Statistics worksheet — GCSE Higher

1.Two classes sat the same test. The 30 pupils in Class A had a mean mark of 72. The 20 pupils in Class B had a mean mark of 82. Work out the mean mark of all 50 pupils.

2.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.

3.A scatter graph of the number of hours, x, that pupils revised against their test score, y, has the line of best fit y = 2.5x + 15. Amelia wants a score of at least 80. Work out the least whole number of hours of revision the line of best fit suggests she needs.

4.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.

5.The heights, h cm, of 80 plants are grouped like this: 0 ≤ h < 20, 14 plants; 20 ≤ h < 40, 22 plants; 40 ≤ h < 50, 16 plants; 50 ≤ h < 80, 28 plants. Write down the class interval that contains the lower quartile.

6.The number of pets owned by each of 19 pupils in a class is recorded: 0 pets — 7 pupils, 1 pet — 3 pupils, 2 pets — 4 pupils, 3 pets — 5 pupils. Work out the median number of pets.

7.A scatter graph shows the height, x cm, and the mass, y kg, of 20 pupils in Year 10. The heights on the graph run from 150 cm to 180 cm, and the line of best fit is y = 0.9x − 85. Nadia puts x = 90 into this equation to estimate the mass of a two-year-old child who is 90 cm tall. Is her estimate reliable? Give a reason for your answer.

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 masses, m kg, of 60 parcels are grouped like this: 0 ≤ m < 5, 22 parcels; 5 ≤ m < 10, 20 parcels; 10 ≤ m < 20, 9 parcels; 20 ≤ m < 30, 5 parcels; 30 ≤ m < 50, 4 parcels. Write down the class interval that contains the median mass.

10.A gym draws a histogram of the times, t minutes, that its members spend on one machine. The bar for 0 ≤ t < 10 has a frequency density of 1.8 per minute, the bar for 10 ≤ t < 25 has a frequency density of 3.2 per minute, and the bar for 25 ≤ t < 55 has a frequency density of 0.9 per minute. Members who spend 10 minutes or more on the machine pay an extra charge. Work out the number of members who pay the extra charge.

11.Priya travels to work by one of two routes and records her journey times, in minutes, over several weeks. Route 1 has a median of 34 minutes and an interquartile range of 22 minutes. Route 2 has a median of 41 minutes and an interquartile range of 6 minutes. Priya wants the more reliable route for getting to an important meeting on time. Which route should she choose, and why?

12.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.

13.There are 10,000 pupils in a city. A researcher picks a sample of 500 of them by drawing names at random from a list of every pupil in the city. Give the reason why this method gives a representative sample.

14.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.

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.