gives the mean absolute deviation from the mean of the elements in list.


  • For the list {x1,x2,,xn}, the mean deviation is given by , where is the mean of the list.
  • MeanDeviation handles both numerical and symbolic data.
  • MeanDeviation[{{x1,y1,},{x2,y2,},}] gives {MeanDeviation[{x1,x2,}],MeanDeviation[{y1,y2,},]}.


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Basic Examples  (2)

MeanDeviation of a list:

MeanDeviation of columns of a matrix:

Scope  (9)

Exact input yields exact output:

Approximate input yields approximate output:

MeanDeviation for a matrix gives columnwise means:

Works with large arrays:

SparseArray data can be used just like dense arrays:

Find the mean deviation of WeightedData:

Find the mean deviation of EventData:

Find the mean deviation for TimeSeries:

The mean deviation depends only on the values:

Find the mean deviation of data involving quantities:

Generalizations & Extensions  (1)

Compute results for a SparseArray:

Applications  (3)

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

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

Choose a few slice times:

Plot mean deviations over these paths:

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

Plot the mean deviation respective of the mean:

Properties & Relations  (4)

MeanDeviation is the Mean of absolute deviations from the Mean:

MeanDeviation is equivalent to the 1norm of the deviations divided by the Length:

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

MeanDeviation as a scaled ManhattanDistance from the Mean:

Neat Examples  (1)

Ratio of MeanDeviation to MedianDeviation for increasing sample size:

Wolfram Research (2007), MeanDeviation, Wolfram Language function,


Wolfram Research (2007), MeanDeviation, Wolfram Language function,


Wolfram Language. 2007. "MeanDeviation." Wolfram Language & System Documentation Center. Wolfram Research.


Wolfram Language. (2007). MeanDeviation. Wolfram Language & System Documentation Center. Retrieved from


@misc{reference.wolfram_2023_meandeviation, author="Wolfram Research", title="{MeanDeviation}", year="2007", howpublished="\url{}", note=[Accessed: 01-June-2023 ]}


@online{reference.wolfram_2023_meandeviation, organization={Wolfram Research}, title={MeanDeviation}, year={2007}, url={}, note=[Accessed: 01-June-2023 ]}