Statistics worksheet — GCSE Foundation

1.A random sample of 50 pupils at a school were asked whether they prefer sport to music. 30 of the 50 pupils said they prefer sport. The school has 500 pupils altogether. Work out an estimate for the number of the 500 pupils who prefer sport.

2.A café owner in Brighton records the midday temperature, x °C, and the number of hot chocolates sold, y, on 12 days. The temperatures recorded run from 4 °C to 18 °C, and the line of best fit is y = −3x + 74. The forecast for tomorrow gives a midday temperature of 12 °C. Work out the number the line of best fit predicts, and write down how much confidence the owner can have in it.

3.The seven members of Team A took 20, 21, 22, 23, 24, 25 and 40 seconds to finish a task. The seven members of Team B took 20, 30, 32, 34, 36, 38 and 40 seconds. Tomás says that because the two teams have the same range, their times are spread out in the same way. Is Tomás right? Give a reason for your answer.

4.Amelia's mean mark over four tests is 29. Her first three marks are 31, 26 and 26. Work out her fourth mark.

5.A study found that people who drink more coffee tend to concentrate better at work. A coffee company says that this shows that drinking coffee improves concentration. Give the reason why this conclusion cannot be drawn.

6.A charity shop in Bath holds 2,000 books. Volunteer A checks a random sample of 50 books and finds 35 paperbacks. Volunteer B checks a different random sample of 50 books and finds 31 paperbacks. Work out the estimate each sample gives for the whole stock, and write down what the shop should do next.

7.Work out the median of these five numbers: 2, 4, 7, 12, 26

8.A shop recorded the number of books it sold on five days: 100, 40, 70, 20, 60. Work out the range of the numbers of books sold.

9.A pie chart shows the favourite sport of the 40 pupils in a class: football 50%, netball 25%, tennis 15% and swimming 10%. Work out how many pupils chose football.

10.The masses of eight school bags, in kilograms, are 3, 4, 4, 5, 6, 7, 8 and 11. Work out the median mass.

11.A bus company runs two routes into the centre of Exeter. On ten weekdays the journey time on Route 1 was, in minutes: 22, 23, 24, 24, 25, 25, 26, 26, 27 and 28. On Route 2 it was: 18, 19, 20, 20, 21, 22, 26, 30, 36 and 38. A commuter must reach the centre on time every day. Work out the mean and the range for each route, and write down which route she should take.

12.The number of pets owned by each of 19 pupils in a class is recorded: 0 pets — 7 pupils, 1 pet — 3 pupils, 2 pets — 4 pupils, 3 pets — 5 pupils. Work out the median number of pets.

13.A survey of 25 pupils in Derby records how many siblings each has: 0 siblings — 6 pupils, 1 sibling — 10 pupils, 2 siblings — 6 pupils, 3 siblings — 3 pupils. Calculate the mean number of siblings.

14.A school has 1,000 pupils. A student wants to estimate how many of them walk to school, so she asks 8 pupils in her own class. She says her sample is large enough to give a reliable estimate for the whole school. Is she right? Give a reason for your answer.

15.Priya wants to find out the favourite sport of the 900 pupils at her school. She asks 5 pupils, chosen at random. Give a reason why her sample may not give a reliable result.