Averages · The three centres
Mean, Median & Mode Calculator
The three “averages” — and why they can tell different stories. Paste your numbers to get all three at once, plus range, sum and count, laid out on a number line so you can see when the mean is being dragged away from the typical value.
Tip: try adding one very large value and watch the mean move while the median barely budges.
Result
In plain English
“The average” is really three different things, and they can tell different stories about the same data. When they disagree, that disagreement is usually the most interesting thing in the dataset.
- mean
- The everyday average: add everything up and divide by how many. It shares the total out equally — but a single huge value drags it around.
- median
- The middle value once the numbers are sorted. Half the data sit below it, half above. Barely moved by outliers, so often the more honest “typical” figure.
- mode
- The value that appears most often. The only average that works for non-numbers too (the most common colour, say). There can be more than one, or none.
- range
- The gap between the largest and smallest value — the simplest measure of spread.
- when they split
- If the mean sits well above the median, a few large values are pulling it up (right-skew); below, a few small ones are pulling it down. The median is the safer summary then.
Frequently asked
When should I use the median instead of the mean?
When the data are skewed or contain outliers. The mean is dragged toward extreme values (a few very high incomes, say), while the median — the middle value — barely moves. If the mean and median differ noticeably, the median is the more honest “typical” figure.
Can a data set have more than one mode?
Yes. If two or more values tie for most frequent, the data are multimodal and all of them are modes. If every value occurs equally often (including all-unique data), there is no mode at all.
What's the difference between the mean, median and mode?
The mean shares the total out equally (sum ÷ count), the median is the middle value once sorted, and the mode is the most common value. They answer different questions and only coincide for a perfectly symmetric, single-peaked distribution.
What is a skewed distribution, and how do the averages line up?
A distribution is skewed when one tail is longer than the other. With right-skew (a long high tail, like incomes) the mean is pulled above the median, which itself sits above the mode; left-skew reverses the order. When the three averages drift apart, that very ordering tells you which way — and roughly how far — the data lean, and the median is usually the most honest summary of the typical value.