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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.
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.
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.
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.
Formulas are standard public references (see our methodology). External standards are cited in the text where they apply.
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