Standard Deviation

Updated 28 Sep 2026

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What it is
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  the square root of the Variance — expresses spread in the same units as the original data, unlike variance (which is in squared units)
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Formula
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  sample: $s=\sqrt{s^2}$
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  population: $\sigma=\sqrt{\sigma^2}$
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Grouped sample formula
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  $s\approx\sqrt{\dfrac{n\sum_i f_i m_i^2-(\sum_i f_i m_i)^2}{n(n-1)}}$
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  $m_i$ is a class midpoint and $n=\sum_i f_i$
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Caution
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  the approximation arises from replacing observations with their class midpoints
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Related
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  Variance
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  Measures of Dispersion

Linked references 6