Standard Deviation Calculator
Calculate the standard deviation and variance of a list of numbers, for either a full population or a sample.
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Your result
2.138
Standard deviation
AI explanation
Formula
Population: σ² = Σ(x−mean)² / n. Sample: s² = Σ(x−mean)² / (n−1). Standard deviation = √varianceWorked example
Population standard deviation of 2, 4, 4, 4, 5, 5, 7, 9
| Field | Value |
|---|---|
| Numbers | 2, 4, 4, 4, 5, 5, 7, 9 |
| Data type | population |
| Standard deviation | 2 |
| Variance | 4 |
| Mean | 5 |
Assumptions
- Sample standard deviation uses Bessel's correction (dividing by n−1 instead of n), the standard adjustment when your data is a sample rather than the entire population.
- A sample calculation requires at least 2 numbers.
Frequently asked questions
Should I choose "sample" or "population"?
Choose "population" if your data represents the entire group you care about. Choose "sample" if your data is a subset used to estimate the characteristics of a larger population — sample standard deviation is slightly larger to account for the extra uncertainty.
What does standard deviation actually measure?
It measures how spread out the numbers are from the mean — a small standard deviation means the values are clustered close to the mean; a large one means they're spread widely.
How is standard deviation related to variance?
Standard deviation is the square root of variance. Variance is in squared units, while standard deviation is in the same units as the original data, which is why standard deviation is more commonly reported.