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MovingMedian[list,r]

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

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Basic Examples  
Scope  
Generalizations & Extensions  
Applications  
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MovingMedian

MovingMedian[list,r]

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

Details

Examples

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Basic Examples  (2)

Moving median of a vector:

Wolfram Language code: MovingMedian[{1, 2, 5, 6, 1, 4, 3}, 3]

Moving median of a matrix:

Wolfram Language code: MovingMedian[{{1, 2}, {5, 3}, {1, 4}, {3, 2}, {5, 5}}, 2]

Scope  (5)

Compute moving medians for any numeric data:

Wolfram Language code: MovingMedian[{1, E, Sqrt[Pi], 2, 10, E ^ 2}, 3]

Obtain results at machine precision:

Wolfram Language code: MovingMedian[N[{1, 5, 7, 3, 6, 2}], 3]

Obtain results for lists of any precision:

Wolfram Language code: MovingMedian[N[{1, 5, 7, 3, 6, 2}, 25], 3]

Moving medians of matrices are matrices:

Wolfram Language code: data = RandomReal[5, {10, 2}]
Wolfram Language code: MovingMedian[data, 4]

Moving median of a TimeSeries:

Wolfram Language code: ts = TemporalData[TimeSeries, {{{0., 0.24628521289687533, 0.3703374944231774, 0.4717582177179417, 0.3940302965227978, 0.5618705948857727, 0.2584747970316238, 0.5201131120145466, 0.8157396141130544, 0.7246714521345359, 0.8447350569180434, 0.756 ... 652867661, -2.5881471131731897, -2.578676175222997, -2.2907776293136597}}, {{0, 1., 0.01}}, 1, {"Continuous", 1}, {"Continuous", 1}, 1, {ValueDimensions -> 1, ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}}}, False, 10.1];
Wolfram Language code: Show[ListPlot[ts], ListLinePlot[Table[MovingMedian[ts, k], {k, {2, 5, 15}}]]]

Generalizations & Extensions  (2)

Compute results for a SparseArray:

Wolfram Language code: sp = SparseArray[{{i_, i_} :> i, {i_, j_} /; j < i :> (i + j)}, {100, 10}]
Wolfram Language code: MovingMedian[sp, 5]

Compute the moving median of a numeric TimeSeries for various window lengths:

Wolfram Language code: ts = TimeSeries[TimeEventSeries`TimestampData[Association["UniformlySpacedQ" -> True, "Count" -> 61, "Endpoints" -> TabularColumn[Association["Data" -> {{0., 0.6}, {}, None}, "ElementType" -> "Real64"]], "MinimumTimeIncrement" -> 0.01]], Ta ... 86436505, -0.344485981849591, -0.32017664131197604, -0.339944678008272, -0.4962959466695484, -0.5235950374532581, -0.588853370532945, -0.8359919314597413, -0.9675284674456728}, {}, None}, "ElementType" -> "Real64"]], Association[]];
Wolfram Language code: wspec = {3, 7, 12};
Wolfram Language code: res = Table[MovingMedian[ts, k], {k, wspec}];

Incomplete windows are dropped, and the result is placed on the right end of each window:

Wolfram Language code: Tabular[Table[{wspec[[i]], res[[i]]["FirstTime"]}, {i, 3}], {"k", "first time"}]
Wolfram Language code: Show[ListPlot[ts, PlotStyle -> Gray], ListLinePlot[res, PlotLegends -> wspec]]

Applications  (2)

Smooth noisy data:

Wolfram Language code: data = Range[20] + RandomReal[{-2, 2}, 20]
Wolfram Language code: smoothed = MovingMedian[data, 5]
Wolfram Language code: ListPlot[data]
Wolfram Language code: ListPlot[smoothed]

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

Wolfram Language code: data = TimeSeries@FinancialData["GE", "Jan. 1, 2000"]
Wolfram Language code: DateListPlot[MovingMedian[data, 100]]

Properties & Relations  (3)

A moving median is a sequence of medians:

Wolfram Language code: MovingMedian[{1, 3, 5, 2, 2, 4, 10, 5}, 4]
Wolfram Language code: Table[Median[Take[{1, 3, 5, 2, 2, 4, 10, 5}, {i, i + 3}]], {i, 5}]

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

Wolfram Language code: data = RandomReal[10, 10]
Wolfram Language code: MovingMedian[data, 2] == MovingAverage[data, 2]

MovingMedian is equivalent to MovingMap of Median:

Wolfram Language code: data = RandomInteger[{-10, 10}, 10]
Wolfram Language code: MovingMedian[data, 3]
Wolfram Language code: MovingMap[Median, data, Quantity[3, "Events"]]
Wolfram Language code: % === %%

Possible Issues  (1)

MovingMedian requires numeric values:

Wolfram Language code: MovingMedian[{a, b, c}, 2]
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.

CMS

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

BibTeX

@misc{reference.wolfram_2026_movingmedian, author="Wolfram Research", title="{MovingMedian}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/MovingMedian.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_movingmedian, organization={Wolfram Research}, title={MovingMedian}, year={2007}, url={https://reference.wolfram.com/language/ref/MovingMedian.html}, note=[Accessed: 12-June-2026]}