InterquartileRange
InterquartileRange[list]
gives the difference between the upper and lower quartiles for the elements in list.
InterquartileRange[dist]
gives the difference between the upper and lower quartiles for the distribution dist.
Details

- InterquartileRange is a robust measure of dispersion.
- With {q1,q2,q3}=Quartiles[list], InterquartileRange[list] is equivalent to q3-q1.
- InterquartileRange[dist] is equivalent to Quantile[dist,3/4]-Quantile[dist,1/4].
- InterquartileRange[list,{{a,b},{c,d}}]
uses the quantile definition specified by parameters a, b, c, d.
Examples
open allclose allBasic Examples (2)
Scope (13)
Data (10)
Exact input yields exact output:
Approximate input yields approximate output:
InterquartileRange for a matrix gives columnwise ranges:
SparseArray data can be used just like dense arrays:
Compute results using other parametrizations:
Find the interquartile range for WeightedData:
Find the interquartile range for EventData:
Find the interquartile range for TemporalData:
Find the interquartile range of TimeSeries:
Applications (6)
InterquartileRange indicates the spread of values:
InterquartileRange can be used as a check for agreement between data and a distribution:
Find the interquartile range of the data:
Compare with the interquartile range of the distribution:
Identify periods of high volatility in stock data using an annual moving interquartile range:
Find the interquartile ranges for the girth, height, and volume of timber, respectively, in 31 felled black cherry trees:
Compute InterquartileRange for slices of a collection of paths of a random process:
Plot of the interquartile range for the selected times:
Find the interquartile range of the heights for the children in a class:
Properties & Relations (4)
InterquartileRange is the difference of linearly interpolated Quantile values:
QuartileDeviation is half the interquartile range:
InterquartileRange is the difference between the first and third quartiles:
BoxWhiskerChart shows the interquartile range for data:
Possible Issues (1)
InterquartileRange requires numeric values:

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