Standard Deviation Calculator
Population and sample standard deviation
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About this calculator
Standard deviation measures how spread out numbers are around the mean. Use the sample version when your data is a subset of a larger group, and the population version when you have every value.
The formula
σ = √(Σ(x − mean)² ÷ N) | s = √(Σ(x − mean)² ÷ (N − 1))
Worked example2, 4, 4, 4, 5, 5, 7, 9 → mean 5, population σ = 2, sample s ≈ 2.138.
Frequently asked questions
Sample or population?
Sample if the numbers are a sample from a bigger group; population if they are the whole group.
What does a high value mean?
Values are widely spread. A low value means they cluster near the mean.
Why divide by N − 1?
It corrects the bias of estimating the mean from the same sample.
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