Mean Median Mode Calculator
The sorted values
How often each value appears
| Value | Times | Share |
|---|
Three averages, three different questions
Mean — add everything up, divide by how many. It uses every value, which is its strength and its weakness: one extreme number moves it.
Median — sort them, take the middle. Extremes cannot drag it anywhere, which is why income, house prices and response times are almost always reported as medians.
Mode — whichever value turns up most. The only one that works on things that are not numbers at all, like the most common shirt size sold.
When the mean and median disagree
That gap is worth noticing. If the mean is well above the median, a few large values are pulling it up — the distribution is skewed right, which is what a handful of very high salaries does to an average. If they are close, the data is roughly symmetrical. Both are shown here side by side for that reason.
Sample or population standard deviation
The sample version divides by n−1, the population version by n. The n−1 is not arbitrary: measuring spread around a mean you estimated from the same data underestimates the real spread, and dividing by one less corrects for it. Use the sample figure unless your numbers really are every member of the group — a class of 30 where you have all 30, not a survey of 30 people out of thousands.
What the quartiles tell you
Q1 and Q3 are the values a quarter and three quarters of the way through. The distance between them, the interquartile range, covers the middle half of the data and ignores the tails entirely — a more robust description of spread than the full range, which is decided by two values.
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Frequently Asked Questions
The mean is the total divided by how many values there are. The median is the middle value once they are sorted. The mode is whichever value appears most often. They answer different questions, and when they disagree that disagreement is itself information.
When a few extreme values would drag the mean somewhere unrepresentative. Salaries are the standard example: one very large salary lifts the mean above what almost everyone earns, while the median stays in the middle where most people actually are.
Because there are two of them. The sample standard deviation divides by n−1 and the population one divides by n. Both are shown here. Use the sample version when your numbers are a sample of something larger, which is the usual case; use the population one only when you have every member of the group.
Yes. If two values tie for the most frequent, the set is bimodal and both are listed. If every value appears exactly once there is no mode at all, which is stated rather than shown as a misleading first value.
By the exclusive method: the median splits the data, then Q1 is the median of the values below it and Q3 the median of the values above, with the overall median left out of both halves. Some textbooks use an inclusive method that gives slightly different figures on small sets — neither is wrong, they are different conventions.
Commas, spaces, tabs, semicolons or one number per line. Paste a column straight out of a spreadsheet and it will read correctly.