Compute sample and population standard deviation, variance and mean for a data set.
Compute sample and population standard deviation, variance and mean for a data set.
Enter values above and click Calculate — results will appear here with the formula explained.
Standard deviation summarizes how spread out a data set is around its mean. A small value means the numbers cluster tightly; a large value means they scatter widely. It is expressed in the same units as the data itself, unlike variance, which is squared.
Whether to divide by n or n − 1 depends on your data. If your values are the entire population of interest, divide by n. If they are a sample used to estimate a larger population, dividing by n − 1 corrects the small downward bias that samples otherwise introduce.
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Standard deviation summarizes how spread out a data set is around its mean. A small value means the numbers cluster tightly; a large value means they scatter widely. It is expressed in the same units as the data itself, unlike variance, which is squared. Formula: s = √( Σ(xᵢ − x̄)² ÷ (n − 1) ) [sample]; replace (n − 1) with n for a population
Standard Deviation Calculator computes compute sample and population standard deviation, variance and mean for a data set. Formula: s = √( Σ(xᵢ − x̄)² ÷ (n − 1) ) [sample]. Example: For 4, 8, 6, 5, 3, 10 the mean is 6.
Compute sample and population standard deviation, variance and mean for a data set. Formula: s = √( Σ(xᵢ − x̄)² ÷ (n − 1) ) [sample]; replace (n − 1) with n for a population
| Field | What to enter |
|---|---|
| Data values (separate with commas, spaces or new lines) | e.g. 4, 8, 6, 5, 3, 10 |
| Data type | Enter a value |
All fields use the exact formulas shown below — results include step-by-step breakdowns you can verify by hand.
Standard deviation summarizes how spread out a data set is around its mean. A small value means the numbers cluster tightly; a large value means they scatter widely. It is expressed in the same units as the data itself, unlike variance, which is squared.
Whether to divide by n or n − 1 depends on your data. If your values are the entire population of interest, divide by n. If they are a sample used to estimate a larger population, dividing by n − 1 corrects the small downward bias that samples otherwise introduce.
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For 4, 8, 6, 5, 3, 10 the mean is 6. Squared deviations sum to 34, so the population variance is 34 ÷ 6 ≈ 5.667 and σ ≈ 2.38. As a sample estimate, dividing by 5 instead gives s ≈ 2.61.
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