B: fewer than 20 min - 10; fewer than 30 min - 40; fewer than 40 min - 70; fewer than 50 min - 92; fewer than 60 min - 100.

   (a)

   Using linear interpolation, estimate the median time for Race A, correct to 1 decimal place.

   [4 marks]

   (b)

   Using linear interpolation, estimate the median time for Race B, correct to 1 decimal place.

   [4 marks]

   (c)

   Compare the median times for Race A and Race B, stating which race had the faster typical time and by how much, correct to 1 decimal place. Comment on what this suggests about the overall pace of runners in each race.

   [5 marks]

   Total for question 4: 13 marks

End of questions