The Mean, Median and Mode Calculator takes any list of numbers and returns the three classic measures of central tendency, plus the range, sum and count. It is ideal for students, teachers and anyone summarising a data set without opening a spreadsheet. Paste your numbers and every statistic updates instantly.
How it works
You enter values separated by commas, spaces or new lines. The tool then computes:
- Mean — the arithmetic average: sum of all values divided by the count.
- Median — the middle value once the numbers are sorted. With an even count, it averages the two middle values.
- Mode — the value (or values) that appear most often. If every value appears equally often, there is no mode; if several tie, all are listed.
- Range — the largest value minus the smallest.
- Sum and count — the total and how many values there are.
Worked example
For the list 4, 8, 6, 4, 10:
- Sum = 32, count = 5, so mean = 32 ÷ 5 = 6.4.
- Sorted: 4, 4, 6, 8, 10 → median = 6 (the middle value).
- 4 appears twice, more than any other, so mode = 4.
- Range = 10 − 4 = 6.
| Statistic | Value |
|---|---|
| Mean | 6.4 |
| Median | 6 |
| Mode | 4 |
| Range | 6 |
| Sum | 32 |
When to use mean, median, and mode
All three describe the “centre” of a data set, but they respond differently to outliers and distribution shape.
Mean is the most sensitive to extreme values. One unusually large number pulls the mean up significantly while leaving the median unchanged. For example, a list of salaries in a small company will have a mean that is pulled up by a high earner, even if most employees earn much less. In such situations the median often gives a more representative picture of the “typical” value.
Median is resistant to outliers. It simply finds the middle of the sorted list. This is why median household income and median house price are used in official statistics — they are not skewed by a handful of multimillion-pound properties or incomes.
Mode is the only measure that works for non-numeric categorical data (like the most common shoe size in a sales order). For numerical data it is most useful when data clusters around a few specific values — like test scores clustering at certain mark bands — rather than being continuously distributed.
Edge cases to watch
- Even-count lists: The median is the average of the two middle values. For the list 1, 3, 5, 7 the median is (3 + 5) ÷ 2 = 4, which may not appear in the data at all.
- No mode: If all values appear exactly once, there is no mode. The tool reports “none” in this case.
- Multiple modes: If two or more values tie for most frequent, all are listed as co-modes (a bimodal or multimodal distribution). This is common in scored assessments with mark bands.
- Repeated identical values: A list like 5, 5, 5, 5 gives mean = median = mode = 5, and range = 0.
Everything is computed in your browser, so the data you enter is never uploaded.