Editing Standard deviation (section)

{{Short description|In statistics, a measure of variation}}
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{{Use dmy dates|date=October 2020}}
[[File:Standard deviation diagram.svg|thumb|A plot of [[normal distribution]] (or bell-shaped curve) where each band has a width of 1 standard deviation&nbsp;– See also: [[68–95–99.7 rule]].]]
[[File:Normal-distribution-cumulative-density-function.svg|thumb|Cumulative probability of a normal distribution with expected value 0 and standard deviation 1]]

In [[statistics]], the '''standard deviation''' is a measure of the amount of variation of the values of a variable about its [[Expected value|mean]].<ref name=StatNotes>{{Cite journal|last1=Bland|first1=J.M.|last2=Altman|first2=D.G.|title=Statistics notes: measurement error|date=1996|journal=BMJ |volume=312|issue=7047|pages=1654|pmc=2351401|pmid=8664723|doi=10.1136/bmj.312.7047.1654}}</ref> A low standard [[Deviation (statistics)|deviation]] indicates that the values tend to be close to the [[mean]] (also called the [[expected value]]) of the set, while a high standard deviation indicates that the values are spread out over a wider range. The standard deviation is commonly used in the determination of what constitutes an [[outlier]] and what does not. Standard deviation may be abbreviated '''SD''' or '''std dev''', and is most commonly represented in mathematical texts and equations by the lowercase [[Greek alphabet|Greek letter]] '''[[Sigma|σ]]''' (sigma), for the population standard deviation, or the [[Latin script|Latin letter]] '''''[[s]]''''', for the sample standard deviation.

The standard deviation of a [[random variable]], [[Sample (statistics)|sample]], [[statistical population]], [[data set]], or [[probability distribution]] is the [[square root]] of its [[variance]]. (For a finite population, variance is the average of the [[squared deviations from the mean]].) A useful property of the standard deviation is that, unlike the variance, it is expressed in the same unit as the data. Standard deviation can also be used to calculate [[standard error]] for a finite sample, and to determine [[statistical significance]].

When only a [[statistical sample|sample]] of data from a population is available, the term ''standard deviation of the sample'' or ''sample standard deviation'' can refer to either the above-mentioned quantity as applied to those data, or to a modified quantity that is an unbiased estimate of the ''population standard deviation'' (the standard deviation of the entire population).