Statistics worksheet — GCSE Higher

1.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.

2.In a histogram of the distances, d metres, thrown by some athletes, the bar covering 20 ≤ d < 60 has a constant frequency density of 1.8 per metre. Estimate the number of throws of at least 20 metres but less than 35 metres.

3.A teacher records the number of pets owned by each of 25 pupils in a class; each pupil owns 0, 1, 2, 3 or 4 pets. The teacher wants to show how many pupils own each number of pets. Write down the most suitable type of chart for this data, and give a reason for your answer.

4.In a scatter graph of the age, in years, and the wingspan, in cm, of 20 birds of the same species, all the points lie close to a rising line of best fit except one, which lies a long way below the line. That bird was later found to have a damaged wing. Give a reason why this point should not be used when drawing the line of best fit.

5.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.

6.The 120 pupils in Year 11 at a school sat a maths test. Their marks m are grouped into classes of unequal width: 0 ≤ m < 40, 12 pupils; 40 ≤ m < 60, 24 pupils; 60 ≤ m < 70, 36 pupils; 70 ≤ m ≤ 100, 48 pupils. A histogram is drawn for these data. Work out the frequency density of the class 40 ≤ m < 60.

7.A histogram is drawn for the masses, m grams, of 200 letters. The bar for 0 ≤ m < 50 has a frequency density of 1.2 per gram and the bar for 50 ≤ m < 100 has a frequency density of 1.8 per gram. All the remaining letters lie in the class 100 ≤ m < 200. Work out the frequency density of the bar for 100 ≤ m < 200.

8.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.

9.In a histogram of the times, t minutes, taken by some people to complete a task, the class 15 ≤ t < 30 contains 24 people. Work out the frequency density for this class.

10.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.

11.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.

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

13.A frequency polygon for the mass, in kg, of 40 parcels at a delivery depot is drawn by plotting one point at the midpoint of each class, joined by straight lines: (5, 6), (15, 10), (25, 16), (35, 6), (45, 2). Every class has a width of 10 kg. Write down the modal class.

14.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.

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.