Statistics worksheet — GCSE Foundation

1.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.

2.Four books have 120, 200, 160 and 80 pages. Work out the mean number of pages.

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

4.A bar chart is drawn for a set of categorical data. Write down what the height of each bar represents.

5.A council wants to find out what all residents of a town think about a new cycle lane. It posts a survey only on its website and asks people to fill it in online. Give a reason why this sample is likely to be biased.

6.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.

7.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.

8.A sector of a pie chart stands for 25% of the data. Work out the angle at the centre of that sector.

9.A garden centre records its total sales, in pounds, at the end of each of the twelve months of one year, to see how sales change over time. Write down the most suitable type of chart to show this time series data.

10.A council in Leeds wants to know what local people think about letting shops stay open later in the evening. It rings landline telephone numbers between 10 am and 2 pm on a Tuesday. Write down which group is most likely to be under-represented in the sample, and give a reason for your answer.

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

12.For each of 30 fires in one county, the number of fire engines sent and the cost of the damage were recorded. The scatter graph of the data shows strong positive correlation. A newspaper prints the headline "Sending more fire engines causes more damage". Is the newspaper right? Give a reason for your answer.

13.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.

14.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.

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.