Question

Let$x_1,x_2,x_3,...,x_n$, be $n$ observations and $a$ be the arithmetic mean then the formula for the standard deviation is given by?

Answer 1

Defining standard deviation.

Standard deviation is a measure of the amount of variation or spread of a set of values. The standard deviation is expressed as $\sigma$.

The formula of standard deviation is $\sigma =\sqrt{\frac{\sum _{i=1}^n{(x_i-a)}^2}{n}}$ where $a$ is the arithmetic mean.

Hence the formula for the standard deviation is given by $\sigma =\sqrt{\frac{\sum _{i=1}^n{(x_i-a)}^2}{n}}$.