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MedianDeviation
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MedianDeviation

Updated in 14.1

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gives the median absolute deviation from the median of the elements in data.

Details

Examples

open allclose all

Basic Examples  (3)Summary of the most common use cases

MedianDeviation of a list:

In[1]:=1
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https://wolfram.com/xid/0purq6q8q6-wd9
Out[1]=1

MedianDeviation of columns of a matrix:

In[1]:=1
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https://wolfram.com/xid/0purq6q8q6-vu6sr
Out[1]=1

MedianDeviation of a list of dates:

In[1]:=1
✖
https://wolfram.com/xid/0purq6q8q6-t7ech
Out[1]=1

Scope  (18)Survey of the scope of standard use cases

Basic Uses  (6)

Exact input yields exact output:

In[1]:=1
✖
https://wolfram.com/xid/0purq6q8q6-ug7y2
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0purq6q8q6-bcry2t
Out[2]=2

Approximate input yields approximate output:

In[1]:=1
✖
https://wolfram.com/xid/0purq6q8q6-ksx55
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0purq6q8q6-d02ofx
Out[2]=2

Find the median deviation of WeightedData:

In[1]:=1
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https://wolfram.com/xid/0purq6q8q6-f1vfw
In[2]:=2
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https://wolfram.com/xid/0purq6q8q6-qyv0h
Out[2]=2

Find the median deviation of EventData:

In[1]:=1
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https://wolfram.com/xid/0purq6q8q6-e67u14
In[2]:=2
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https://wolfram.com/xid/0purq6q8q6-or2nrz
Out[2]=2

Find the median deviation of TimeSeries:

In[1]:=1
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https://wolfram.com/xid/0purq6q8q6-tolh7
Out[1]=1

The median deviation depends only on the values:

In[2]:=2
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https://wolfram.com/xid/0purq6q8q6-hfeo7e
Out[2]=2

Find the median deviation of data involving quantities:

In[1]:=1
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https://wolfram.com/xid/0purq6q8q6-jopin9
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0purq6q8q6-e8c21s
Out[2]=2

Array Data  (5)

MedianDeviation for a matrix works columnwise:

In[2]:=2
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https://wolfram.com/xid/0purq6q8q6-ezu2uz
Out[2]=2

MedianDeviation for a tensor gives the columnwise median deviation at the first level:

In[3]:=3
✖
https://wolfram.com/xid/0purq6q8q6-lw96ov
Out[3]=3

Works with large arrays:

In[1]:=1
✖
https://wolfram.com/xid/0purq6q8q6-nknun
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0purq6q8q6-ma3v2m
Out[2]=2

When the input is an Association, median deviation works on its values:

In[1]:=1
✖
https://wolfram.com/xid/0purq6q8q6-cs7n5q
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0purq6q8q6-rvy4yi
Out[2]=2

SparseArray data can be used just like dense arrays:

In[1]:=1
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https://wolfram.com/xid/0purq6q8q6-n691tv
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0purq6q8q6-drrysl
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0purq6q8q6-l4ct3
Out[3]=3
In[4]:=4
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https://wolfram.com/xid/0purq6q8q6-d6csj0
Out[4]=4

Find the median deviation of a QuantityArray:

In[1]:=1
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https://wolfram.com/xid/0purq6q8q6-lgwnaj
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0purq6q8q6-k03qc6
Out[2]=2

Image and Audio Data  (2)

Channelwise median deviation value of an RGB image:

In[1]:=1
✖
https://wolfram.com/xid/0purq6q8q6-hfby9q
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0purq6q8q6-phlz4o
Out[2]=2

Median deviation value of a grayscale image:

In[3]:=3
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https://wolfram.com/xid/0purq6q8q6-ue2gq5
Out[3]=3

On audio objects, MedianDeviation works channelwise:

In[1]:=1
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https://wolfram.com/xid/0purq6q8q6-nq1jnz
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0purq6q8q6-mjmudf
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0purq6q8q6-bs38vd
Out[3]=3

Date and Time  (5)

Compute median deviation of dates:

In[1]:=1
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https://wolfram.com/xid/0purq6q8q6-b1smxx
In[2]:=2
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https://wolfram.com/xid/0purq6q8q6-pa4nmn
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0purq6q8q6-uok1il
Out[3]=3

Compute the weighted median deviation of dates:

In[1]:=1
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https://wolfram.com/xid/0purq6q8q6-c98kbd
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0purq6q8q6-8c1had
In[3]:=3
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https://wolfram.com/xid/0purq6q8q6-8y1qb7
In[4]:=4
✖
https://wolfram.com/xid/0purq6q8q6-mun51z
Out[4]=4
In[5]:=5
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https://wolfram.com/xid/0purq6q8q6-t71b2h
Out[5]=5

Compute the median deviation of dates given in different calendars:

In[1]:=1
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https://wolfram.com/xid/0purq6q8q6-wbzcuv
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0purq6q8q6-9ius88
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0purq6q8q6-qe5gbw
Out[3]=3

Compute the median deviation of times:

In[1]:=1
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https://wolfram.com/xid/0purq6q8q6-et9bla
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0purq6q8q6-ztsexm
Out[2]=2

