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| In [[probability theory]] and [[statistics]], the '''relative standard deviation (RSD''' or '''%RSD)''' is the [[absolute value]] of the [[coefficient of variation]]. It is often expressed as a percentage. A similar term that is sometimes used is the '''relative variance''' which is the square of the coefficient of variation.<ref>Dodge, Y. (2003) ''The Oxford Dictionary of statistical Terms'', OUP. ISBN 0-19-920613-9</ref> Also, the '''relative standard error''' is a measure of a statistical estimate's reliability obtained by dividing the [[Standard error (statistics)|standard error]] by the estimate; then multiplied by 100 to be expressed as a percentage.
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| The relative standard deviation is widely used in [[analytical chemistry]] to express the precision and repeatability of an [[assay]]. It is also commonly used in fields such as [[engineering]] or [[physics]] when doing quality assurance studies and [[ANOVA gauge R&R]].
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| The equation of the relative standard deviation, given as a percentage is as follows:
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| :<math>{\%RSD} = \frac{s}{\bar{x}} \times 100</math>
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| where <math>{s}</math> is equal to the [[standard deviation]], and <math>\bar{x}</math> is equal to the [[mean]].<ref>{{cite web|title=Calculations for Assessing Data Quality|url=http://agg.pnnl.gov/docs/conducting-work/ex22.stm|accessdate=13 September 2013}}</ref> A lower percentage indicates a lower variability in the data set. Equally, a higher percentage indicates the data set is more varied.
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| == Examples ==
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| A data set of [100, 100, 100] has constant values. Its standard deviation is 0 and average is 100:
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| : 100% × 0 / 100 = 0%
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| A data set of [90, 100, 110] has more variability. Its standard deviation is 10 and its average is 100:
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| : 100% × 10 / 100 = 10%
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| A data set of [1, 5, 6, 8, 10, 40, 65, 88] has more variability again. Its standard deviation is 30.78.. and its average is 27.875:
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| : 100% × 30.78 / 27.875 = 110.41% | |
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| ==See also==
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| * [[Standard error (statistics)#Relative_standard_error|Relative Standard Error]]
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| ==Notes==
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| {{Reflist}}
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| [[Category:Statistical deviation and dispersion]]
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| [[Category:Statistical terminology]]
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| {{stat-stub}}
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