Find the standard deviation and variance of a data set.
Find the mean, square each deviation, average them and take the root. For 2, 4, 4, 4, 5, 5, 7, 9 the population standard deviation is 2.
Standard deviation measures how spread out numbers are around their mean. Enter your data and choose sample (n − 1) or population (N) to get the standard deviation and variance, the mean, the sum of squares, the standard error of the mean and the coefficient of variation, with a working table that shows each value's deviation and squared deviation.
A small standard deviation means values cluster near the mean; a large one means they are spread out. See the Average Calculator, Statistics Calculator, Z-Score Calculator and Confidence Interval Calculator.
The calculator applies the standard method step by step.
| Item | Value |
|---|---|
| Sample standard deviation (s) | 2.1380899353 |
| Population standard deviation (σ) | 2 |
| Sample variance (s²) | 4.57142857143 |
| Population variance (σ²) | 4 |
| Mean | 5 |
| Count | 8 |
| Sum of squares (Σ(x − mean)²) | 32 |
| Standard error of the mean | 0.755928946018 |
| Coefficient of variation | 42.761799% |
| Value (x) | Deviation (x − mean) | Squared deviation |
|---|---|---|
| 2 | -3 | 9 |
| 4 | -1 | 1 |
| 4 | -1 | 1 |
| 4 | -1 | 1 |
| 5 | 0 | 0 |
| 5 | 0 | 0 |
| 7 | 2 | 4 |
| 9 | 4 | 16 |
| Data | Standard deviation |
|---|---|
| 2, 4, 4, 4, 5, 5, 7, 9 | 2 |
| 1, 2, 3, 4, 5 | 1.58113883008 |
| 10, 12, 23, 23, 16, 23, 21, 16 | 5.23722936566 |
| 4, 8, 15, 16, 23, 42 | 13.4907375632 |
| 5, 5, 5, 5 | 0 |
A measure of how far, on average, values are from the mean.
Population divides by N when you have every value; sample divides by n − 1 when your data is a sample, correcting a bias.
The square of the standard deviation — the average squared distance from the mean.
Low means values are close to the mean; high means they are spread widely. It must be judged relative to the mean.
The standard deviation of the sample mean: s ÷ √n. It shrinks as the sample grows.
The standard deviation divided by the mean, as a percentage — useful for comparing spread across different scales.
It uses the standard method: σ = √(Σ(x − μ)² ÷ N) s = √(Σ(x − x̄)² ÷ (n − 1)) The full working and a worked example are shown on this page.
Decimal results use standard double-precision arithmetic (about 15–16 significant digits). Tools that work with whole numbers — big numbers, factors, bases, combinations — use exact integer arithmetic, so no digits are lost.
Yes for checking your work and learning the method. The steps and formula are shown so you can understand the answer, but follow your teacher's rules about calculators in exams.
No. Everything is calculated in your browser and nothing you enter is uploaded or saved.
