Standard Deviation Calculator
Free standard deviation calculator. Paste a list of numbers and get the mean, median, mode, range, variance and both the population and sample standard deviation.
| Population | Sample | |
|---|---|---|
| Standard deviation | ||
| Variance |
What it does
Standard deviation says how spread out a set of numbers is. Two groups can share the same average and look nothing alike: one clustered tightly, the other scattered. The mean tells you where the middle is; the deviation tells you how much to trust it. This page also gives the median and the mode, which describe the middle differently and are harder to mislead with one extreme value.
How to use it
- Paste or type your numbers. Any mix of spaces, commas, semicolons and line breaks works.
- The statistics update as you type.
- Use the population figure when your numbers are the whole group, and the sample figure when they are a sample drawn from a larger one.
The arithmetic runs in your browser. Nothing you type is sent anywhere and nothing is stored, so you can use these with real numbers.
Frequently asked questions
Population or sample — which one do I want?
If your numbers are everything you care about — the marks of every student in the class — use population. If they are a sample you are using to estimate something bigger, use sample, which divides by one less and gives a slightly larger figure to account for what the sample missed.
Why does my spreadsheet give a different number?
Almost always because of that choice. Spreadsheets have both: STDEV.P for population and STDEV.S for sample. Many online calculators show one without saying which, which is why the numbers do not match.
What is the difference between mean and median?
The mean is the total divided by the count; the median is the middle value once sorted. One very large number drags the mean far away from where most of the data sits, and leaves the median almost untouched — which is why incomes are usually reported as medians.
Can there be more than one mode?
Yes. If two values tie for most frequent, both are shown. If every value appears the same number of times there is no mode at all, because nothing stands out.
Wikipedia — Standard deviation
Wikipedia — Variance
Wikipedia — Bessel's correction
Wikipedia — Median
Wikipedia — Mode