Standard Deviation Calculator
Compute standard deviation, variance, mean and the full set of descriptive statistics.
What the Standard Deviation Calculator does
Standard deviation is the typical distance between a value and the mean, in the same units as the data. Small means tightly clustered; large means widely scattered. Use the sample formula when your numbers are a subset drawn from a bigger group.
Formula
σ = √(Σ(x − μ)² ÷ n)s = √(Σ(x − x̄)² ÷ (n − 1))
Inputs explained
| Input | Unit | Required | Notes |
|---|---|---|---|
| Numbers | text | Yes | Separate values with commas, spaces or new lines. |
| Data set type | one of 2 options | Yes | — |
How to use it
- Choose Data set type.
- Enter Numbers.
- Select Calculate.
Worked example
Five delivery times in minutes: 28, 31, 27, 35, 29.
- Numbers
- 28, 31, 27, 35, 29
- Type
- Sample
Mean 30, sample standard deviation ≈ 3.16 minutes.
Frequently asked questions
Should I use sample or population?
Population when your data is the entire group you care about. Sample when it is a subset used to estimate a larger population — that covers most real analysis.
What counts as a high standard deviation?
It depends on scale. Compare it to the mean using the coefficient of variation, which is shown above as a percentage.