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



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Basic Examples  (3)

MeanDeviation of a list of numbers:

MeanDeviation of symbolic data:

MeanDeviation of the columns of a matrix:

Scope  (13)

Basic Uses  (6)

Exact input yields exact output:

Approximate input yields approximate output:

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:

Array Data  (5)

MeanDeviation for a matrix works columnwise:

MeanDeviation for a tensor works across the first index: »

Works with large arrays:

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

SparseArray data can be used just like dense arrays:

Find mean deviation of a QuantityArray:

Image and Audio Data  (2)

Channelwise mean deviation value of an RGB image:

Mean deviation value of a grayscale image:

On audio objects, MeanDeviation works channelwise:

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, (updated 2023).


Wolfram Research (2007), MeanDeviation, Wolfram Language function, (updated 2023).


Wolfram Language. 2007. "MeanDeviation." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2023.


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


@misc{reference.wolfram_2024_meandeviation, author="Wolfram Research", title="{MeanDeviation}", year="2023", howpublished="\url{}", note=[Accessed: 17-June-2024 ]}


@online{reference.wolfram_2024_meandeviation, organization={Wolfram Research}, title={MeanDeviation}, year={2023}, url={}, note=[Accessed: 17-June-2024 ]}