# 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×sx¯100×sx¯

Where −

·        ss = the sample standard deviation

·        x¯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.

2.84×100=2842.84×100=284

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

(49+51.3+52.7+55.8)4=208.84=52.2.(49+51.3+52.7+55.8)4=208.84=52.2.

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

284|52.2|=5.44.284|52.2|=5.44.

The RSD is:

52.2±5.452.2±5.4%

Note that the RSD is expressed as a percentage.