Statistics worksheet — GCSE Higher

1.A council wants to find out what all residents of a town think about a new cycle lane. It posts a survey only on its website and asks people to fill it in online. Give a reason why this sample is likely to be biased.

2.A histogram shows the times, t minutes, taken by 120 visitors to complete an escape room. The bar for 0 ≤ t < 10 has a frequency density of 5 visitors per minute, the bar for 10 ≤ t < 20 has a frequency density of 2 visitors per minute, the bar for 20 ≤ t < 40 has a frequency density of 1.5 visitors per minute, and the bar for 40 ≤ t < 60 has a frequency density of 1 visitor per minute. Work out which class contains the median time.

3.The delivery times, in minutes, of 15 parcels are given in order: 5, 8, 10, 12, 14, 15, 17, 19, 21, 23, 25, 27, 29, 31, 34. Work out the interquartile range of these times.

4.A town council wants to find out about the eating habits of the people who live in the town. It asks only the members of a local sports club. Give a reason why this sample is biased.

5.A box plot for the ages of 40 members of a gym is drawn from this five-number summary: minimum 15, lower quartile 22, median 29, upper quartile 38, maximum 61. Work out the interquartile range shown by this box plot.

6.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.

7.In a histogram of the masses, m grams, of some pebbles, the bar for the class 50 ≤ m < 80 has a frequency density of 2.4 per gram. Work out the number of pebbles in this class.

8.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.

9.The mean of the four numbers 10, 15, 20 and x is 18. Work out the value of x.

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

11.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.

12.Marta is drawing a cumulative frequency diagram for the times, t seconds, of 100 telephone calls. The grouped frequencies are: 0 ≤ t < 10, 7 calls; 10 ≤ t < 20, 19 calls; 20 ≤ t < 30, 34 calls; 30 ≤ t < 40, 40 calls. Write down the coordinates of the point Marta should plot for the class 20 ≤ t < 30.

13.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.

14.A stacked bar for one day at a café in Norwich shows total drink sales of 50 drinks, split into three parts: 22 were tea, 15 were coffee and the rest were hot chocolate. Work out the number of hot chocolates sold.

15.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.