Compute the median deviation of times with different time zone specifications:

In[1]:=1
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https://wolfram.com/xid/0purq6q8q6-mrqghz
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0purq6q8q6-1d7sk5
Out[2]=2

Applications  (4)Sample problems that can be solved with this function

Obtain a robust estimate of dispersion when extreme values are present:

In[1]:=1
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https://wolfram.com/xid/0purq6q8q6-b99oaf
Out[1]=1

Measures based on the Mean are heavily influenced by extreme values:

In[2]:=2
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https://wolfram.com/xid/0purq6q8q6-3fz1a
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0purq6q8q6-ppqioq
Out[3]=3

Identify periods of high volatility in stock data using a five-year moving median deviation:

In[1]:=1
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https://wolfram.com/xid/0purq6q8q6-nj16d1
In[2]:=2
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https://wolfram.com/xid/0purq6q8q6-kfgcti
In[3]:=3
✖
https://wolfram.com/xid/0purq6q8q6-bef0x
Out[3]=3

Compute median deviations for slices of a collection of paths of a random process:

In[1]:=1
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https://wolfram.com/xid/0purq6q8q6-8se1zg

Choose a few slice times:

In[2]:=2
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https://wolfram.com/xid/0purq6q8q6-52xxug
In[3]:=3
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https://wolfram.com/xid/0purq6q8q6-iakfqb

Plot median deviations over these paths:

In[4]:=4
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https://wolfram.com/xid/0purq6q8q6-tvmkqe
Out[4]=4

Find the median deviation of the heights for the children in a class:

In[1]:=1
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https://wolfram.com/xid/0purq6q8q6-cevfij
In[2]:=2
✖
https://wolfram.com/xid/0purq6q8q6-fllmtw
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0purq6q8q6-celepo
Out[3]=3

Plot the median deviation respective of the median:

In[4]:=4
✖
https://wolfram.com/xid/0purq6q8q6-g98mgx
Out[4]=4

Properties & Relations  (2)Properties of the function, and connections to other functions

MedianDeviation is the Median of absolute deviations from the Median:

In[1]:=1
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https://wolfram.com/xid/0purq6q8q6-793v1
In[2]:=2
✖
https://wolfram.com/xid/0purq6q8q6-b9x4up
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0purq6q8q6-bhsxlb
Out[3]=3

For large uniform datasets, MedianDeviation and MeanDeviation are nearly the same:

In[1]:=1
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https://wolfram.com/xid/0purq6q8q6-dso2q7
In[2]:=2
✖
https://wolfram.com/xid/0purq6q8q6-hfsstq
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0purq6q8q6-vy95m
Out[3]=3

Possible Issues  (1)Common pitfalls and unexpected behavior

MedianDeviation requires real numeric values:

In[1]:=1
✖
https://wolfram.com/xid/0purq6q8q6-g88
Out[1]=1

Neat Examples  (1)Surprising or curious use cases

Ratio of MedianDeviation to MeanDeviation for increasing sample size:

In[3]:=3
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https://wolfram.com/xid/0purq6q8q6-ph16p
In[5]:=5
✖
https://wolfram.com/xid/0purq6q8q6-jq0tcn
Out[5]=5
Wolfram Research (2007), MedianDeviation, Wolfram Language function, https://reference.wolfram.com/language/ref/MedianDeviation.html (updated 2024).
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Wolfram Research (2007), MedianDeviation, Wolfram Language function, https://reference.wolfram.com/language/ref/MedianDeviation.html (updated 2024).

Text

Wolfram Research (2007), MedianDeviation, Wolfram Language function, https://reference.wolfram.com/language/ref/MedianDeviation.html (updated 2024).

✖
Wolfram Research (2007), MedianDeviation, Wolfram Language function, https://reference.wolfram.com/language/ref/MedianDeviation.html (updated 2024).

CMS

Wolfram Language. 2007. "MedianDeviation." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2024. https://reference.wolfram.com/language/ref/MedianDeviation.html.

✖
Wolfram Language. 2007. "MedianDeviation." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2024. https://reference.wolfram.com/language/ref/MedianDeviation.html.

APA

Wolfram Language. (2007). MedianDeviation. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MedianDeviation.html

✖
Wolfram Language. (2007). MedianDeviation. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MedianDeviation.html

BibTeX

@misc{reference.wolfram_2025_mediandeviation, author="Wolfram Research", title="{MedianDeviation}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/MedianDeviation.html}", note=[Accessed: 25-March-2025 ]}

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@misc{reference.wolfram_2025_mediandeviation, author="Wolfram Research", title="{MedianDeviation}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/MedianDeviation.html}", note=[Accessed: 25-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_mediandeviation, organization={Wolfram Research}, title={MedianDeviation}, year={2024}, url={https://reference.wolfram.com/language/ref/MedianDeviation.html}, note=[Accessed: 25-March-2025 ]}

✖
@online{reference.wolfram_2025_mediandeviation, organization={Wolfram Research}, title={MedianDeviation}, year={2024}, url={https://reference.wolfram.com/language/ref/MedianDeviation.html}, note=[Accessed: 25-March-2025 ]}