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TrimmedVariance
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TrimmedVariance

Updated in 14.1

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TrimmedVariance[list,f]

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

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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.

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

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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 allclose all

Basic Examples  (4)Summary of the most common use cases

Trimmed variance after removing extreme values:

In[1]:=1
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https://wolfram.com/xid/0gfret6wydge-cacnen
Out[1]=1

Trimmed variance after removing the smallest extreme values:

In[1]:=1
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https://wolfram.com/xid/0gfret6wydge-clbc5x
Out[1]=1

Trimmed variance of a list of dates:

In[1]:=1
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https://wolfram.com/xid/0gfret6wydge-wpdopd
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0gfret6wydge-ziof1v
Out[2]=2

Trimmed variance of a symbolic distribution:

In[1]:=1
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https://wolfram.com/xid/0gfret6wydge-b133z2
Out[1]=1

Scope  (10)Survey of the scope of standard use cases

Data  (9)

Exact input yields exact output:

In[1]:=1
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https://wolfram.com/xid/0gfret6wydge-ug7y2
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0gfret6wydge-bcry2t
Out[2]=2

Approximate input yields approximate output:

In[1]:=1
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https://wolfram.com/xid/0gfret6wydge-ksx55
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0gfret6wydge-d02ofx
Out[2]=2

TrimmedVariance for a matrix gives columnwise variances:

In[1]:=1
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https://wolfram.com/xid/0gfret6wydge-jywoa6
Out[1]=1

Trimmed variance works with large arrays:

In[1]:=1
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https://wolfram.com/xid/0gfret6wydge-enve04
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0gfret6wydge-if5yx4
Out[2]=2

SparseArray data can be used just like dense arrays:

In[1]:=1
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https://wolfram.com/xid/0gfret6wydge-2bvdh
In[2]:=2
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https://wolfram.com/xid/0gfret6wydge-paeyu
Out[2]=2

Trimmed variance of a TimeSeries:

In[1]:=1
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https://wolfram.com/xid/0gfret6wydge-tg8p6z
In[2]:=2
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https://wolfram.com/xid/0gfret6wydge-ffhpdi
Out[2]=2

Trimmed variance depends only on the values:

In[3]:=3
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https://wolfram.com/xid/0gfret6wydge-fy9fte
Out[3]=3

Trimmed variance works with data involving quantities:

In[1]:=1
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https://wolfram.com/xid/0gfret6wydge-jopin9
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0gfret6wydge-e8c21s
Out[2]=2

Compute trimmed variance of dates:

In[1]:=1
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https://wolfram.com/xid/0gfret6wydge-b1smxx
In[2]:=2
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https://wolfram.com/xid/0gfret6wydge-pa4nmn
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0gfret6wydge-uok1il
Out[3]=3
In[4]:=4
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https://wolfram.com/xid/0gfret6wydge-o9ersi
Out[4]=4

Compute trimmed variance of times:

In[1]:=1
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https://wolfram.com/xid/0gfret6wydge-et9bla
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0gfret6wydge-ztsexm
Out[2]=2

List of times with different time zone specifications:

In[3]:=3
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https://wolfram.com/xid/0gfret6wydge-mrqghz
Out[3]=3
In[4]:=4
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https://wolfram.com/xid/0gfret6wydge-ow7hca
Out[4]=4

Distributions  (1)

Trimmed variance for a univariate distribution:

In[5]:=5
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https://wolfram.com/xid/0gfret6wydge-hbq28j
Out[5]=5
In[6]:=6
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https://wolfram.com/xid/0gfret6wydge-rxz55
Out[6]=6
In[7]:=7
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https://wolfram.com/xid/0gfret6wydge-eiu3ke
Out[7]=7

Applications  (2)Sample problems that can be solved with this function

Obtain a robust estimate of dispersion when outliers are present:

In[1]:=1
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https://wolfram.com/xid/0gfret6wydge-cexxtn
Out[1]=1

