In the area of probability and statistics, standard deviation is a measurement of the spread of values of elements like probability distribution, random variable etc. It is basically the square root of the variance. Standard deviation is simply the root mean square or the RMS deviation of values from their arithmetic mean.

Standard deviation is the most commonly used measurement of statistical dispersion, which measures how broadly spread the values in one particular data group actually are. If the data points are all near to the mean, then the standard deviation is near to the figure zero, and vice versa. If all values of the data are same, then the standard deviation would be the figure zero. The formula for standard deviation of a random variable is given below: σ = √ E (( X – E (X))2) = √ E(X2) – (E(X)))2

In the above formula, E(X) is the expected value of X.

Standard deviation is the most commonly used measurement of statistical dispersion, which measures how broadly spread the values in one particular data group actually are. If the data points are all near to the mean, then the standard deviation is near to the figure zero, and vice versa. If all values of the data are same, then the standard deviation would be the figure zero. The formula for standard deviation of a random variable is given below: σ = √ E (( X – E (X))2) = √ E(X2) – (E(X)))2

In the above formula, E(X) is the expected value of X.