How this calculator works
Variance averages squared deviations from the arithmetic mean. For a complete population the divisor is n. When the mean is estimated from a sample and the target is the broader population variance, the usual unbiased estimator divides by n - 1. This focused comparison shows the divisor and individual squared deviations, making the choice explicit. Standard deviation is the square root of variance and returns to the original measurement unit. Observations receive equal weight.
Formula
Mean = sum(x_i)/n. SS = sum[(x_i - mean)²]. Sample variance = SS/(n - 1); population variance = SS/n; SD = sqrt(variance).
Worked example
For 1, 2, 3 the mean is 2 and squared deviations sum to 2. Sample variance is 2/2 = 1; population variance is 2/3. Their SDs are 1 and approximately 0.816497.
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Frequently asked questions
Which divisor should I choose?
Use n for the complete group you intend to describe. Use n - 1 when independent sampled observations estimate a larger population variance.
Can variance be negative?
Not mathematically. Squared deviations are non-negative; negative inputs themselves are valid observations.
Why are variance units squared?
Each deviation is squared before averaging. Use standard deviation when you need a spread in the original unit.