LRW: Standard Deviation

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Standard Deviation

The standard deviation is a measure of the "spread" (or dispersion) of a distribution.

(1)

$\sigma_X = \sqrt{Var(X)}$

Where Var(X) is the Variance.

The standard deviation of a discrete random variable is the root-mean-square (RMS) deviation of its values from the mean.

(2)

$\sigma = \sqrt{\frac{1}{N} \sum_{i=1}^N (x_i - \overline{x})^2}\,,$

The standard deviation of a continuous real-valued random variable is:

(3)

$\sigma = \sqrt{\int (x-\mu)^2 \, p(x) \, dx}\,,$

where $\mu = \int x \, p(x) \, dx\,,$ is the expectation E(X)

page_revision: 7, last_edited: 1223241944|%e %b %Y, %H:%M %Z (%O ago)

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