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WinsorizedMean—Wolfram Language Documentation

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• See Also
  • Mean
  • TrimmedMean
  • Median
  • BiweightLocation
  • WinsorizedVariance
  • TrimmedVariance
  • CensoredDistribution
  • Quantile
  • RankedMin
  • RankedMax
• Related Guides
  • Descriptive Statistics
  • Statistical Moments and Generating Functions
  • Date & Time
  • Robust Descriptive Statistics

WinsorizedMean[list,f]

gives the mean of the elements in list after replacing the fraction f of the smallest and largest elements by the remaining extreme values.

WinsorizedMean[list,{f₁,f₂}]

gives the mean when the fraction f₁ of the smallest elements and the fraction f₂ of the largest elements are replaced by the remaining extreme values.

WinsorizedMean[dist,…]

gives the winsorized mean of a univariate distribution dist.

• WinsorizedMean gives a robust estimate of the mean, with more extreme values replaced by less extreme ones.
• The winsorizing 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 replaced by the remaining extreme values.
• WinsorizedMean[list,{f₁,f₂}] gives the mean of Clip[list,{z₁,z₂}] where z₁ equals RankedMin[list,1+], z₂ equals RankedMax[list,1+], and n equals the length of list. »
• WinsorizedMean of a univariate WeightedData data gives the weighted mean of the censored data. »
• WinsorizedMean[{{x₁,y₁,…},{x₂,y₂,…},…},f] gives {WinsorizedMean[{x₁,x₂,…},f],WinsorizedMean[{y₁,y₂,…},f],…}. »
• WinsorizedMean[dist,{f₁,f₂}] gives Mean[CensoredDistribution[Quantile[dist,{f₁,1-f₂}],dist]] for a univariate distribution dist. »

Winsorized mean after removing extreme values:

Winsorized mean after removing the smallest extreme values:

Winsorized mean of a list of dates:

Winsorized mean of a symbolic distribution:

Exact input yields exact output:

Approximate input yields approximate output:

Winsorized mean of a matrix gives columnwise means:

Winsorized mean of a large array:

SparseArray data can be used just like dense arrays:

WinsorizedMean of a univariate WeightedData:

Compare with the mean of the unweighted data:

Winsorized mean of a TimeSeries:

The winsorized mean depends only on the values:

Winsorized mean works with data involving quantities:

Compute winsorized mean of dates:

Compute winsorized mean of times:

List of times with different time zone specifications:

Winsorized mean of a univariate distribution:

Obtain a robust estimate of the location when outliers are present:

Extreme values have a large influence on the mean:

Simulate a trajectory with heavy-tailed measurement noise:

The underlying signal and simulated path with noise:

Smooth the trajectory using a moving WinsorizedMean:

Increasing the block size gives a smoother trajectory:

Find a winsorized mean for the heights of children in a class:

The 5% winsorized mean:

Compare few winsorized means:

Plot the winsorized mean as a function of the fraction parameter:

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