Statistics Calculator
Calculate mean, median, mode, range, sample and population standard deviation and variance from a list of numbers.
| Value | Deviation (x − mean) | Squared Deviation |
|---|---|---|
| 4 | -2 | 4 |
| 8 | 2 | 4 |
| 6 | 0 | 0 |
| 5 | -1 | 1 |
| 3 | -3 | 9 |
| 9 | 3 | 9 |
| 7 | 1 | 1 |
Each row shows how far that data point sits from the mean (6) — squaring those distances and averaging them is exactly how the standard deviation above is built.
- Count7
- Sum42
- Median6
- ModeNone
- Range6
- Sample Std. Deviation2.1602
- Population Std. Deviation2
- Sample Variance4.6667
About the Statistics Calculator
This is the all-in-one version of the summary statistics students and analysts reach for constantly: mean, median, mode, range, variance and standard deviation, all computed from one list of numbers instead of running six separate calculators. It's the kind of tool that gets used to check a stats homework set, summarize a small survey or experiment's results, or get a quick read on a spreadsheet column without opening actual statistics software.
Every one of these numbers answers a slightly different question about a data set: where's the center (mean, median, mode), how spread out is it (range, variance, standard deviation). Seeing them together, computed from the same data, makes it much easier to spot what each one is actually telling you rather than memorizing definitions in isolation.
How it’s calculated
Mean is the plain average: sum every value and divide by the count. Median is the middle value once the data is sorted (or the average of the two middle values, for an even-sized data set) — it ignores extreme values in a way the mean doesn't. Mode is whichever value (or values) appear most often; a data set can have no mode, one mode, or several tied modes.
Variance measures spread by averaging the squared distance of every point from the mean — squaring keeps negative and positive deviations from canceling out, and standard deviation is just the square root of variance, which brings the units back to match the original data instead of squared units.
This calculator reports both the sample standard deviation (dividing by N−1) and the population standard deviation (dividing by N). Sample standard deviation is the one to use almost always in practice, since real data is nearly always a sample of some larger population rather than the population itself — dividing by N−1 instead of N corrects for the fact that a sample tends to slightly underestimate the true spread.
Frequently asked questions
What's the difference between sample and population standard deviation?
Population standard deviation divides by N and is used when your data literally is the entire group you care about. Sample standard deviation divides by N−1 and is used when your data is a subset representing a larger population — which is the far more common real-world situation, so it's usually the right one to reach for.
Why does a data set sometimes have no mode?
If every value in the data set appears exactly once, there's no value that occurs more often than any other, so there's technically no mode. This calculator reports 'None' in that case rather than picking an arbitrary value.
When should I use median instead of mean?
When the data has outliers or is skewed. A handful of extreme values can drag the mean far from where most of the data actually sits, while the median — being just the middle value — stays much more resistant to that kind of distortion.
What's the difference between variance and standard deviation?
Variance is the average squared distance from the mean; standard deviation is its square root. Standard deviation is usually more useful for interpretation because it's back in the same units as the original data — variance of a data set measured in dollars would be in dollars squared, which doesn't mean anything intuitive.
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