Average Calculator

Your numbers

How it works

Mean is the everyday "average": add everything up and divide by how many numbers there are. Median is the middle value once the list is sorted — with an even count, it is the mean of the two middle values. Mode is the most frequent value; a list can have one mode, several modes (multimodal), or no mode at all when every value appears the same number of times. Range is simply maximum minus minimum.

Standard deviation measures spread — how far the numbers typically sit from the mean. It comes in two flavors, and this page labels both: the population version divides the squared differences by the count (use it when your list is the whole set you care about — every student in the class, every day of the month). The sample version divides by count − 1 instead, which corrects for the fact that a sample tends to understate the spread of the bigger group it came from (use it when your list is a sample — a few measured parts standing in for a whole production run).

Worked example: for 4, 8, 15, 16, 23, 42 the sum is 108 and the count is 6, so the mean is 18. Sorted, the two middle values are 15 and 16, so the median is 15.5. No value repeats, so there is no mode. The range is 42 − 4 = 38.

Frequently asked questions

Mean or median — which should I use? The median resists outliers. One very large value (a single huge bill, one mansion in a list of house prices) drags the mean up but barely moves the median, which is why incomes and house prices are usually reported as medians.

Which standard deviation do I report? Population if you have every value in the group; sample if you measured a subset and want to describe the wider group. With large lists the two nearly agree; with short lists the sample figure is noticeably larger, and that difference is the correction doing its job.

Can the mode be more than one number? Yes — if two values tie for most frequent, the list is bimodal (two modes), and three or more tied values make it multimodal. All of them are listed here rather than picking a winner.