# 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:

## Formula

${100 \times \frac{s}{\bar x}}$

Where −

• ${s}$ = the sample standard deviation

• ${\bar x}$ = 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.

${2.84 \times 100 = 284}$

Step 3 - Find the sample mean, ${\bar x}$. 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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