Statistics worksheet — GCSE Higher

1.Work out the median of these six numbers: 13, 21, 22, 36, 37, 47

2.A scatter graph shows the number of hours of sunshine, x, and the number of visitors, y, at an outdoor swimming pool in Torquay on each of 15 days. The line of best fit passes through the points (5, 150) and (15, 350). Work out the estimated number of visitors on a day with 8 hours of sunshine, using the line of best fit.

3.Box plots summarise the test scores of two classes. Class X: minimum 20, lower quartile 45, median 60, upper quartile 70, maximum 95. Class Y: minimum 35, lower quartile 50, median 58, upper quartile 65, maximum 80. Which statement about the two classes is correct?

4.A school has 1200 pupils. A teacher wants to take a random sample of 60 of them. Write down which of these methods gives a random sample.

5.The seven members of Team A took 20, 21, 22, 23, 24, 25 and 40 seconds to finish a task. The seven members of Team B took 20, 30, 32, 34, 36, 38 and 40 seconds. Tomás says that because the two teams have the same range, their times are spread out in the same way. Is Tomás right? Give a reason for your answer.

6.The weekly wages of the five people who work at a small garage in Norwich are £420, £440, £460, £480 and £1,500. Write down which average better describes a typical wage at this garage, and give a reason for your answer.

7.A two-way table records whether each of the 30 pupils in a class passed maths and whether they passed science. 18 pupils passed maths, 12 pupils passed science and 8 pupils passed both. Work out how many pupils passed at least one of the two subjects.

8.A scientist has grouped the lifetimes, in hours, of 300 batteries into classes of unequal width. She wants a diagram in which the number of batteries in a class is given by the area of its bar. Write down the type of diagram she should draw.

9.Two classes at a school in Coventry sit the same maths test, out of 20 marks. Class A has a mean mark of 14 and a range of 6. Class B has a mean mark of 14 and a range of 14. Write a sentence comparing the two classes, using the mean and the range.

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

11.A bus company records the delay, d minutes, of 250 buses: 0 ≤ d < 2, 60 buses; 2 ≤ d < 5, 90 buses; 5 ≤ d < 10, 75 buses; 10 ≤ d < 20, 25 buses. The company refunds the fare whenever a bus is more than 8 minutes late. Estimate the number of refunds it must pay.

12.In a histogram of the lengths, x cm, of some rods, the bar for 10 ≤ x < 30 has a frequency density of 3 per cm. The bar for 30 ≤ x < 45 is twice as tall as the bar for 10 ≤ x < 30. Work out the number of rods with a length in the class 30 ≤ x < 45.

13.The times, t minutes, taken by 120 runners to finish a fun run are summarised by these cumulative frequencies: t < 20, 8 runners; t < 30, 26 runners; t < 40, 74 runners; t < 50, 110 runners; t < 60, 120 runners. Work out the number of runners who took 40 minutes or longer to finish.

14.A factory made 3,000 phone cases last week. Shift A checked a random sample of 100 cases and found that 34 were scratched. Shift B checked a different random sample of 50 cases and found that 21 were scratched. Using the COMBINED results from both shifts, work out an estimate for the number of scratched cases made last week.

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