Statistics worksheet — GCSE Foundation

1.A café in York counts the number of customers in each of the nine hours it is open on one day: 4, 4, 4, 11, 13, 15, 18, 22 and 25. The owner says that a typical hour has about 4 customers, because 4 is the mode. Is the owner right? Give a reason for your answer.

2.Ben and Chloe each sat five maths tests. Ben's marks were 62, 64, 65, 66 and 68. Chloe's marks were 40, 52, 65, 78 and 90. Both pupils have a mean mark of 65. Their teacher says the mean on its own does not describe the two sets of marks well. Give a reason why the teacher is right.

3.A scatter graph plots the number of years, x, that 20 employees have worked at a company against their salary, y. All the plotted points lie between x = 1 and x = 15. Write down the word used to describe an estimate for y made using a value of x that lies between 1 and 15.

4.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.

5.A school has 1,500 pupils. The head teacher takes a random sample of 150 of them from the school register and asks how long they spend on homework. Rory says the sample is too small for the result to mean anything. Is Rory right? Give a reason for your answer.

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.A scatter graph plots the shoe size and the spelling test score of 25 pupils. The points are scattered with no pattern across the graph. Write down the type of correlation shown.

8.A Year 10 class has 20 boys with a mean height of 150 cm and 10 girls with a mean height of 168 cm. Work out the mean height of all 30 pupils in the class.

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

10.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.

11.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.

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

13.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.

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

15.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.