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[[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]] | [[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|last1=Dekking|first1=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" / | 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|last1=Dekking|first1=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" /> | ||
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|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" /> | 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|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" /> | ||
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| rowspan=" | | rowspan="13" |Q<sub>2</sub>=87<br /> (median of whole table) | ||
| rowspan="6" |Q<sub>1</sub>=31<br /> (median of lower half, from row 1 to 6) | | rowspan="6" |Q<sub>1</sub>=31<br /> (median of lower half, from row 1 to 6) | ||
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==References== | ==References== | ||
<references> | |||
<ref name=Upton>{{cite book |title=Understanding Statistics |first1=Graham|last1=Upton|first2=Ian|last2= Cook|year=1996 |publisher=Oxford University Press |isbn=0-19-914391-9 |page=55 |url=https://books.google.com/books?id=vXzWG09_SzAC&q=interquartile+range&pg=PA55}}</ref> | <ref name=Upton>{{cite book |title=Understanding Statistics |first1=Graham|last1=Upton|first2=Ian|last2= Cook|year=1996 |publisher=Oxford University Press |isbn=0-19-914391-9 |page=55 |url=https://books.google.com/books?id=vXzWG09_SzAC&q=interquartile+range&pg=PA55}}</ref> | ||
<ref name= ZK>Zwillinger, D., Kokoska, S. (2000) ''CRC Standard Probability and Statistics Tables and Formulae'', CRC Press. {{ISBN|1-58488-059-7}} page 18.</ref> | <ref name= ZK>Zwillinger, D., Kokoska, S. (2000) ''CRC Standard Probability and Statistics Tables and Formulae'', CRC Press. {{ISBN|1-58488-059-7}} page 18.</ref> | ||
</references> | |||
==External links== | ==External links== | ||