### Relative standard deviation

It has been suggested that this article be merged into Coefficient of variation. (Discuss) Proposed since April 2013. |

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.^{[1]} Also, the **relative standard error** is a measure of a statistical estimate's reliability obtained by dividing the standard error by the estimate; then multiplied by 100 to be expressed as a percentage.

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.

The equation of the relative standard deviation, given as a percentage is as follows:

- $\{\backslash \%RSD\}\; =\; \backslash frac\{s\}\{\backslash bar\{x\}\}\; \backslash times\; 100$

where $\{s\}$ is equal to the standard deviation, and $\backslash bar\{x\}$ is equal to the mean.^{[2]} A lower percentage indicates a lower variability in the data set. Equally, a higher percentage indicates the data set is more varied.

## Examples

A data set of [100, 100, 100] has constant values. Its standard deviation is 0 and average is 100:

- 100% × 0 / 100 = 0%

A data set of [90, 100, 110] has more variability. Its standard deviation is 8.16 and its average is 100:

- 100% × 8.16 / 100 = 8.16%

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:

- 100% × 30.78 / 27.875 = 110.41%

## See also

- Relative Standard Error

## Notes

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