MedianDeviation

MedianDeviation[list]

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

Details

  • MedianDeviation is a robust measure of dispersion.
  • For the list {x1,x2,…,xn}, the median deviation is given by the median of the list {x1– ,…,xn –}, where is the median of the list.
  • MedianDeviation[{{x1,y1,…},{x2,y2,…},…}] gives {MedianDeviation[{x1,x2,…}],MedianDeviation[{y1,y2,…}],…}.

Examples

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Basic Examples  (2)

MedianDeviation of a list:

MedianDeviation of columns of a matrix:

Scope  (8)

Exact input yields exact output:

Approximate input yields approximate output:

Works with large arrays:

SparseArray data can be used just like dense arrays:

Find the median deviation of WeightedData:

Find the median deviation of EventData:

Find the median deviation of TimeSeries:

The median deviation depends only on the values:

Find the median deviation of data involving quantities:

Generalizations & Extensions  (1)

Compute results for a SparseArray:

Applications  (4)

Obtain a robust estimate of dispersion when extreme values are present:

Measures based on the Mean are heavily influenced by extreme values:

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

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

Choose a few slice times:

Plot median deviations over these paths:

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

Plot the median deviation respective of the median:

Properties & Relations  (2)

MedianDeviation is the Median of absolute deviations from the Median:

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

Possible Issues  (1)

MedianDeviation requires real numeric values:

Neat Examples  (1)

Ratio of MedianDeviation to MeanDeviation for increasing sample size:

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2022_mediandeviation, author="Wolfram Research", title="{MedianDeviation}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/MedianDeviation.html}", note=[Accessed: 01-April-2023 ]}

BibLaTeX

@online{reference.wolfram_2022_mediandeviation, organization={Wolfram Research}, title={MedianDeviation}, year={2007}, url={https://reference.wolfram.com/language/ref/MedianDeviation.html}, note=[Accessed: 01-April-2023 ]}