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Year 7 · Key Stage 3 · free KS3 maths worksheet

Averages

12 original questions, 37 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 seven numbers.

3  7  7  4  9  7  2

Write down the mode of these numbers.

1 mark
Show answer
7
2

Here are four numbers.

6  11  9  14

Work out the mean of these numbers.

2 marks
Show answer
10
3
  1. Find the median of these numbers.
    14   9   21   11   17   9   12
  2. Here are the heights, in cm, of six pupils. Find the median height.
    152   147   160   155   149   158
3 marks
Show answer
a) 12 b) 153.5 cm
4

A shoe shop records the sizes of the last eight pairs of trainers it sold.

5  7  6  5  8  5  9  6

  1. Write down the modal shoe size.
  2. Work out the range of the shoe sizes.
3 marks
Show answer
a) 5 b) 4
5

A group of Year 7 pupils and a group of Year 8 pupils did the long jump.

MedianRange
Year 72.9 m1.2 m
Year 83.3 m0.8 m

Make two comparisons between the long jumps of the two year groups.

2 marks
Show answer
Year 8 jumped further on average (higher median). Year 8 were more consistent (smaller range).
6

Seven friends write down how much pocket money they get each week.

£5   £8   £6   £10   £5   £7   £15

  1. Work out the mean, the median, the mode and the range.
  2. Which average best represents the pocket money of the friends? Give a reason for your answer.
4 marks
Show answer
a) mean £8, median £7, mode £5, range £10 b) The median: the mean is pulled up by the £15, and the mode is the lowest amount
7

Here are the numbers of goals scored by Ayo and Ben in their last six football matches.

Ayo213222
Ben051402
  1. Work out the mean and the range for each player.
  2. The coach wants a player who scores steadily every match. Which player should she choose? Give a reason.
4 marks
Show answer
a) Ayo: mean 2, range 2. Ben: mean 2, range 5 b) Ayo: the means are the same, but Ayo has the smaller range so he is more consistent
8

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
9

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
10

20 pupils each timed how long it took them to solve a puzzle.

Time (t seconds)Frequency
0 < t ≤ 103
10 < t ≤ 208
20 < t ≤ 306
30 < t ≤ 403
  1. Write down the modal class.
  2. Work out an estimate for the mean time.
  3. Why is your answer to part (b) only an estimate?
4 marks
Show answer
a) 10 < t ≤ 20 b) 19.5 seconds c) we do not know the exact times, so we use the midpoint of each class
11

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
12
  1. Three cards each have a whole number on them. The mode of the numbers is 5 and the mean is 6. Work out the three numbers.
  2. Three different cards each have a whole number on them. The median is 7, the range is 6 and the mean is 7. Work out the three numbers.
4 marks
Show answer
a) 5, 5, 8 b) 4, 7, 10

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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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