Statistics – Relative Standard Deviation

In probability theory and statistics, the coefficient of variation (CV), also known as relative standard deviation (RSD), is a standardized measure of dispersion of a probability distribution or frequency distribution.

Relative Standard Deviation, RSD is defined and given by the following probability function:



Where −

·        ss = the sample standard deviation

·        x¯x¯ = sample mean


Problem Statement:

Find the RSD for the following set of numbers: 49, 51.3, 52.7, 55.8 and the standard deviation are 2.8437065.


Step 1 – Standard deviation of sample: 2.8437065 (or 2.84 rounded to 2 decimal places).

Step 2 – Multiply Step 1 by 100. Set this number aside for a moment.


Step 3 – Find the sample mean, x¯x¯. The sample mean is:


Step 4Divide Step 2 by the absolute value of Step 3.


The RSD is:


Note that the RSD is expressed as a percentage.

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