A shoe shop records the sizes of the last eight pairs of trainers it sold.
5 7 6 5 8 5 9 6
Write down the modal shoe size.
Work out the range of the shoe sizes.
3 marks
Show answer
a) 5b) 4
2
A hockey team played 25 matches. The table shows the number of goals the team scored in each match.
Goals scored
Frequency
0
4
1
7
2
9
3
3
4
2
Write down the modal number of goals scored.
Work out the total number of goals the team scored in the 25 matches.
3 marks
Show answer
a) 2b) 42
3
The table shows the number of children in each of 20 families.
Number of children
Frequency
0
3
1
8
2
6
3
3
Work out the mean number of children per family.
3 marks
Show answer
1.45
4
24 pupils were asked how many books they read in the summer holidays.
Number of books
Frequency
0
5
1
6
2
7
3
4
4
2
Dev says, "The median is 7 because 7 is the middle frequency."
Explain why Dev is wrong and work out the median number of books.
Work out the total number of books the 24 pupils read.
4 marks
Show answer
a) median = 2; 7 is a frequency, not a number of booksb) 40
5
A small firm has six employees. Their yearly salaries are
£22 000 £24 000 £25 000 £25 000 £27 000 £97 000
The firm wants to advertise a job and tell applicants the "typical" salary.
Work out the mean salary and the median salary.
Which average should the firm use to describe the typical salary? Give a reason for your answer.
4 marks
Show answer
a) mean £36 667, median £25 000b) median, since £97 000 is much bigger than the rest and pulls the mean up
6
There are 10 boys and 15 girls in a class.
The mean score of the 10 boys in a test was 6.2.
The mean score of the 15 girls in the same test was 5.8.
Mr Field says, "The mean score for the whole class was 6."
Show that Mr Field is wrong.
3 marks
Show answer
Whole-class mean = 5.96, not 6
7
The table shows the number of items bought by each of 40 customers at a corner shop.
Number of items
Frequency
1
12
2
15
3
9
4
4
Work out the mean number of items bought per customer.
Kai says, "The mode is 15." Explain the mistake Kai has made.
4 marks
Show answer
a) 2.125b) Kai has given the largest frequency instead of the data value; the mode is 2
8
Two classes, A and B, sat the same maths test. The five-figure summaries of their marks are shown in the table.
Lowest
Lower quartile
Median
Upper quartile
Highest
Class A
12
25
38
46
60
Class B
20
30
38
40
52
Work out the interquartile range for each class.
Compare the marks of the two classes. Refer to the median and the interquartile range in your answer.
4 marks
Show answer
a) Class A 21, Class B 10b) same median (38), so similar average performance; B has the smaller IQR so is more consistent
9
Nine students in Year 7 and nine students in Year 11 ran a race. Here are their times, in seconds.
Year 7: 12 15 15 18 20 21 24 26 28
Year 11: 8 10 13 14 16 19 22 25 27
Compare the times of the Year 7 students with the times of the Year 11 students.
4 marks
Show answer
Year 11 median (16 s) is lower than Year 7 median (20 s), so Year 11 were faster on average; Year 7 range (16 s) is smaller than Year 11 range (19 s), so Year 7 times were more consistent
10
Two cafés each recorded the waiting times, in minutes, of seven customers.
Café X: 4 5 5 6 7 8 9
Café Y: 3 4 4 5 5 6 25
Work out the mean and the range of the waiting times for each café.
Zara says, "Café X is better because its mean waiting time is lower." Work out the median for each café and explain why the median gives a fairer comparison here.
5 marks
Show answer
a) X: mean 6.3, range 5; Y: mean 7.4, range 22b) median X = 6, Y = 5; one extreme wait (25) inflates the mean for Y
11
The table shows information about the times, t seconds, taken by 40 swimmers to complete one length of a pool.
Time (t seconds)
Frequency
20 < t ≤ 30
8
30 < t ≤ 40
15
40 < t ≤ 50
12
50 < t ≤ 60
5
Work out an estimate for the mean time.
Explain why your answer to part (a) is an estimate.
4 marks
Show answer
a) 38.5 secondsb) Because the data is grouped, the exact times are unknown and midpoints are used
12
The table shows information about the distances, d km, that 40 employees travel to work.
Distance (d km)
Frequency
0 < d ≤ 5
9
5 < d ≤ 10
16
10 < d ≤ 15
11
15 < d ≤ 20
4
Work out an estimate for the mean distance travelled.
Write down the modal class.
Work out the fraction of the employees who travel more than 10 km. Give your fraction in its simplest form.
5 marks
Show answer
a) 8.75 kmb) 5 < d <= 10c) 3/8
Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.