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Standard deviation

The standard deviation measures how much the values spread around the mean. A small standard deviation means the values lie close together. In production it is used to judge whether a process is consistent enough.

s=1n−1∑(xi−xˉ)2s = \sqrt{\frac{1}{n-1}\sum (x_i - \bar x)^2}sample standard deviation

Symbols

ssstandard deviation
xˉ\bar xmean
nnnumber of values

Example

Measurements 4, 6 and 8: xˉ=6\bar x = 6.

s=(4+0+4)/2=2s = \sqrt{(4 + 0 + 4)/2} = 2.

The standard deviation has the same unit as the data, unlike the variance.
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Part of Foundations of Mathematics: Statistics and probability.