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Grade 2 · Foundation · free GCSE maths worksheet

Mode, median and range

Averages and spread from a small list.

14 original questions, 38 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

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

The stem and leaf diagram shows the masses, in grams, of some tomatoes.

StemLeaves
21  4  6
30  2  5  8
43  7

Key: 2 | 1 = 21 grams

Find the range of the masses.

2 marks
Show answer
26 grams
3

Here are five numbers.

3, 5, 8, 9, 12

Write down the median.

1 mark
Show answer
8
4

Here are five numbers.

12  5  19  8  3

Work out the range of these numbers.

1 mark
Show answer
16
5

Seven children have these ages.

12, 9, 15, 11, 9, 14, 10

Work out the median age.

2 marks
Show answer
11
6

A shoe shop wants to know which size to order the most of. Here are the sizes of the shoes sold in one hour.

5, 6, 6, 7, 6, 5, 8, 6, 7

Which average should the shop use: mode, median or mean? Give your answer and work it out.

2 marks
Show answer
mode, 6
7

Here are the scores of six players in a game.

6, 3, 8, 5, 9, 2

Work out the median score.

2 marks
Show answer
5.5
8

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
9

23 pupils were asked how many brothers and sisters they have. The bar chart shows the results.

  1. Write down the mode.
  2. Work out the median.
  3. Write down the range.
01234012345678910Number of brothers and sistersFrequency
4 marks
Show answer
a) 1 b) 1 c) 4
10

20 pupils were asked how many goals they scored in one match. The table shows the results.

Goals01234
Number of pupils46532
  1. Write down the mode.
  2. Write down the range.
  3. Work out the median.
4 marks
Show answer
a) 1 b) 4 c) 1.5
11

Five friends write down how much money (in £) they have saved.

4, 5, 5, 6, 80

Zainab says, "The mean is the best average to show a typical amount."

  1. Work out the mean.
  2. Work out the median.
  3. Which average is better to show a typical amount? Give a reason.
4 marks
Show answer
a) £20 b) £5 c) median, because 80 is much bigger than the others
12

Ten cards each have a number written on them:

2  3  3  5  5  5  7  8  8  9

  1. Write down the mode of the numbers.
  2. One card is picked at random. Find the probability that the number on the card is greater than 7.
3 marks
Show answer
a) 5 b) 3/10
13

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
14

Some pupils counted the goals scored in each of 20 matches. The frequency table shows the results.

Goals01234
Number of matches35624

The bars for 0 goals and 1 goal are already drawn on the chart.

  1. Complete the bar chart.
  2. Write down the mode.
  3. Work out the median.
  4. Work out the range.
01234012345678GoalsNumber of matches
5 marks
Show answer
a) bars of height 6, 2 and 4 for 2, 3 and 4 goals b) 2 c) 2 d) 4

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.

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