Statistics worksheet — GCSE Higher

1.The mean of 5 numbers is 8. Work out the total of the 5 numbers.

2.A pictogram shows the number of cars sold by a garage in Plymouth each month, where each whole car symbol represents 8 cars sold and a half symbol represents 4 cars. March shows 3 whole symbols and one half symbol. Work out how many cars were sold in March.

3.The marks scored by 11 pupils in a test are given in order: 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42. Work out the lower quartile of these marks.

4.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.

5.An estate agent in Leeds lists the prices of the five houses sold on one street last year: £170,000, £150,000, £580,000, £140,000 and £160,000. A newspaper wants to print one figure for a typical price on this street. Work out the mean and the median, and write down which figure the newspaper should print.

6.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.

7.The times, in seconds, taken by 11 runners to finish a race are given in order: 40, 42, 45, 47, 50, 52, 55, 58, 60, 63, 65. Work out the upper quartile of these times.

8.A dual bar chart shows the number of hours of rain recorded in Leeds and in Bristol on each of four days. Leeds: Monday 3 hours, Tuesday 5 hours, Wednesday 2 hours, Thursday 4 hours. Bristol: Monday 4 hours, Tuesday 4 hours, Wednesday 6 hours, Thursday 2 hours. Work out the greatest amount, in hours, by which Bristol's rainfall exceeded Leeds's rainfall on a single day.

9.The mean of the numbers x, 20 and 30 is equal to the mean of the numbers 15 and 25. Work out the value of x.

10.Four pairs of variables are listed below. Write down the pair that you would expect to show negative correlation.

11.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.

12.A sports shop in Cardiff sold 40 pairs of football boots last month: 4 pairs of size 6, 5 pairs of size 7, 8 pairs of size 8, 13 pairs of size 9 and 10 pairs of size 10. The manager will order 40 pairs for next month and wants as many pairs as possible to be in a size customers will buy. Work out the mean size and the modal size, and write down which of the two he should use.

13.A shop compares customer waiting times, in minutes, at two branches over one week. Branch A had a median of 12 minutes and an interquartile range of 5 minutes. Branch B had a median of 9 minutes and an interquartile range of 11 minutes. Compare the waiting times at the two branches.

14.A scatter graph shows the midday temperature, x °C, and the number of ice creams sold at a seaside kiosk, y. The line of best fit is y = 3x − 20. Give a reason why the y-intercept of this line of best fit is not a sensible estimate of the number of ice creams sold.

15.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.