Work out an average, and know which one you need
Paste a list of numbers. You get every common average and spread measure at once, with an explanation of what each one is actually telling you.
Average calculator
Mean, median or mode: which one to use
All three are called "the average" in everyday speech, and they answer different questions. Picking the wrong one is the most common way a true number tells a false story.
| Measure | What it tells you | Use it when | Avoid it when |
|---|---|---|---|
| Mean | The total shared out equally | Values cluster around a centre with no extreme outliers | A few very large or very small values dominate |
| Median | The middle value once sorted | Income, house prices, response times, anything skewed | You need the figures to add back up to a known total |
| Mode | The value that appears most often | Categories, shoe sizes, survey answers | Every value is unique, or several tie |
| Weighted mean | An average where some values count more | Grades by credits, prices by volume, blended rates | Weights are arbitrary or unknown |
How each figure is worked out
Mean
Add every value, divide by how many there are. Ten numbers adding to 250 give a mean of 25.
Median
Sort the values, take the middle one. With an even count there are two middle values, so the median is the mean of that pair.
Standard deviation
How far a typical value sits from the mean. A small figure means the values are packed together; a large one means they are spread out. The calculator above shows both the sample version, which divides by n−1 and is the one you want for a sample of a bigger group, and the population version, which divides by n and is for when you have measured everything.
Range and quartiles
The range is simply the largest value minus the smallest. Quartiles cut the sorted list into four equal parts, so the interquartile range covers the middle half and quietly ignores the extremes at both ends.
Worked example
Seven salaries: 24k, 26k, 27k, 28k, 29k, 31k and 210k. The mean is about 53.6k, which describes nobody in the room. The median is 28k, which describes almost everyone. The single large value has pulled the mean away from the group, and that is exactly the situation the median exists for.
Common questions
What is the difference between the average and the mean?
In everyday speech average usually means the arithmetic mean: add the values and divide by how many there are. In statistics average is a broader word that also covers the median and the mode, which is why the same data can honestly produce more than one average.
When should I use the median instead of the mean?
Use the median whenever a few very high or very low values would drag the mean away from the bulk of the data. Salaries, house prices, waiting times and page views are the usual cases.
Should I use sample or population standard deviation?
Use the sample version, which divides by n minus one, when your numbers are a sample drawn from a larger group. Use the population version when the numbers are the whole group you care about.
Is anything I paste sent to a server?
No. The calculation runs entirely in your browser and the numbers never leave your device.