QuartileDeviation
QuartileDeviation[list]
gives the quartile deviation or semi-interquartile range of the elements in list.
QuartileDeviation[dist]
gives the quartile deviation or semi-interquartile range of the distribution dist.
Details

- QuartileDeviation is a robust measure of dispersion.
- QuartileDeviation[list] is equivalent to InterquartileRange[list]/2.
- QuartileDeviation[list,{{a,b},{c,d}}] uses the Quantile definition specified by parameters a, b, c, d.
Examples
open allclose allBasic Examples (2)
Scope (14)
Data (11)
Exact input yields exact output:
Approximate input yields approximate output:
QuartileDeviation for a matrix gives columnwise ranges:
SparseArray data can be used just like dense arrays:
Compute results using other parametrizations:
Find the quartile deviation for WeightedData:
Find the quartile deviation for EventData:
Find the quartile deviation for TemporalData:
Find the quartile deviation for TimeSeries:
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 quartile deviation:
Compute QuartileDeviation for slices of a collection of paths of a random process:
Plot of the quartile deviations for the selected times:
Find the quartile deviation of the heights for the children in a class:
Properties & Relations (3)
QuartileDeviation is half the difference of linearly interpolated Quantile values:
InterquartileRange is twice QuartileDeviation:
QuartileDeviation is half the difference between the first and third quartiles:
Possible Issues (1)
QuartileDeviation requires numeric values:

Neat Examples (1)
The distribution of QuartileDeviation estimates for 20, 100 and 300 samples:
Text
Wolfram Research (2007), QuartileDeviation, Wolfram Language function, https://reference.wolfram.com/language/ref/QuartileDeviation.html (updated 2017).
CMS
Wolfram Language. 2007. "QuartileDeviation." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2017. https://reference.wolfram.com/language/ref/QuartileDeviation.html.
APA
Wolfram Language. (2007). QuartileDeviation. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/QuartileDeviation.html