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Wolfram Language & System Documentation Center
TrimmedVariance
  • See Also
    • Variance
    • StandardDeviation
    • Covariance
    • Correlation
    • WinsorizedVariance
    • BiweightMidvariance
    • QnDispersion
    • SnDispersion
    • MeanDeviation
    • MedianDeviation
    • TruncatedDistribution
    • TrimmedMean
  • Related Guides
    • Descriptive Statistics
    • Robust Descriptive Statistics
    • Statistical Moments and Generating Functions
    • Date & Time
    • See Also
      • Variance
      • StandardDeviation
      • Covariance
      • Correlation
      • WinsorizedVariance
      • BiweightMidvariance
      • QnDispersion
      • SnDispersion
      • MeanDeviation
      • MedianDeviation
      • TruncatedDistribution
      • TrimmedMean
    • Related Guides
      • Descriptive Statistics
      • Robust Descriptive Statistics
      • Statistical Moments and Generating Functions
      • Date & Time

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
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Data  
Distributions  
Applications  
Properties & Relations  
Possible Issues  
See Also
Related Guides
History
Cite this Page
BUILT-IN SYMBOL
  • See Also
    • Variance
    • StandardDeviation
    • Covariance
    • Correlation
    • WinsorizedVariance
    • BiweightMidvariance
    • QnDispersion
    • SnDispersion
    • MeanDeviation
    • MedianDeviation
    • TruncatedDistribution
    • TrimmedMean
  • Related Guides
    • Descriptive Statistics
    • Robust Descriptive Statistics
    • Statistical Moments and Generating Functions
    • Date & Time
    • See Also
      • Variance
      • StandardDeviation
      • Covariance
      • Correlation
      • WinsorizedVariance
      • BiweightMidvariance
      • QnDispersion
      • SnDispersion
      • MeanDeviation
      • MedianDeviation
      • TruncatedDistribution
      • TrimmedMean
    • Related Guides
      • Descriptive Statistics
      • Robust Descriptive Statistics
      • Statistical Moments and Generating Functions
      • Date & Time

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

open all close all

Basic Examples  (4)

Trimmed variance after removing extreme values:

Trimmed variance after removing the smallest extreme values:

Trimmed variance of a list of dates:

Trimmed variance of a symbolic distribution:

Scope  (10)

Data  (9)

Exact input yields exact output:

Approximate input yields approximate output:

TrimmedVariance for a matrix gives columnwise variances:

Trimmed variance works with large arrays:

SparseArray data can be used just like dense arrays:

Trimmed variance of a TimeSeries:

Trimmed variance depends only on the values:

Trimmed variance works with data involving quantities:

Compute trimmed variance of dates:

Compute trimmed variance of times:

List of times with different time zone specifications:

Distributions  (1)

Trimmed variance for a univariate distribution:

Applications  (2)

Obtain a robust estimate of dispersion when outliers are present:

Extreme values have a large influence on the Variance:

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

Plot the trimmed variance as a function of trimmed fraction:

Plot the square root of the trimmed variance with respect to the trimmed mean:

Properties & Relations  (5)

A 0% TrimmedVariance is equivalent to Variance:

TrimmedVariance approaches 0 as f approaches 1/2:

TrimmedVariance of a distribution is the variance of its TruncatedDistribution:

Variance of the TruncatedDistribution with appropriate bounds:

TrimmedVariance of a sample gives an estimate of the variance of a truncated distribution:

Variance of the TruncatedDistribution with appropriate bounds:

TrimmedVariance drops the data beyond a certain quantile level, then computes the sample variance:

WinsorizedVariance clips the data beyond a certain quantile level, then computes the sample variance:

Plot the sorted data against the sample with elements removed and the clipped sample:

Possible Issues  (1)

TrimmedVariance requires numeric values:

See Also

Variance  StandardDeviation  Covariance  Correlation  WinsorizedVariance  BiweightMidvariance  QnDispersion  SnDispersion  MeanDeviation  MedianDeviation  TruncatedDistribution  TrimmedMean

Related Guides

    ▪
  • Descriptive Statistics
  • ▪
  • Robust Descriptive Statistics
  • ▪
  • Statistical Moments and Generating Functions
  • ▪
  • Date & Time

History

Introduced in 2017 (11.1) | Updated in 2024 (14.1)

Wolfram Research (2017), TrimmedVariance, Wolfram Language function, https://reference.wolfram.com/language/ref/TrimmedVariance.html (updated 2024).

Text

Wolfram Research (2017), TrimmedVariance, Wolfram Language function, https://reference.wolfram.com/language/ref/TrimmedVariance.html (updated 2024).

CMS

Wolfram Language. 2017. "TrimmedVariance." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2024. https://reference.wolfram.com/language/ref/TrimmedVariance.html.

APA

Wolfram Language. (2017). TrimmedVariance. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/TrimmedVariance.html

BibTeX

@misc{reference.wolfram_2025_trimmedvariance, author="Wolfram Research", title="{TrimmedVariance}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/TrimmedVariance.html}", note=[Accessed: 01-December-2025]}

BibLaTeX

@online{reference.wolfram_2025_trimmedvariance, organization={Wolfram Research}, title={TrimmedVariance}, year={2024}, url={https://reference.wolfram.com/language/ref/TrimmedVariance.html}, note=[Accessed: 01-December-2025]}

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