Mean, Median, Mode & Range Calculator

Which average should you actually use?

The mean adds everything up and divides by the count. It uses every value, which is its strength and its weakness: one extreme number drags it a long way. In the default data above, six values sit between 12 and 31, one is 94, and the mean lands at 29.6 — higher than all but one of the numbers.

The median is the middle value once the list is sorted. It does not care how extreme the extremes are, only how many there are. For income, house prices, response times and anything else with a long tail, the median is almost always the honest figure.

The mode is the value that appears most often. It is the only one of the three that works on categories rather than numbers, and the only one that can legitimately not exist, or exist several times over.

Quartiles, IQR and what counts as an outlier

Q1 and Q3 are the medians of the lower and upper halves of the sorted data. The gap between them — the interquartile range — contains the middle half of your values, and unlike the full range it is not moved by a single odd result.

Tukey's rule flags anything more than 1.5 × IQR below Q1 or above Q3. It is a convention, not a law of nature: it does not prove a value is wrong, only that it is unusual enough to be worth a second look. Genuine data often contains real outliers, and deleting them because a rule flagged them is how findings get manufactured.

Reading the shape

When the mean sits clearly above the median, the data has a long right tail — a few large values pulling upward. When it sits below, the tail runs left. When they are close, the distribution is roughly symmetric and the mean is safe to quote on its own. This calculator reports which of the three applies.

Frequently Asked Questions