Revision as of 14:03, 1 November 2023 edit 208.185.97.170 (talk) Corrected the definition of the lowest quartile, removed "median" from it ← Previous edit		Revision as of 14:06, 1 November 2023 edit undo 208.185.97.170 (talk) Also, corrected definition of the highest quartile Next edit →
Line 3: In [[statistics]], a '''quartile''' is a type of [[quantile]] which divides the number of data points into four parts, or ''quarters'', of more-or-less equal size. The data must be ordered from smallest to largest to compute quartiles; as such, quartiles are a form of [[order statistic]]. The three main quartiles are as follows: * The first quartile (''Q''<sub>1</sub>) is defined as the middle number between the smallest number ([[Sample minimum\|minimum]]) and the value that falls between the 25th and 75th percentiles of the sample (which cuts off ~~1/4~~the first quarter of all the samples). It is also known as the ''lower'' quartile, as 25% of the data is below this point. * 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~~value that cuts off the last quarter of samples 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>

Quartile: Difference between revisions