Extreme values have a large influence on the Variance:

In[2]:=2
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https://wolfram.com/xid/0gfret6wydge-blrzc0
Out[2]=2

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

In[1]:=1
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https://wolfram.com/xid/0gfret6wydge-cevfij
In[2]:=2
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https://wolfram.com/xid/0gfret6wydge-fllmtw
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0gfret6wydge-celepo
Out[3]=3

Plot the trimmed variance as a function of trimmed fraction:

In[4]:=4
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https://wolfram.com/xid/0gfret6wydge-fgqfgk
In[5]:=5
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https://wolfram.com/xid/0gfret6wydge-doz2wp
Out[5]=5

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

In[6]:=6
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https://wolfram.com/xid/0gfret6wydge-g98mgx
Out[6]=6

Properties & Relations  (5)Properties of the function, and connections to other functions

A 0% TrimmedVariance is equivalent to Variance:

In[1]:=1
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https://wolfram.com/xid/0gfret6wydge-k3hcsh
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0gfret6wydge-fc96q6
Out[2]=2

TrimmedVariance approaches 0 as f approaches 1/2:

In[1]:=1
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https://wolfram.com/xid/0gfret6wydge-dy2d21
In[2]:=2
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https://wolfram.com/xid/0gfret6wydge-ed6bml
Out[2]=2

TrimmedVariance of a distribution is the variance of its TruncatedDistribution:

In[1]:=1
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https://wolfram.com/xid/0gfret6wydge-yd3d3n
In[2]:=2
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https://wolfram.com/xid/0gfret6wydge-lr5uh3
Out[2]=2

Variance of the TruncatedDistribution with appropriate bounds:

In[3]:=3
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https://wolfram.com/xid/0gfret6wydge-clxbr6
In[4]:=4
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https://wolfram.com/xid/0gfret6wydge-u4mwsn
Out[4]=4

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

In[1]:=1
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https://wolfram.com/xid/0gfret6wydge-jcz7or
In[2]:=2
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https://wolfram.com/xid/0gfret6wydge-bj114x
Out[2]=2

Variance of the TruncatedDistribution with appropriate bounds:

In[3]:=3
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https://wolfram.com/xid/0gfret6wydge-31l1ws
In[4]:=4
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https://wolfram.com/xid/0gfret6wydge-mtzrl
Out[4]=4

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

In[1]:=1
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https://wolfram.com/xid/0gfret6wydge-cm3s6i
In[2]:=2
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https://wolfram.com/xid/0gfret6wydge-gmitza
In[3]:=3
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https://wolfram.com/xid/0gfret6wydge-bgojw
Out[3]=3

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

In[4]:=4
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https://wolfram.com/xid/0gfret6wydge-hqnggt
In[5]:=5
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https://wolfram.com/xid/0gfret6wydge-xbwg2
Out[5]=5

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

In[6]:=6
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https://wolfram.com/xid/0gfret6wydge-gc5h1e
In[7]:=7
✖
https://wolfram.com/xid/0gfret6wydge-ts5rus
Out[7]=7

Possible Issues  (1)Common pitfalls and unexpected behavior

TrimmedVariance requires numeric values:

In[1]:=1
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https://wolfram.com/xid/0gfret6wydge-g88
Out[1]=1
Wolfram Research (2017), TrimmedVariance, Wolfram Language function, https://reference.wolfram.com/language/ref/TrimmedVariance.html (updated 2024).
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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).

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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.

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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

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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: 29-March-2025 ]}

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@misc{reference.wolfram_2025_trimmedvariance, author="Wolfram Research", title="{TrimmedVariance}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/TrimmedVariance.html}", note=[Accessed: 29-March-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: 29-March-2025 ]}

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@online{reference.wolfram_2025_trimmedvariance, organization={Wolfram Research}, title={TrimmedVariance}, year={2024}, url={https://reference.wolfram.com/language/ref/TrimmedVariance.html}, note=[Accessed: 29-March-2025 ]}