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Relative Standard Deviation
Statistics - Relative Standard Deviation
In probabipty theory and statistics, the coefficient of variation (CV), also known as relative standard deviation (RSD), is a standardized measure of dispersion of a probabipty distribution or frequency distribution.
Relative Standard Deviation, RSD is defined and given by the following probabipty function:
Formula
${100 imes frac{s}{ar x}}$
Where −
${s}$ = the sample standard deviation
${ar x}$ = sample mean
Example
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.
Solution:
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.
${2.84 imes 100 = 284}$
Step 3 - Find the sample mean, ${ar x}$. The sample mean is:
${frac{(49 + 51.3 + 52.7 + 55.8)}{4} = frac{208.8}{4} = 52.2.}$
Step 4Divide Step 2 by the absolute value of Step 3.
${frac{284}{|52.2|} = 5.44.}$
The RSD is:
${52.2 pm 5.4}$%
Note that the RSD is expressed as a percentage.
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