TrimmedMean

TrimmedMean[list,f]

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

TrimmedMean[list,{f1,f2}]

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

TrimmedMean[list]

gives the 5% trimmed mean TrimmedMean[list,0.05].

TrimmedMean[dist,]

gives the trimmed mean of a univariate distribution dist.

Details

  • TrimmedMean gives a robust estimate of the mean 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.
  • TrimmedMean[list,{f1,f2}] gives the mean of Sort[list,Less]1+;;n-, where n equals the length of list.
  • TrimmedMean[{{x1,y1,},{x2,y2,},},f] gives {TrimmedMean[{x1,x2,},f],TrimmedMean[{y1,y2,},f],}.
  • TrimmedMean[dist,{f1,f2}] gives Mean[TruncatedDistribution[Quantile[dist,{f1,1-f2}],dist]] for a univariate distribution dist.

Examples

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Basic Examples  (3)

Trimmed mean after removing extreme values:

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Trimmed mean after removing the smallest extreme values:

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Trimmed mean of a symbolic distribution:

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Scope  (8)

Applications  (3)

Properties & Relations  (5)

Possible Issues  (1)

See Also

Mean  Quantile  TrimmedVariance  WinsorizedMean  Median  BiweightLocation  WinsorizedVariance

Tutorials

Introduced in 2007
(6.0)
| Updated in 2017
(11.1)