# Relative Standard Deviation Formula

Relative standard deviation is also called percentage relative standard deviation formula, is the deviation measurement that tells us how the different numbers in a particular data set are scattered around the mean. This formula shows the spread of data in percentage.

If the product comes to a higher relative standard deviation, that means the numbers are very widely spread from its mean.Â

If the product comes lower, then the numbers are closer than its average. Â It is also knows as the coefficient of variation.

The formula for the same is given as:

$\large RSD=\frac{s\times 100}{\overline{x}}$

Where,
RSD = Relative standard deviation
sÂ = Standard deviation
$$\begin{array}{l}\overline{x}\end{array}$$
= Mean of the data.

### Solved Examples

QuestionÂ 1: Following are the marks obtained in by 4 students in mathematics examination: 60, 98, 65, 85. Calculate the relative standard deviation ?

Solution:

Formula of the mean is given by:

$$\begin{array}{l}\overline{x}\end{array}$$
=
$$\begin{array}{l}\frac{\sum x}{n}\end{array}$$

$$\begin{array}{l}\overline{x}\end{array}$$
=
$$\begin{array}{l}\frac{60+ 98+ 65+ 85}{4}=77\end{array}$$

Calculation of standard deviation:

 $$\begin{array}{l}x\end{array}$$ $$\begin{array}{l}x-\overline{x}\end{array}$$ $$\begin{array}{l}\left(x-\overline{x}\right)^{2}\end{array}$$ 60 -17 289 98 21 441 65 -12 144 85 8 64 $$\begin{array}{l}\sum \left(x-\overline{x}\right)^{2}=938\end{array}$$

Formula for standard deviation:
S =

$$\begin{array}{l}s=\sqrt{\frac{\sum \left(x-\overline{x}^{2}\right)}{n-1}}\end{array}$$
Â

S =
$$\begin{array}{l}\sqrt{\frac{938}{3}}\end{array}$$

S = 17.66
Relative standard deviation =
$$\begin{array}{l}\frac{s\times 100}{\overline{x}}\end{array}$$
Â

=
$$\begin{array}{l}\frac{17.66\times 100}{77}\end{array}$$
Â

= 22.93%