# SDeviation

## SDeviation(X, *I, w*)

Computes the weighted sample standard deviation -- the square root of the variance.

If *X* is an uncertain quantity, dependent on Analytica distribution functions, the variance is obtained using SDeviation(X).

«X» is evaluated in Sample mode, and the variance along the Run index computed.

Regardless of the variation used, the standard deviation, or weighted standard deviation, is defined as

- [math]\displaystyle{ \sqrt(Variance(X,I,w)) }[/math]

See Variance for additional technical details.

## Optional parameters

### I

The optional «I» parameter can be used to calculate standard deviation along Index «I».

Given a data set indexed by «I», the sample variance along «I» is computed using:

`SDeviation(X, I)`

When the running index, «I», is the system index Run (or not specified), the value of «X» is evaluated in Sample mode and the average value among numeric values computed. If the running index is anything other than Run, then «X» is evaluated in context.

### W

The weighted standard deviation computing by assigning a different "weight" to each point. The weight vector, `wt`

, should be indexed by «I» (or by Run if «I» is not specified), and the weighted variance is computed using one of these forms

`SDeviation(X, w: wt)`

`SDeviation(X, I, w: wt)`

When the «w» parameter is not specified, and the running index «I» is either the Run index or is not specified, then the weighting defaults to the value in the system variable SampleWeighting.

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