Mean, Median, Mode, Range Calculator
Adjust the inputs below. Results update as you type.
How it works
Mean = sum / count. Median = middle value (sorted). Mode = most frequent (may be none or multiple). Range = max − min. Variance = average squared deviation from mean. Standard deviation = √variance. Population vs. sample SD: divide by N or N−1 respectively. Outliers inflate mean and SD but leave median relatively unaffected—use median for skewed distributions like incomes.
Input guidance
- Check units and decimal placement before running calculations.
- For percentage and ratio tasks, define the baseline value clearly.
- Use rounded output carefully and keep full precision for intermediate steps.
The formula
Mean = sum ÷ count. Median = the middle value (or average of the two middle values) when sorted. Mode = most frequent value. Range = maximum − minimum.
Worked example
For 3, 7, 7, 2, 9: mean = 5.6, median = 7, mode = 7, range = 9 − 2 = 7.
More examples to test
- Baseline example: solve with clean numbers first to verify formula direction.
- Edge-case example: test near-zero or boundary values to avoid interpretation errors.
How to interpret results
Use outputs as quick checks, then verify with step-by-step work for graded or high-stakes use.
When this can be inaccurate
Errors usually come from unit mismatch, wrong baseline assumptions, or rounding too early in multistep problems.
Change history
- July 2026: Quality-reviewed for publication with formula checks and explanatory copy updates.
Site-wide corrections also appear on the corrections log.
Build math and logic skills with guided lessons
Educational platform recommendation.
Frequently asked questions
How do I find the median?+
Sort the values and take the middle one. With an even count, average the two central values.
Can there be more than one mode?+
Yes. A dataset is bimodal or multimodal if two or more values tie for most frequent; it has no mode if all values are unique.
What does the range tell me?+
The total spread from smallest to largest value. It is simple but sensitive to outliers, since it depends only on the two extremes.
Why do my classroom and calculator results differ?+
Differences usually come from rounding conventions, order-of-operations handling, or different baseline assumptions.
What is the safest way to validate an answer?+
Recompute with units shown and check against a second method or manual arithmetic for critical problems.