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Mean, median, mode and range: how to work them out

Find the mean, median, mode and range of a data set with clear worked examples, and learn which average to use when there is an outlier.

BeginnerUpdated 5 Nov 2026
KS3GCSEMiddle SchoolHigh School

Curriculum fit: GCSE Maths Statistics (Foundation and Higher). US: Grade 6 and High School Statistics (Interpreting Categorical and Quantitative Data).

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What is it?

Averages describe a typical value in a set of data. The three common averages are the mean, the median and the mode, and the range tells you how spread out the data is.

Each measure suits different situations. For example, the median is often better than the mean when the data contains a very large or very small value.

Key formulas and ideas

  • Mean = sum of all values ÷ number of values.
  • Median = the middle value when the data is in order (or the mean of the two middle values).
  • Mode = the most common value.
  • Range = largest value − smallest value.

Worked examples

Example 1: All four measures

Question: Find the mean, median, mode and range of 3, 5, 5, 7, 10.

  1. Mean: 3 + 5 + 5 + 7 + 10 = 30, and 30 ÷ 5 = 6.
  2. Median: the middle value of the ordered list is 5.
  3. Mode: 5 appears most often.
  4. Range: 10 − 3 = 7.

Answer: Mean 6, median 5, mode 5, range 7

Example 2: Even number of values

Question: Find the median of 2, 4, 6, 8.

  1. There are four values, so the median is halfway between the two middle ones.
  2. The middle values are 4 and 6.
  3. (4 + 6) ÷ 2 = 5.

Answer: 5

Example 3: Effect of an outlier

Question: Data: 4, 5, 6, 5, 40. Which average represents the data better?

  1. Mean = 60 ÷ 5 = 12, which is larger than most values.
  2. Median = 5, which is close to most values.

Answer: The median, because the outlier 40 pulls the mean up

Common mistakes

  • Finding the median without putting the data in order first.
  • Using the middle position instead of the middle value.
  • Confusing the mode with the median.
  • Calculating the range as the difference between two neighbouring values.

Practice questions

1. What is the mean of 2, 4, 4, 6, 9?
2. What is the median of 2, 4, 4, 6, 9?
3. What is the range of 3, 8, 11?
4. What is the mode of 1, 2, 2, 3, 3, 3?
5. Which average is least affected by one extreme value?

Frequently asked questions

When is the median better than the mean?

When there are extreme values (outliers), because they pull the mean up or down but barely affect the median.

Can there be more than one mode?

Yes. If two values are equally common the data is bimodal. If every value appears once there is no mode.

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Sources and review

Reviewed by StudyMorrow editorial review on 5 Nov 2026.