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Mean, Median, Mode & Range

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Short answer

Mean = sum ÷ count. Median = middle value when sorted. Mode = most-frequent value(s). Range = max − min.

Numbers

List of numbers

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Calculation method, coverage and version

Inputs used: List of numbers.
Calculation approach: The calculator applies the rules and assumptions described in “How it works” to the values you enter. Rounding can cause small differences from an official or provider calculation.
Coverage: Maths. UK nations, tax treatment, local rules and provider criteria can differ; check the official sources shown below before acting.
Content version: No page-specific review date is currently published. Treat the result as indicative and verify current rules independently.

Not included unless explicitly requested: personal circumstances not entered, provider discretion, future rule changes, professional fees and case-specific exceptions. Read the full calculator methodology.

How it works

The four central tendency measures answer different questions about your data — mean is the arithmetic average, median is the middle value (less affected by outliers), mode is the most common value, and range is the spread.

Worked example

4, 8, 15, 16, 23, 42 → Mean 18, Median 15.5, no Mode, Range 38.

Who should use this

•Students working through statistics homework
•Anyone summarising survey or test results

Common mistakes

×Forgetting that the median needs the data to be sorted
×Reporting mean when outliers make median more meaningful

Frequently asked questions

When should I use median instead of mean?▾

When data has extreme outliers (e.g. salaries, house prices), median better represents 'typical'.

Can there be more than one mode?▾

Yes — if two or more values tie for most frequent, the data is bimodal or multimodal.

Related calculators

Standard Deviation Calculator →Percentage Calculator →