Percent Relative Standard Deviation

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 Math / Science

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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