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).
Regardless of the variation used, the standard deviation, or weighted standard deviation, is defined as
- $ \sqrt(Variance(X,I,w)) $
See Variance for additional technical details.
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:
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.
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)