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
open allclose allBasic Examples (2)
Scope (8)
Exact input yields exact output:
Approximate input yields approximate output:
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:
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:
Plot median deviations over these paths:
Find the median deviation of the heights for the children in a class:
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:
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