# TrimmedVariance

TrimmedVariance[list,f]

gives the variance of the elements in list after dropping a fraction f of the smallest and largest elements.

TrimmedVariance[list,{f1,f2}]

gives the variance when a fraction f1 of the smallest elements and a fraction f2 of the largest elements are removed.

TrimmedVariance[list]

gives the 5% trimmed variance TrimmedVariance[list,0.05].

TrimmedVariance[dist,]

gives the trimmed variance of a univariate distribution dist.

# Details • TrimmedVariance gives a robust estimate of the variance by excluding extreme values.
• The trimming fraction is determined by the parameters f1 and f2, which indicate the fraction f1 of the smallest elements and the fraction f2 of the largest elements to be removed.
• TrimmedVariance[list,{f1,f2}] gives the variance of Sort[list,Less]1+ ;;n- where n equals the length of list.
• • TrimmedVariance[{{x1,y1,},{x2,y2,},},f] gives {TrimmedVariance[{x1,x2,},f],TrimmedVariance[{y1,y2,},f],}.
• TrimmedVariance[dist,{f1,f2}] gives Variance[TruncatedDistribution[Quantile[dist,{f1,1-f2}],dist]] for a univariate distribution dist.

# Examples

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## Basic Examples(3)

Trimmed variance after removing extreme values:

 In:= Out= Trimmed variance after removing the smallest extreme values:

 In:= Out= Trimmed variance of a symbolic distribution:

 In:= Out= ## Possible Issues(1)

Introduced in 2017
(11.1)