Variance Calculator

Sample (n−1) and population (n) variance — the square of standard deviation.

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General calculation reads

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How Not to Be Wrong
Jordan Ellenberg - math thinking
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The Joy of X
Steven Strogatz - accessible math
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Scientific calculator (Casio fx-991EX)
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How to use this calculator

  • Enter numbers.
  • Read both sample and population variance.

About this calculator

Variance is the average squared deviation from the mean — the square of the standard deviation. Sample variance divides by n−1; population variance divides by n. Variance is harder to interpret directly because its units are squared, but it has nicer math (the variance of a sum of independent variables is the sum of variances).

Frequently asked

Variance vs SD?+
Variance = SD². They contain the same information; SD is in the original units, variance is in squared units.
Why use variance at all?+
Math is cleaner — variances of independent variables add. SD doesn't. So in proofs and theory, variance often appears first; the answer is then square-rooted to SD for interpretation.
When should I use sample variance?+
When your data is a sample drawn from a larger population — almost always in real life.
Are these formulas universal?+
Yes — these are the textbook definitions. Some software defaults to population (Excel's VARP); R defaults to sample (var()).
How does variance relate to F-tests?+
F = ratio of two sample variances. Used to compare variability between groups.

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