Math
Summarize a numeric data set with mean, population standard deviation, and sample standard deviation.
Results update as you type. No calculate button. All calculations run locally in your browser.
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Enter at least one number, separated by commas or spaces.
| Quantity | Value |
|---|---|
| Count (n) | — |
| Mean | — |
| Sum of squared deviations | — |
| Population variance | — |
| Population SD | — |
| Sample variance | — |
| Sample SD | — |
| Minimum / maximum | — |
Sample SD is undefined for a single value (it divides by n − 1 = 0) and is shown as — in that case.
Mean = Σx ÷ n. Population SD = √[Σ(x − mean)² ÷ n]; sample SD uses n − 1 in place of n. Population variance is Σ(x − mean)² ÷ n and sample variance is Σ(x − mean)² ÷ (n − 1).
For 12, 15, 18, 20, 25: mean = 90 ÷ 5 = 18. Squared deviations are 36, 9, 0, 4 and 49, summing to 98. Population SD = √(98 ÷ 5) = √19.6 = 4.4272 (4.427189 to more places). Sample SD = √(98 ÷ 4) = √24.5 = 4.9497. Use Reset example above to reproduce this result, then replace the list with your own data.
Non-numeric entries are ignored; if no numbers remain, no result is shown. Use population SD when the list is the complete population and sample SD when the observations are a sample used to estimate a population. Standard deviation is sensitive to outliers and describes spread only — it does not by itself show the shape of the distribution. Display is rounded to 4 decimal places.
Population SD (÷ n) when your numbers are the whole group you care about. Sample SD (÷ n − 1) when they are a sample and you are estimating the spread of a larger population.
It divides by n − 1 instead of n, which corrects for the fact that a sample mean is fitted to the sample itself. The gap shrinks as n grows.
Population SD is 0 (no spread), and sample SD is undefined, shown as —, because n − 1 is zero.
No. Mean and standard deviation are unchanged by reordering the list.
No, they are skipped. If nothing numeric remains, the page shows — and asks for numbers.
Results are estimates only and do not constitute professional advice.