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Maths · KS3 and GCSE · Interactive lesson

Mean, median, mode and range

Change a small data set. Share totals, order values and count repeats to understand what each summary tells you.

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Start with the idea, then use the method when you are ready. Changing these settings changes the example. Your current practice question is kept.

Start with the idea explains the basics. Use the method builds on them with more detail.

KS3 / GCSE foundations. Start with small lists. The examples include even-sized lists, repeated values and unusual values.

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KS3 / GCSE · start with the idea

By the end of this lesson: Find and explain the mean of a small data set.

The interactive diagram and controls are in Stage 2, “Explore one example”. Read the idea here, then try it next.

The idea in small steps
  • Mean = total ÷ number of values.
  • The mean is the value each item would have if the total were shared equally.
  • Every value contributes to the total used for the mean.
What do the words mean?
Mean
The total shared equally between all the values.
Median
The middle value of an ordered list, or the mean of its middle two values.
Mode
The value or values occurring most often; if none repeats, there is no mode here.
Frequency
How many times a value appears in the data.
Range
Largest value minus smallest value. It describes spread, not an average.
Outlier
A value that lies unusually far from the others in its context.

Change the example

Something to try

Change just the orange value. Compare the ordered list and the result. Why does this measure change, or stay the same?

Notice what changes

Data: 2, 4, 6, 8, 10. mean: 6.Values: 2, 4, 6, 8, 10246810In order: 2, 4, 6, 8, 10Total 30 shared between 5: 6
Mean: 6
About this model

The bars show individual values, not a frequency table; their vertical scale stays fixed. Orange marks the value you can change. A mean or median need not be a value in the original list.

The example you chose
Data: 2, 4, 6, 8, 10. mean: 6.Values: 2, 4, 6, 8, 10246810In order: 2, 4, 6, 8, 10Total 30 shared between 5: 6

Mean: 6

Still picture of the example from Stage 2. Use the back arrow to change it.

Work through it

Starting example: read the steps below

  1. Add all 5 values: 2 + 4 + 6 + 8 + 10 = 30.
  2. There are 5 values, including any zeros.
  3. Share the total equally: 30 ÷ 5 = 6.
  4. Check: 6 × 5 = 30.

Try on your own

Your turn. No rush.

Question 1

Find the mean of these 5 values: 12, 0, 7, 5, 1.

Enter a number or fraction, such as −3, 0.75 or 3/4. You can include the matching unit shown above. If rounding is needed, the question tells you how many decimal places to use.

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Can you explain how to find the mean and what it tells you about the list?

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Useful starting points
Useful starting pointsSharing a total equally
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Notes for parents and tutors

These lessons cover selected KS3 and GCSE ideas for England; they are not a complete course. The level notes explain where GCSE methods or optional extensions begin. Maurice can help you choose material for your course and exam board.

The content draws on the DfE Maths curriculum, DfE Science curriculum and AQA GCSE Physics specification. Level labels are guidance, not exam-board endorsements. For AQA Radioactivity, calculating net decline as a ratio is Higher-tier work. Net means the overall change; ask Maurice whether this extension is relevant to your course. Explanations and practice were reviewed during development on 21 October 2026; Maurice should check their fit before assigning work.

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