Statistics worksheet — GCSE Foundation

1.A scatter graph shows the height, x cm, and the mass, y kg, of 20 pupils in Year 10. The heights on the graph run from 150 cm to 180 cm, and the line of best fit is y = 0.9x − 85. Nadia puts x = 90 into this equation to estimate the mass of a two-year-old child who is 90 cm tall. Is her estimate reliable? Give a reason for your answer.

2.A town council wants to find out about the eating habits of the people who live in the town. It asks only the members of a local sports club. Give a reason why this sample is biased.

3.Four pairs of variables are listed below. Write down the pair that you would expect to show no correlation.

4.A vet records the masses, m kg, of 30 dogs at a clinic in Preston: 0 < m ≤ 10 — 11 dogs, 10 < m ≤ 20 — 5 dogs, 20 < m ≤ 30 — 5 dogs, 30 < m ≤ 40 — 9 dogs. Work out an estimate for the mean mass, in kg, using the midpoint of each class interval.

5.A sports centre in Ipswich has 2,000 members. It wants to know what its members think of its opening hours, so it asks a random sample of 100 of them. Write down what the population is in this survey.

6.A company makes 50,000 light bulbs a day and wants to check how long they last before they fail. Testing a bulb to find out how long it lasts destroys it. Give a reason why the company should test a sample of bulbs rather than every bulb it makes.

7.A two-way table records the favourite subject, Maths or Art, of 60 pupils in Year 10, and whether each pupil is left-handed or right-handed. 9 of the 60 pupils are left-handed, and 6 of those left-handed pupils prefer Art. In total, 24 of the 60 pupils prefer Art. A pupil is chosen at random from the 60. Work out the probability that the pupil is right-handed and prefers Art.

8.A company found that the higher the price it charged for a product, the lower the satisfaction score its customers gave. The price and the satisfaction score are plotted on a scatter graph. Describe the line of best fit that would be drawn on that graph.

9.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.

10.A vertical line chart shows the number of pets owned by each pupil in a class: 0 pets — 5 pupils, 1 pet — 4 pupils, 2 pets — 3 pupils, 3 pets — 3 pupils. Work out the total number of pupils in the class.

11.A pie chart shows how 180 shoppers at a supermarket paid for their shopping. The sector for card payments has an angle of 90° at the centre. Work out how many of the 180 shoppers paid by card.

12.A scatter graph has 50 points. Most of them lie close to a rising line of best fit, but two of them lie a long way from that line. Write down how those two points should be treated.

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.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.

15.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.