Variance

Updated 15 Sep 2026

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What it is
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  a measure of how far data points spread out from the mean
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Sample variance formula
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  $s^2 = \dfrac{\sum_{i=1}^{n}(x_i - \bar{x})^2}{n-1}$
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Grouped-data computational formula
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  $s = \sqrt{\dfrac{n\sum f_i x_i^2 - (\sum f_i x_i)^2}{n(n-1)}}$ , a shortcut avoiding the need to compute each deviation from the mean directly
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Caution
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  this shortcut subtracts two large, similar-magnitude sums — for large data values, this is vulnerable to Catastrophic Cancellation (see the Numerical Methods knowledge base), which can even produce a nonsensical negative variance under limited computational precision
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Related

Linked references 4