Standard deviation : The standard deviation of a random variable $X$ often denoted by $\sigma_X$ is the square root of its variance. It is defined as $\sigma_X=\sqrt{E[(X-E[X])^2]}=\sqrt{E[X^2]-E^2[X]}.$ The standard deviation is a measure for how far outcomes of $X$ will typically deviate from the mean $E[X].$