Robinson Tuition
Year 8 · Key Stage 3 · free KS3 maths worksheet

Averages and statistical measures

12 original questions, 44 marks. Type your answers below for an instant mark and a score (algebra in any equivalent form, e.g. 2sqrt(3) or 2√3), or print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

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The questions

1

Here are the numbers of goals a netball team scored in 9 matches.

14   9   17   12   9   20   11   9   16

Work out

  1. the mode
  2. the median
  3. the mean
  4. the range
4 marks
Show answer
a) 9 b) 12 c) 13 d) 11
2

The table shows the shoe sizes of the students in a year group.

Shoe sizeFrequency
45
59
612
78
86
  1. Write down the modal shoe size.
  2. Work out the number of students in the year group.
  3. Work out how many students have a shoe size of 7 or larger.
3 marks
Show answer
a) 6 b) 40 c) 14
3

The table shows the number of children in each of 20 families.

Number of childrenFrequency
03
18
26
33

Work out the mean number of children per family.

3 marks
Show answer
1.45
4

The table shows the number of pets owned by each of the 25 pupils in class 8B.

Number of petsFrequency
06
18
25
34
42
  1. Work out the median number of pets.
  2. Work out the mean number of pets.
  3. Work out the range.
4 marks
Show answer
a) 1 b) 1.52 c) 4
5

The table shows information about the time, t minutes, that 30 customers waited at a garage.

Time (t minutes)Frequency
0 < t ≤ 104
10 < t ≤ 209
20 < t ≤ 3012
30 < t ≤ 405

Work out an estimate for the mean waiting time.

3 marks
Show answer
21 minutes
6

Year 8 grew 30 sunflowers. The table shows information about their heights, h cm.

Height (h cm)Frequency
0 < h ≤ 503
50 < h ≤ 1007
100 < h ≤ 15012
150 < h ≤ 2008
  1. Write down the modal class.
  2. Write down the class interval that contains the median.
  3. Work out an estimate for the mean height. Give your answer to 1 decimal place.
4 marks
Show answer
a) 100 < h ≤ 150 b) 100 < h ≤ 150 c) 116.7 cm
7

Class 8R did a spelling test. Their mean score was 34 and the range was 18.

Here are the scores of the 6 pupils in a small group from class 8T.

28   41   35   30   39   37

  1. Work out the mean and the range of the 8T scores.
  2. Make two comparisons between the scores of 8R and the scores of the 8T group.
4 marks
Show answer
a) mean 35, range 13 b) 8T higher mean so better on average; 8T smaller range so more consistent
8

Here is the weekly pocket money of 7 friends.

£5   £6   £6   £6   £8   £9   £30

  1. Work out the mean.
  2. Work out the median.
  3. Zak says, "The mean is the best average to show how much pocket money these friends usually get." Explain why Zak is wrong.
4 marks
Show answer
a) £10 b) £6 c) £30 is an outlier that makes the mean too high; the median is better
9

The mean of 8 numbers is 12.

The mean of 5 of these numbers is 9.

Work out the mean of the other 3 numbers.

3 marks
Show answer
17
10

Freya plays six rounds of a quiz. Her mean score for the six rounds is 15.

Here are her scores for the first five rounds.

12  18  9  21  14

Work out her score in the sixth round.

4 marks
Show answer
16
11

The table shows the number of items bought by each of 40 customers at a corner shop.

Number of itemsFrequency
112
215
39
44
  1. Work out the mean number of items bought per customer.
  2. Kai says, "The mode is 15." Explain the mistake Kai has made.
4 marks
Show answer
a) 2.125 b) Kai has given the largest frequency instead of the data value; the mode is 2
12

The table shows information about the lengths, l cm, of 40 courgettes grown on an allotment.

Length (l cm)Frequency
10 < l ≤ 206
20 < l ≤ 3011
30 < l ≤ 4013
40 < l ≤ 5010
  1. Write down the class interval that contains the median.
  2. Work out an estimate for the mean length.
4 marks
Show answer
a) 30 < l <= 40 b) 31.75 cm

Your score

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Every question here is original and written by Robinson Tuition. It follows the Key Stage 3 programme of study; Year 9 sheets end with extension questions for top sets.

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