Math & Statistics
Standard Deviation & Variance Calculator
Updated Sep 3, 2026 Reviewed Sep 3, 2026
Calculate population or sample variance, standard deviation, mean, squared deviations, standard error, and coefficient of variation from pasted numeric data.
Statistical spread
Measure variation in a data set
Result
Calculation summary
Enter values to see the result
Your result, breakdown, assumptions, and warnings will appear here.
Deviation preview
Distance from the mean
Formula
σ = √(Σ(x−μ)²/N); s = √(Σ(x−x̄)²/(n−1))
- Mean
- —
- Variance
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- Standard deviation
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How to use this calculator
- 1Paste observations with common separators.
- 2Choose population or sample.
- 3Inspect deviations and squared deviations.
Formula
σ = √(Σ(x − μ)² / N), s = √(Σ(x − x̄)² / (n − 1))
Population variance divides by N; corrected sample variance divides by n − 1.
Calculation steps
- Calculate the arithmetic mean.
- Square every deviation from the mean.
- Divide by the selected divisor and take the square root.
Worked example
For population 2, 4, 6, variance is 8/3 and standard deviation is about 1.633.
Assumptions
- Observations have equal weight.
- Sample mode uses Bessel’s correction.
- Coefficient of variation is undefined at zero mean.
Sources
Frequently asked questions
Population or sample?
Use population for the complete group and sample when estimating a larger group.
Why n minus one?
Bessel’s correction reduces estimation bias.
Can deviation be negative?
No, standard deviation is non-negative.
Why is CV missing?
It is undefined when the mean is zero.
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