Mean, Median and Mode Calculator
Three different things get called 'the average', and choosing between them can change the story a dataset tells.
Mean, median and mode
The mean uses every value, which makes it efficient and also makes it fragile: a single extreme value drags it a long way. The median uses only position, so it does not care how extreme an outlier is. The mode is the only one that works on categories as well as numbers — the most common eye colour has no mean.
With the default values {12, 15, 15, 22, 96} the mean is 32, which is larger than four of the five numbers. The median of 15 describes the data far better. That single outlier of 96 is doing all the work.
Choosing the honest one
Consider nine people earning £25,000 and one earning £500,000. The mean is £72,500 — a figure nobody in the room earns. The median is £25,000, which describes nine of them exactly.
This is why income, house price and waiting time statistics are almost always reported as medians. In a right-skewed distribution, where a long tail of large values pulls the mean upward, the mean stops describing the typical case.
| Situation | Use |
|---|---|
| Roughly symmetric data, no outliers | Mean |
| Skewed data: income, house prices, response times | Median |
| Categories, or where the most common value matters | Mode |
| Compounding rates (investment returns, growth) | Geometric mean |
Why spread matters as much as centre
Two datasets can share a mean of 50 and be nothing alike: {49, 50, 51} and {0, 50, 100}. An average quoted without a measure of spread is half a description.
The range is simple but rests entirely on the two most extreme points. The standard deviation measures typical distance from the mean and uses all the data. The interquartile range — the span of the middle half — is the robust choice when outliers are present, which is why box plots are built on it. Our standard deviation calculator covers this properly.
Frequently asked questions
Can a dataset have more than one mode?
Yes. Two values tied for most frequent make it bimodal. A genuinely bimodal distribution usually means two distinct groups have been mixed together, which is often the most interesting finding in the data.
What is the difference between population and sample standard deviation?
The divisor. Population divides by n. Sample divides by n−1, correcting for the fact that a sample systematically underestimates the spread of the population it came from. Use the sample version whenever your numbers are a subset of something larger.
When should I use a geometric mean?
For rates that compound. Averaging +50 % and −50 % arithmetically gives 0 %, but £100 becomes £150 and then £75 — an actual loss of 25 %. The geometric mean, the nth root of the product of the growth factors, gets this right.