Statistics worksheet — GCSE Foundation

1.Five friends have heights, in cm, of 150, 152, 155, 158 and 160. A sixth friend, with a height of 170 cm, joins the group. Write down what happens to the mean and the range of the heights once this sixth friend is included.

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

3.A stem-and-leaf diagram, described in words, shows the ages of 9 people at a family party. The stem is the tens digit: stem 1 has leaves 4 and 8; stem 2 has leaves 0, 3, 5 and 9; stem 3 has leaves 1 and 6; stem 4 has leaf 2. Work out the median age.

4.A quality inspector weighs a random sample of 50 packets of crisps from one day's production and finds their mean mass is 32.4 g. The factory makes 20,000 packets that day. Work out an estimate for the total mass, in kg, of all the packets made that day.

5.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.

6.A scatter graph of the number of ice creams sold at a seaside kiosk in Bournemouth and the number of sunburn cases treated at a nearby pharmacy, recorded on the same 30 days, shows strong positive correlation. Which statement about this correlation is correct?

7.The mean of three numbers is 50. A fourth number, 100, is added to the set. Work out the mean of the four numbers.

8.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.

9.A dual bar chart shows how many boys and how many girls are in a class. The bar for boys stands at 14 and the bar for girls stands at 16. Work out how many pupils are in the class altogether.

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

11.Seven pupils were asked how many books they had read last month. Their answers were 3, 5, 5, 7, 8, 5, 3. Write down the mode.

12.A bar chart shows the number of books borrowed from a school library on each of five days. The bar heights are: Monday 12, Tuesday 18, Wednesday 9, Thursday 15 and Friday 21. Work out the total number of books borrowed over the five days.

13.A café sold 10 sandwiches on each of four days: 10, 10, 10, 10. Work out the range of the numbers sold.

14.Isla wants to find out the favourite television programme of the pupils at her school. She asks only her own close group of friends. Write down what is wrong with her sample.

15.A pie chart of the favourite hobby of a group of pupils has three sectors: reading 50%, sport 25% and music 25%. Write down, as a fraction in its simplest form, the share of the pie chart taken up by the reading sector.