MeanDeviation

MeanDeviation[data]

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

Details

Examples

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Basic Examples  (4)

MeanDeviation of a list of numbers:

MeanDeviation of symbolic data:

MeanDeviation of the columns of a matrix:

MeanDeviation of a list of dates:

Scope  (18)

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:

Date and Time  (5)

Compute mean deviation of dates:

Compute the weighted mean deviation of dates:

Compute the mean deviation of dates given in different calendars:

Compute the mean deviation of times:

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

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 1‐norm 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, https://reference.wolfram.com/language/ref/MeanDeviation.html (updated 2024).

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2025_meandeviation, author="Wolfram Research", title="{MeanDeviation}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/MeanDeviation.html}", note=[Accessed: 24-May-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_meandeviation, organization={Wolfram Research}, title={MeanDeviation}, year={2024}, url={https://reference.wolfram.com/language/ref/MeanDeviation.html}, note=[Accessed: 24-May-2025 ]}