Statistics worksheet — GCSE Foundation

1.Grace asked 12 children how many brothers and sisters they have. Her results, in order, were 0, 0, 1, 1, 1, 1, 2, 2, 3, 3, 4, 6. Work out the median number of brothers and sisters.

2.There are 10,000 pupils in a city. A researcher picks a sample of 500 of them by drawing names at random from a list of every pupil in the city. Give the reason why this method gives a representative sample.

3.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.

4.A vertical line chart shows the number of goals scored by a football team in each of its 20 matches: 0 goals in 4 matches, 1 goal in 7 matches, 2 goals in 6 matches and 3 goals in 3 matches. Write down the modal number of goals.

5.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.

6.A line graph shows the temperature in a greenhouse at the end of each of six hours. The six readings were 10 °C, 14 °C, 18 °C, 22 °C, 26 °C and 30 °C. Describe the trend shown by the line graph.

7.A sports club has 300 women members and 200 men members, 500 members in total. The club committee wants to choose a sample of 40 members that is in proportion to the club's membership. Work out how many women should be in the sample.

8.A vet records the weights, in kilograms, of 7 dogs, in the order she weighs them: 18, 12, 50, 10, 20, 14, 16. Work out the median weight.

9.A gym in Cardiff has a scatter graph of the number of training sessions, x, attended by each member and the weight lost, y kg. The line of best fit is y = 0.4x + 1. Members want to lose at least 9 kg. Using the line of best fit, work out the least whole number of sessions needed to reach this target.

10.In a scatter graph of the age, in years, and the wingspan, in cm, of 20 birds of the same species, all the points lie close to a rising line of best fit except one, which lies a long way below the line. That bird was later found to have a damaged wing. Give a reason why this point should not be used when drawing the line of best fit.

11.A scatter graph has 12 plotted points. Four pupils each draw a line of best fit on the same graph and count how many of the 12 points lie above their line and how many lie below it: Amir — 10 above, 2 below. Priya — 6 above, 6 below. Kofi — 2 above, 10 below. Leah — 0 above, 12 below. Write down the name of the pupil whose line was drawn correctly, so that the points are roughly balanced above and below it.

12.A shop sold seven pairs of shoes in these sizes: 4, 4, 5, 6, 6, 6, 9. Write down the modal size.

13.A composite (stacked) bar for a charity bake sale in Durham shows the number of cakes sold, split into three types. The bar has a total height of 80 cakes: 34 were sponge cakes, 26 were chocolate cakes and the rest were fruit cakes. Work out the percentage of the cakes sold that were fruit cakes.

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