InterquartileRange [data]
gives the difference between the upper and lower quartiles for the elements in data.
InterquartileRange [data,{{a,b},{c,d}}]
uses the quantile definition specified by parameters a, b, c, d.
InterquartileRange [dist]
gives the difference between the upper and lower quartiles for the distribution dist.
InterquartileRange
InterquartileRange [data]
gives the difference between the upper and lower quartiles for the elements in data.
InterquartileRange [data,{{a,b},{c,d}}]
uses the quantile definition specified by parameters a, b, c, d.
InterquartileRange [dist]
gives the difference between the upper and lower quartiles for the distribution dist.
Details
- InterquartileRange is also known as IQR.
- InterquartileRange is a robust measure of dispersion, which means it is not very sensitive to outliers.
- InterquartileRange [data] is given by , where is given by Quartiles [data]. »
- For MatrixQ data, the interquartile range is computed for each column vector with InterquartileRange [{{x1,y1,…},{x2,y2,…},…}], equivalent to {InterquartileRange[{x1,x2,…}],InterquartileRange[{y1,y2,…}]}. »
- For ArrayQ data, the interquartile range is equivalent to ArrayReduce [InterquartileRange,data,1]. »
- InterquartileRange [data,{{a,b},{c,d}}] uses the Quartiles definition specified by parameters a, b, c, d. »
- Common choices of parameters {{a,b},{c,d}} include:
-
{{0, 0}, {1, 0}} inverse empirical CDF{{0, 0}, {0, 1}} linear interpolation (California method){{1/2, 0}, {0, 0}} element numbered closest to p n{{1/2, 0}, {0, 1}} linear interpolation (hydrologist method; default){{0, 1}, {0, 1}} mean‐based estimate (Weibull method){{1, -1}, {0, 1}} mode‐based estimate{{1/3, 1/3}, {0, 1}} median‐based estimate{{3/8, 1/4}, {0, 1}} normal distribution estimate
- The default choice of parameters is {{1/2,0},{0,1}}. »
- The data can have the following additional forms and interpretations:
-
Association the values (the keys are ignored) »SparseArray as an array, equivalent to Normal [data] »QuantityArray quantities as an array »WeightedData based on the underlying EmpiricalDistribution »EventData based on the underlying SurvivalDistribution »
- InterquartileRange [dist] is given by , where is given by Quartiles [dist]. »
- For a random process proc, the interquartile range function can be computed for a slice distribution at time t, SliceDistribution [proc,t], as InterquartileRange [SliceDistribution [proc,t]]. »
Examples
open all close allBasic Examples (3)
Interquartile range for a list of exact numbers:
Interquartile range for a list of dates:
Interquartile range of a parametric distribution:
Scope (22)
Basic Uses (8)
Exact input yields exact output:
Approximate input yields approximate output:
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 :
The interquartile range depends only on the values:
Find the interquartile range for data involving quantities:
Array Data (5)
InterquartileRange for a matrix gives columnwise ranges:
Interquartile range for a tensor works across the first index:
Works with large arrays:
When the input is an Association , InterquartileRange works on its values:
SparseArray data can be used just like dense arrays:
Find interquartile range of a QuantityArray :
Image and Audio Data (2)
Channelwise interquartile range values of an RGB image:
Interquartile range intensity value of a grayscale image:
Interquartile range amplitude of all channels:
Date and Time (4)
Compute interquartile range of dates:
Compute the weighted interquartile range of dates:
Compare the simple interquartile range:
Compute the interquartile range of dates given in different calendars:
Compute the interquartile range of times:
List of times with different time zone specifications:
Distributions and Processes (3)
Find the interquartile range for a parametric distribution:
Interquartile range for a derived distribution:
Data distribution:
Interquartile range for a time slice of a random process:
Applications (6)
InterquartileRange indicates the spread of values:
InterquartileRange can be used as a check for agreement between data and a distribution:
Generate a random sample:
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:
Choose a few slice times:
Plot of the interquartile range for the selected times:
Find the interquartile range of the heights for the children in a class:
Plot the interquartile range respective of the median:
Properties & Relations (4)
InterquartileRange is the difference of linearly interpolated Quantile values:
InterquartileRange is the difference between the first and third quartiles:
QuartileDeviation is half the interquartile range:
BoxWhiskerChart shows the interquartile range for data:
Possible Issues (1)
InterquartileRange requires numeric values in data:
The symbolic closed form may exist for some distributions:
Neat Examples (1)
The distribution of InterquartileRange estimates for 20, 100, and 300 samples:
Tech Notes
Related Guides
History
Introduced in 2007 (6.0) | Updated in 2017 (11.1) ▪ 2023 (13.3) ▪ 2024 (14.1)
Text
Wolfram Research (2007), InterquartileRange, Wolfram Language function, https://reference.wolfram.com/language/ref/InterquartileRange.html (updated 2024).
CMS
Wolfram Language. 2007. "InterquartileRange." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2024. 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
BibTeX
@misc{reference.wolfram_2025_interquartilerange, author="Wolfram Research", title="{InterquartileRange}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/InterquartileRange.html}", note=[Accessed: 17-November-2025]}
BibLaTeX
@online{reference.wolfram_2025_interquartilerange, organization={Wolfram Research}, title={InterquartileRange}, year={2024}, url={https://reference.wolfram.com/language/ref/InterquartileRange.html}, note=[Accessed: 17-November-2025]}