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MovingMedian
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MovingMedian

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MovingMedian[list,r]

gives the moving median of list, computed using spans of r elements.

Details

Examples

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Basic Examples  (2)Summary of the most common use cases

Moving median of a vector:

In[1]:=1
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https://wolfram.com/xid/01yp86vks5k-c18qvo
Out[1]=1

Moving median of a matrix:

In[1]:=1
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https://wolfram.com/xid/01yp86vks5k-g33se6
Out[1]=1

Scope  (5)Survey of the scope of standard use cases

Compute moving medians for any numeric data:

In[1]:=1
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https://wolfram.com/xid/01yp86vks5k-cq771q
Out[1]=1

Obtain results at machine precision:

In[1]:=1
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https://wolfram.com/xid/01yp86vks5k-yve
Out[1]=1

Obtain results for lists of any precision:

In[1]:=1
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https://wolfram.com/xid/01yp86vks5k-dftm52
Out[1]=1

Moving medians of matrices are matrices:

In[1]:=1
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https://wolfram.com/xid/01yp86vks5k-f6w30t
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/01yp86vks5k-hrjjx3
Out[2]=2

Moving median of a TimeSeries:

In[1]:=1
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https://wolfram.com/xid/01yp86vks5k-nv4lr8
In[2]:=2
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https://wolfram.com/xid/01yp86vks5k-fa5nzt
Out[2]=2

Generalizations & Extensions  (1)Generalized and extended use cases

Compute results for a SparseArray:

In[1]:=1
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https://wolfram.com/xid/01yp86vks5k-l4ct3
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/01yp86vks5k-d6csj0
Out[2]=2

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

Smooth noisy data:

In[1]:=1
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https://wolfram.com/xid/01yp86vks5k-j42qsa
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/01yp86vks5k-biof3w
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/01yp86vks5k-wjb0f
Out[3]=3
In[4]:=4
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https://wolfram.com/xid/01yp86vks5k-czj2v8
Out[4]=4

Compute the 100-day moving median of a financial time series:

In[1]:=1
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https://wolfram.com/xid/01yp86vks5k-mbxbnh
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/01yp86vks5k-cq2lfi
Out[2]=2

Properties & Relations  (3)Properties of the function, and connections to other functions

A moving median is a sequence of medians:

In[1]:=1
✖
https://wolfram.com/xid/01yp86vks5k-bxc2b1
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/01yp86vks5k-i0fg4m
Out[2]=2

A two‐term MovingMedian is equivalent to a two‐term MovingAverage:

In[1]:=1
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https://wolfram.com/xid/01yp86vks5k-i96jjd
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/01yp86vks5k-1z6z5
Out[2]=2

MovingMedian is equivalent to MovingMap of Median:

In[1]:=1
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https://wolfram.com/xid/01yp86vks5k-cb4t6a
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/01yp86vks5k-ok4d32
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/01yp86vks5k-ig9mo
Out[3]=3
In[4]:=4
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https://wolfram.com/xid/01yp86vks5k-cqtk8k
Out[4]=4

Possible Issues  (1)Common pitfalls and unexpected behavior

MovingMedian requires numeric values:

In[1]:=1
✖
https://wolfram.com/xid/01yp86vks5k-g88
Out[1]=1
Wolfram Research (2007), MovingMedian, Wolfram Language function, https://reference.wolfram.com/language/ref/MovingMedian.html.
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Wolfram Research (2007), MovingMedian, Wolfram Language function, https://reference.wolfram.com/language/ref/MovingMedian.html.

Text

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

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

CMS

Wolfram Language. 2007. "MovingMedian." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/MovingMedian.html.

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Wolfram Language. 2007. "MovingMedian." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/MovingMedian.html.

APA

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

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

BibTeX

@misc{reference.wolfram_2025_movingmedian, author="Wolfram Research", title="{MovingMedian}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/MovingMedian.html}", note=[Accessed: 04-May-2025 ]}

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@misc{reference.wolfram_2025_movingmedian, author="Wolfram Research", title="{MovingMedian}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/MovingMedian.html}", note=[Accessed: 04-May-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_movingmedian, organization={Wolfram Research}, title={MovingMedian}, year={2007}, url={https://reference.wolfram.com/language/ref/MovingMedian.html}, note=[Accessed: 04-May-2025 ]}

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@online{reference.wolfram_2025_movingmedian, organization={Wolfram Research}, title={MovingMedian}, year={2007}, url={https://reference.wolfram.com/language/ref/MovingMedian.html}, note=[Accessed: 04-May-2025 ]}