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Quartile: Difference between revisions

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* The second quartile (''Q''<sub>2</sub>) is the median of a data set; thus 50% of the data lies below this point.
* The third quartile (''Q''<sub>3</sub>) is the middle value between the median and the highest value ([[Sample maximum and minimum|maximum]]) of the data set. It is known as the ''upper'' quartile, as 75% of the data lies below this point.<ref name=":0">{{Cite book|title=A modern introduction to probability and statistics: understanding why and how|url=https://archive.org/details/modernintroducti0000unse_h6a1|url-access=limited|date=2005|publisher=Springer|others=Dekking, Michel, 1946–|isbn=978-1-85233-896-1|location=London|pages=[https://archive.org/details/modernintroducti0000unse_h6a1/page/236/ 236-238]|oclc=262680588}}</ref>
Along with the minimum and maximum of the data (which are also quartiles), the three quartiles described above provide a [[five-number summary]] of the data. This summary is important in statistics because it provides information about both the [[Mean (Statistics)|center]] and the [[Statistical dispersion|spread]] of the data. Knowing the lower and upper quartile provides information on how big the spread is and if the dataset is [[Skewness|skewed]] toward one side. Since quartiles divide the number of data points evenly, the [[Range (statistics)|range]] is usually not the same between quartiles (i.e. usually ''Q''<sub>3</sub>-''Q''<sub>2</sub> = ''Q''<sub>2</sub>-''Q''<sub>1</sub>) and is instead known as the [[interquartile range]] (IQR). While the maximum and minimum also show the spread of the data, the upper and lower quartiles can provide more detailed information on the location of specific data points, the presence of [[outlier]]s in the data, and the difference in spread between the middle 50% of the data and the outer data points.<ref>{{Cite web |url=https://magoosh.com/statistics/quartiles-used-statistics/ |archive-url=https://web.archive.org/web/20191210060305/https://magoosh.com/statistics/quartiles-used-statistics/ |archive-date=2019-12-10 |url-status=deviated |title=How are Quartiles Used in Statistics? |last=Knoch |first=Jessica |date=February 23, 2018 |website=[[Magoosh]] |access-date=February 24, 2023}}{{cbignore}}</ref>
 
== Definitions ==