Average Calculator
Find the mean, median, mode and range of any list of numbers, and see which average actually describes your data best.
How to use this calculator
- 1Paste or type your numbers, separated by commas, spaces or new lines.
- 2Compare the mean and median. A large gap between them tells you the data is skewed.
- 3Use the frequency table to spot repeated values and outliers.
How the calculation works
Mean = Σx / n Median = middle value when sorted Mode = most frequent value Geometric mean = ⁿ√(x₁ × x₂ × … × xₙ)- Σx
- The sum of all the values
- n
- How many values there are
With an even number of values, the median is the average of the two middle ones.
A dataset can have no mode, one mode, or several. Continuous measurements usually have no meaningful mode.
The geometric mean is computed as exp(mean of the logs) rather than multiplying every value together first — mathematically identical, but it avoids overflowing on a long list of large numbers.
Worked example
12, 15, 18, 22, 15, 30, 15
- 1.Sum = 127, count = 7, so the mean is 127 ÷ 7 = 18.14.
- 2.Sorted: 12, 15, 15, 15, 18, 22, 30. The middle value is the 4th, which is 15.
- 3.15 appears three times, more than any other value, so the mode is 15.
- 4.The range is 30 − 12 = 18.
Result: Mean 18.14, median 15, mode 15
Why "average" can mean three different things
In everyday speech, "average" almost always means the mean: add everything up and divide by how many values there are. Statisticians use "average" as an umbrella term covering three distinct measures — mean, median and mode — and each one answers a slightly different question about where the "middle" of a dataset really is.
Picking the wrong one is not just a technicality. A single very large or very small value can drag the mean a long way from where most of the data actually sits, while the median and mode barely move — so the "average" you choose can tell very different stories about the same numbers.
Mean, median and mode, side by side
Each measure looks at the data differently, and each has a situation where it is clearly the right tool.
- Mean — the sum of all values divided by how many there are. It uses every single data point, which makes it sensitive to outliers — one unusually large or small value shifts it noticeably.
- Median — the middle value once the data is sorted, or the average of the two middle values for an even-sized dataset. It ignores how extreme the outer values are, only their order, which makes it far more resistant to outliers.
- Mode — the value that appears most often. It is the only one of the three that also works for non-numeric data, like the most common shoe size or favourite colour in a survey.
The classic example: income
Household income is the textbook illustration of why the choice matters. A small number of very high earners pull the mean well above what a typical household actually takes home, so news reports and economic statistics almost always quote median income instead — it reflects the experience of the person in the middle far more honestly than an average dragged upward by a handful of outliers.
Where these measures show up
These three measures turn up constantly outside the statistics classroom.
- Test scores and grading — class averages use the mean, but "typical" performance is often better represented by the median when a few very low or very high scores are present.
- Real estate — median home price is the standard figure for a housing market, precisely because a handful of high-end sales would otherwise distort a mean.
- Sports statistics — batting averages, points-per-game and similar figures are means calculated over a season.
- Weather — an "average high temperature" for a given date is a mean taken over many years of historical records.
Mistakes worth watching for
A few habits explain most confusion between the different averages.
- Assuming the mean represents "most" people — in a skewed dataset, the mean can be a value that hardly anyone in the data actually has.
- Ignoring outliers entirely — a single data-entry error — an extra zero on one value — can shift a mean dramatically without being obvious just by looking at the summary number.
- Expecting every dataset to have a mode — when every value is different, or all values appear the same number of times, there is no meaningful mode at all.
What this assumes, and where it stops
Assumptions
- All values are treated as equally weighted. For weighted averages, repeat values or use a weighted-mean tool.
Limitations
- The mean is highly sensitive to outliers — one extreme value can drag it far from where most of the data sits.
- The mode is unstable for continuous data, where exact repeats are rare or accidental.
Common questions
When should I use the median instead of the mean?
Whenever the data is skewed or contains outliers. Income is the classic example: a handful of very high earners pull the mean well above what a typical person earns, while the median stays representative. If the mean and median differ substantially, prefer the median.
Can a dataset have more than one mode?
Yes. If two or more values tie for the highest frequency, the data is bimodal or multimodal, and all of them are reported. Multiple modes often signal that you are looking at two different populations mixed together.
Formula and content last reviewed on .
Results are estimates for information only, not professional advice.
Related calculators
Tools people commonly use alongside the average calculator.