Online Calculators & Tools

In probability and statistics, the *standard deviation* of a random variable is the average distance of a random variable from the mean value.

It represents how the random variable is distributed near the mean value. Small standard deviation indicates that the random variable is distributed near the mean value. Big standard deviation indicates that the random variable is distributed far from the mean value.

The standard deviation is the square root of the variance of random variable X, with mean value of μ.

From the definition of the standard deviation we can get

For continuous random variable with mean value μ and probability density function f(x):

or

For discrete random variable X with mean value μ and probability mass function P(x):

or