Box plot: Difference between revisions

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[[File:Michelsonmorley-boxplot.svg|thumb|upright=1.5|Figure 1. Box plot of data from the [[Michelson–Morley experiment#Michelson experiment (1881)|Michelson experiment]]]]

In [[descriptive statistics]], a '''box plot''' or '''boxplot''' is a method for graphically demonstrating graphically the locality, spread and skewness groups of numerical data through their [[quartile]]s.<ref>{{Cite book|last=C.|first=Dutoit, S. H.|url=http://worldcat.org/oclc/1019645745|title=Graphical exploratory data analysis.|date=2012|publisher=Springer|isbn=978-1-4612-9371-2|oclc=1019645745}}</ref> In addition to the box on a box plot, there can be lines (which are called ''whiskers'') extending from the box indicating variability outside the upper and lower quartiles, thus, the plot is also called the '''box-and-whisker plot''' and the '''box-and-whisker diagram'''. [[Outlier]]s that differ significantly from the rest of the dataset<ref>{{Cite journal|last=Grubbs|first=Frank E.|date=February 1969|title=Procedures for Detecting Outlying Observations in Samples|url=http://dx.doi.org/10.1080/00401706.1969.10490657|journal=Technometrics|volume=11|issue=1|pages=1–21|doi=10.1080/00401706.1969.10490657|issn=0040-1706}}</ref> may be plotted as individual points beyond the whiskers on the box-plot.

Box plots are [[non-parametric]]: they display variation in samples of a [[statistical population]] without making any assumptions of the underlying [[probability distribution|statistical distribution]]<ref>{{Cite book|last=Richard.|first=Boddy|url=http://worldcat.org/oclc/940679163|title=Statistical Methods in Practice : for Scientists and Technologists.|date=2009|publisher=John Wiley & Sons|isbn=978-0-470-74664-6|oclc=940679163}}</ref> (though Tukey's boxplot assumes symmetry for the whiskers and normality for their length). The spacings in each subsection of the box-plot indicate the degree of [[statistical dispersion|dispersion]] (spread) and [[skewness]] of the data, which are usually described using the [[five-number summary]]. In addition, the box-plot allows one to visually estimate various [[L-estimator]]s, notably the [[interquartile range]], [[midhinge]], [[range (statistics)|range]], [[mid-range]], and [[trimean]]. Box plots can be drawn either horizontally or vertically.