# Given data points are 28, 30, 29, 26, 31 and 30, find standard deviation step by step?

Oct 25, 2017

Standard Deviation is $1.633$

#### Explanation:

Arithmetic Mean is simply sum of all data points divided by their number and as here data points are $28 , 30 , 29 , 26 , 31$ and $30$, their mean is

$\frac{28 + 30 + 29 + 26 + 31 + 30}{6} = \frac{174}{6} = 29$

Deviations from mean are values of data points minus arithmetc mean and here they are $28 - 29 = - 1$, $30 - 29 = 1$, $29 - 2 = 0$, $26 - 29 = - 3$, $31 - 29 = 2$ and $30 - 29 = 1$ respectively.

Squares of the deviations are $1 , 1 , 0 , 9 , 4$ and $1$.

As variance is average of square of the deviations , variance is $\frac{1 + 1 + 0 + 9 + 4 + 1}{6} = \frac{16}{6} = \frac{8}{3} = 2.6667$

and Standard Deviation is square root of variance i.e. $\sqrt{2.6667} = 1.633$