Editing Quartile (section)

{{Short description|Statistic which divides data into four same-sized parts for analysis}}
{{Use mdy dates|date=May 2020}}

In [[statistics]], '''quartiles''' are a type of [[quantile|quantiles]] which divide 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 quartiles, resulting in four data divisions, are as follows:
* The first quartile (''Q''<sub>1</sub>) is defined as the 25th [[percentile]] where lowest 25% data is below this point. It is also known as the ''lower'' quartile.
* 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 75th percentile where lowest 75% data is below this point. It is known as the ''upper'' quartile, as 75% of the data lies below this point.<ref name=":0">{{Cite book |author=Dekking, Michel <!--1946–  --> |url=https://archive.org/details/modernintroducti0000unse_h6a1 |title=A modern introduction to probability and statistics: understanding why and how |date=2005 |publisher=Springer |isbn=978-1-85233-896-1 |location=London |pages=[https://archive.org/details/modernintroducti0000unse_h6a1/page/236/ 236-238] |oclc=262680588 |url-access=limited}}</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 generally not the same between adjacent quartiles (i.e. usually (''Q''<sub>3</sub> - ''Q''<sub>2</sub>) ≠ (''Q''<sub>2</sub> - ''Q''<sub>1</sub>)). [[Interquartile range]] (IQR) is defined as the difference between the 75th and 25th percentiles or ''Q''<sub>3</sub> - ''Q''<sub>1</sub>. 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>