# 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: