 # 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.

If the product comes lower, then the numbers are closer than its average.  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
s = Standard deviation
$$\begin{array}{l}\overline{x}\end{array}$$
= Mean of the data.

### Solved Examples

Question 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 =

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

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

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

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

= 22.93%