Standard Deviation Calculator
Enter your data set to calculate the standard deviation and variance. Choose whether your data is a sample of a larger group or the entire population.
Sample standard deviation (s)
5.24
Variance
27.43
Mean
18
Count
8
Sum of squared deviations
192
How this was worked out
- Step 1Mean = 18
- Step 2Deviations from the mean: -8, -6, 5, 5, -2, 5, 3, -2
- Step 3Variance = Σ(x − mean)² ÷ 8 − 1 = 27.43
- Step 4Standard deviation = √27.43 = 5.24
Formula
σ = √(Σ(x − μ)² ÷ N) s = √(Σ(x − x̄)² ÷ (n − 1))
Example
Input
10, 12, 23, 23, 16, 23, 21, 16
Result
Sample SD ≈ 5.24
Frequently asked questions
Use sample if your data is drawn from a larger group (most real-world cases). Use population only if your data includes every member of the group.
No. It is a square root of a squared quantity, so it is always zero or positive.
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