Variance measures how spread out data values are from the mean.
Sample variance uses n−1 (Bessel's correction). Population variance uses n.
Standard deviation = √variance. Same units as original data.
This calculator is appropriate for any analysis that will be presented, reported, or used to make decisions. Accurate statistical metrics are the foundation of valid conclusions.
Choosing population standard deviation when the data is a sample is the most common statistical error with this type of calculation. Unless your dataset covers every possible member of the group, use sample SD (with n−1 denominator) for valid inference.
A quality engineer analyses the diameter measurements of 25 machined parts: mean 50.02 mm, standard deviation 0.08 mm. With a tolerance of ±0.25 mm, the process is well within specification — and the SD confirms the manufacturing variation is low enough that virtually no parts will fall outside tolerance.
Variance measures the average squared deviation from the mean. Formula: σ² = Σ(x−μ)²/N.
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