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`%RSD = sigma / bar x * 100%`

Enter a value for all fields

The **Percent Relative Standard Deviation** calculator computes the percent relative standard deviation based on the standard deviation for a sample and the mean for the sample.

**INSTRUCTIONS:** Enter the following:

- (
**σ**) Sample Standard Deviation - (
**`barx`**) Sample Mean

**Percent Relative Standard Deviation (%RSD):** The calculator returns the percent.

The percent relative standard deviation (%RSD) is also known as the coefficient of variation (CV). The %RSD is a measure of the dispersion of a probability distribution. Dividing the standard deviation by the mean of the data provides the relative magnitude of the standard deviation. This equation returns the %RSD as the percentage; i.e. an RSD for `sigma` = .05 and a `barx` = 1.0 should give you 5.0 percent as the output.

The equation for the Percent Relative Standard Deviation is :

%RSD = `sigma / barx` x 100%

where:

- `sigma` = standard deviation for the sample
- `barx` = mean for sample

The formula for statistical mean is the sum of observations divided by the number of observations as follows:

- `barx = (sum_1^n(x_n))/n`

where:

- `barx` is the statistical mean
- x
_{n}are the observations - n is the number of observations

The formula for sample standard deviation:

`sigma = sqrt((sum_1^n(x_n-mu)^2)/(n-1))`

where:

- σ is the standard deviation (sample or population)
- n is the number of observations
- μ is the statistical mean

*This equation is also represented in the Science/Chemistry/Analytical domain*

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- Range in a Set - this is the difference between the max and the min.
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