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TrimmedMean—Wolfram Language Documentation

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• See Also
  • Mean
  • Quantile
  • TrimmedVariance
  • WinsorizedMean
  • Median
  • BiweightLocation
  • WinsorizedVariance
  • MeanShiftFilter
• Related Guides
  • Descriptive Statistics
  • Statistical Moments and Generating Functions
  • Robust Descriptive Statistics
  • Date & Time
• Tech Notes
  • Descriptive Statistics

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[dist,…]

gives the trimmed mean of a univariate distribution dist.

• 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.

Trimmed mean after removing extreme values:

Trimmed mean after removing the smallest extreme values:

Trimmed mean of a list of dates:

Trimmed mean of a symbolic distribution:

Exact input yields exact output:

Approximate input yields approximate output:

TrimmedMean for a matrix gives columnwise means:

Trimmed mean works with large arrays:

SparseArray data can be used just like dense arrays:

Trimmed mean of a TimeSeries:

Trimmed mean depends only on the values:

Trimmed mean works with data involving quantities:

Compute trimmed mean of dates:

Compute trimmed mean of times:

List of times with different time zone specifications:

The trimmed mean for a univariate distribution:

Obtain a robust estimate of 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 TrimmedMean:

Increasing the block size gives a smoother trajectory:

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

Compare a few trimmed means:

Plot the trimmed mean as a function of trimmed fraction:

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