Mean, Median and Mode Calculator — With Range and Std Dev

Enter any list of numbers separated by commas or spaces to instantly calculate the mean, median, mode, range, standard deviation, variance, and more — with a full sorted view and frequency breakdown.

Created by Ashar PervaizLast updated 24 October 2026

When the Three Averages Disagree, That Is the Finding

Mean, median and mode are usually taught as three ways of doing the same job. They are better understood as three different questions, and the interesting cases are the ones where they give different answers.

Take seven salaries at a small company, in thousands: 24, 26, 27, 28, 30, 32 and 210.

Six of the seven people earn less than the mean. It is a perfectly correct arithmetic average and a poor description of a typical salary at that company, because one value is pulling it upward on its own. The median is unmoved by that value: shifting the top salary to 500 would change the mean to nearly 95 and leave the median at exactly 28.

This is what people mean by saying the median is robust. It depends on the position of values rather than their size, so extremes cannot drag it.

The Gap Between Mean and Median Is Itself a Measurement

Comparing the two tells you about the shape of the data without plotting anything.

It is worth running this check before deciding which figure to report. If the two are close, use the mean — it uses every value and is easier to work with algebraically. If they are far apart, the mean is describing the tail rather than the typical case.

This is also why income and house price statistics are almost always published as medians. It is not a stylistic choice; the mean of a right-skewed distribution describes a person who does not exist.

Which One Should You Actually Report?

Reporting more than one is usually better than choosing. Stating a mean of 53.9 alongside a median of 28 tells the reader more than either number alone, and it tells them immediately that something in the data is unusual.

Mode Is the Only One That Works on Non-Numbers

Mean and median both require values you can add or rank. Mode only requires that you can tell whether two values are the same, which makes it the only average available for categorical data.

There is no mean favourite colour and no median blood type. There is a most common one, and that is the mode. For survey answers, product choices, error codes or sizes, it is not a lesser option — it is the only one defined.

No Mode, Two Modes, or All of Them

Mode has edge cases the other two do not, and they are worth recognising rather than treating as errors.

• No mode. In 1, 2, 3, 4, 5 every value appears once. Some conventions say there is no mode; others say every value is one. Either way the measure is telling you nothing useful about this data.
• Two modes. In 1, 1, 2, 2, 3 both 1 and 2 appear twice. A bimodal result often means two different groups have been combined into one dataset — two shifts, two age groups, two product lines — and the honest response is usually to separate them rather than to report one average.
• A mode that is not central at all. Nothing requires the most frequent value to sit near the middle. It can be the lowest or highest value in the set, which is why mode alone is a poor summary of numeric data.

Centre Without Spread Is Half the Story

Two datasets can share a mean and describe completely different situations. Spread is what separates them, and the two common measures behave very differently.

Range is the largest value minus the smallest. It uses exactly two numbers and ignores everything in between, which makes it entirely determined by extremes.

Standard deviation measures how far values sit from the mean on average, using every value in the set. It is in the same units as the data, which is why it is usually reported instead of variance — variance is the same quantity in squared units, useful in the algebra and awkward to interpret.

Adding one outlier shows the difference between all four measures at once. Start with 2, 3, 3, 4, 5 and add a single value of 100:

One value out of six multiplied the mean by more than five and the range by more than thirty, while the median moved by half a point. If your summary statistics change dramatically when a single observation is added, that observation deserves examination before the statistics are reported.

Two Ways an Average Goes Wrong

Averaging averages. Two class averages cannot be averaged unless the classes are the same size. A class of 10 averaging 70 and a class of 30 averaging 90 do not combine to 80. The correct figure weights by group size: (10 × 70 + 30 × 90) ÷ 40 = 85. The naive answer is five marks out, and the error grows as the groups become more unequal.

Averaging too few values. A mean of three numbers is extremely sensitive to each one; a mean of three hundred is not. Nothing in the calculation warns you which you are looking at, so report the count alongside the average. A single figure with no sample size behind it cannot be evaluated by anyone reading it.

For descriptive statistics on values you have already computed, the percentage calculator handles proportional comparisons, and the matrix calculator covers linear algebra rather than descriptive measures. The math formula library has the definitions behind this page — mean, median, range, variance, standard deviation and the z-score — if you need to show the working rather than just the answer.