1. 1
   A gym has 900 members, split into three membership tiers: 540 Standard, 270 Premium and 90 Elite. The manager wants to take a sample of 60 members, stratified by membership tier.

   (a)

   How many Premium members should be included in the stratified sample?

   [1 mark]

   • A18
   • B12
   • C15
   • D24

   (b)

   How many Elite members should be included in the stratified sample?

   [1 mark]

   • A4
   • B6
   • C9
   • D12

   (c)

   The manager instead selects every 15th member from an alphabetical list of all 900 members, starting at a randomly chosen member between the 1st and 15th. How many members will be in this systematic sample?

   [1 mark]

   • A45
   • B50
   • C60
   • D75

   Total for question 1: 3 marks

2. 2
   A coffee shop recorded the number of hot drinks sold in each of five hours during a Saturday morning: 9am-10am: 32, 10am-11am: 45, 11am-12pm: 58, 12pm-1pm: 41, 1pm-2pm: 27.

   (a)

   Find the range of the number of hot drinks sold across the five hours.

   [2 marks]

   (b)

   Describe the trend in hot drink sales shown by the data from 9am to 2pm.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A running club recorded the times, in minutes, taken by 9 members to complete a 5 km training run: 22, 23, 24, 24, 25, 26, 27, 29, 35.

   (a)

   Calculate the mean time and the median time for the group.

   [3 marks]

   (b)

   One member, who ran in 35 minutes, believes this time is unusually high compared with the rest of the group. Compare the range of all 9 times with the range of the remaining 8 times (excluding 35), and comment on whether removing this time significantly changes the spread of the data.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A phone company measured the battery life, in hours, of a sample of 40 new phones from a production batch, grouped into a frequency table: 8 to under 10 hours: 5 phones; 10 to under 12 hours: 14 phones; 12 to under 14 hours: 15 phones; 14 to under 16 hours: 6 phones.

   (a)

   Calculate an estimate of the mean battery life for this sample. Show your working.

   [4 marks]

   (b)

   State the modal class. Then estimate the proportion of phones in the sample with a battery life of at least 12 hours, giving your answer as a percentage.

   [4 marks]

   (c)

   The company wants to check whether this sample fairly represents its full production batch of 4000 phones made that day. It plans to select a simple random sample of 40 phones using a random number generator applied to a numbered list of all 4000 phones, and to compare the estimated mean of 12.1 hours found above with the known population mean of 11.4 hours for the full batch. (i) Give one advantage of using simple random sampling here rather than choosing the first 40 phones that come off the production line. (ii) Calculate the percentage difference between the sample mean and the population mean, and comment on whether the sample provides a reasonable estimate.

   [5 marks]

   Total for question 4: 13 marks

5. 5
   A council wants to find out how residents of a town of 12,000 people feel about a new recycling scheme. It selects a sample of 150 residents by choosing every 80th name from the electoral register, starting at a randomly chosen point between 1 and 80.

   (a)

   What is this sampling method called?

   [1 mark]

   • AStratified sampling
   • BSystematic sampling
   • COpportunity sampling
   • DQuota sampling

   (b)

   To be representative, 30% of the town's residents are aged under 30. How many of the 150 sampled residents should be aged under 30?

   [1 mark]

   • A30
   • B38
   • C45
   • D52

   (c)

   Only 105 of the 150 selected residents return their completed questionnaire. What is the response rate, to the nearest whole per cent?

   [1 mark]

   • A60%
   • B65%
   • C75%
   • D70%

   Total for question 5: 3 marks

6. 6
   A car park recorded the number of vehicles entering during each of five consecutive 10-minute periods one morning: 18, 25, 31, 22, 14.

   (a)

   Find the range of the number of vehicles entering across the five periods.

   [2 marks]

   (b)

   The car park manager wants to display this data to show the changing pattern of arrivals over time. State the most appropriate type of statistical diagram for this purpose, and give one reason for your choice.

   [2 marks]

   Total for question 6: 4 marks

7. 7
   A cafe tracked the waiting time, in minutes, for 8 customers during a lunch rush: 3, 4, 4, 5, 6, 6, 7, 21.

   (a)

   Calculate the interquartile range (IQR) of the waiting times.

   [3 marks]

   (b)

   One customer waited 21 minutes due to a till malfunction that is not typical of normal service. Calculate the mean waiting time, and explain why the median is a more appropriate average than the mean to describe a typical waiting time for this data set.

   [3 marks]

   Total for question 7: 6 marks

8. 8
   A supermarket recorded the amount spent, in pounds, by a sample of 50 customers at the checkout, grouped into a frequency table: £0 to under £20: 8 customers; £20 to under £40: 19 customers; £40 to under £60: 15 customers; £60 to under £80: 8 customers.

   (a)

   Calculate an estimate of the mean amount spent per customer.

   [4 marks]

   (b)

   Estimate the percentage of customers who spent less than £40.

   [4 marks]

   (c)

   The manager wants to compare this weekday sample with a Saturday sample, where the estimated mean spend was £45.60 from a systematic sample of every 20th customer through the till between 9am and 5pm. (i) Give one reason why a systematic sample taken only between 9am and 5pm might not fairly represent all Saturday customers. (ii) Using your estimate of £39.20 from part (a), calculate the percentage increase in mean spend from the weekday sample to the Saturday sample.

   [5 marks]

   Total for question 8: 13 marks

End of questions