Editing Interquartile range (section)

{{Short description|Measure of statistical dispersion}}
{{Redirect|IQR}}
[[Image:Boxplot vs PDF.svg|250px|thumb|[[Boxplot]] (with an interquartile range) and a [[probability density function]] (pdf) of a Normal {{maths|N(0,σ<sup>2</sup>)}} Population]]

In [[descriptive statistics]], the '''interquartile range''' ('''IQR''') is a measure of [[statistical dispersion]], which is the spread of the data.<ref name=":1">{{Cite book|last=Dekking|first=Frederik Michel|url=http://link.springer.com/10.1007/1-84628-168-7|title=A Modern Introduction to Probability and Statistics|last2=Kraaikamp|first2=Cornelis|last3=Lopuhaä|first3=Hen Paul|last4=Meester|first4=Ludolf Erwin|date=2005|publisher=Springer London|isbn=978-1-85233-896-1|series=Springer Texts in Statistics|location=London|doi=10.1007/1-84628-168-7}}</ref> The IQR may also be called the '''midspread''', '''middle 50%''', '''fourth spread''', or '''H‑spread.''' It is defined as the difference between the 75th and 25th [[percentiles]] of the data.<ref name="Upton" /><ref name="ZK" /><ref>{{Cite book|last=Ross|first=Sheldon|title=Introductory Statistics|publisher=Elsevier|year=2010|isbn=978-0-12-374388-6|location=Burlington, MA|pages=103–104}}</ref> To calculate the IQR, the data set is divided into [[quartile]]s, or four rank-ordered even parts via linear interpolation.<ref name=":1" /> These quartiles are denoted by ''Q''<sub>1</sub> (also called the lower quartile), ''Q''<sub>2</sub> (the [[median]]), and ''Q''<sub>3</sub> (also called the upper quartile). The lower quartile corresponds with the 25th percentile and the upper quartile corresponds with the 75th percentile, so IQR = ''Q''<sub>3</sub> −  ''Q''<sub>1</sub><ref name=":1" /><sub>.</sub>

The IQR is an example of a [[trimmed estimator]], defined as the 25% trimmed [[Range (statistics)|range]], which enhances the accuracy of dataset statistics by dropping lower contribution, outlying points.<ref name=":2">{{Cite book|last=Kaltenbach|first=Hans-Michael|url=https://www.worldcat.org/oclc/763157853|title=A concise guide to statistics|date=2012|publisher=Springer|isbn=978-3-642-23502-3|location=Heidelberg|oclc=763157853}}</ref> It is also used as a [[Robust measures of scale|robust measure of scale]]<ref name=":2" /> It can be clearly visualized by the box on a [[box plot]].<ref name=":1" />