The standard deviation is the square root of the variance for a distribution. Like the variance, it is a measure of dispersion about the mean and is useful for describing the “average” deviation.
For example, you can calculate the standard deviation of the values 1, 3, 6, 7, and 9 by finding the square root of the variance that is calculated in the variance example below.
The standard deviation, denoted as s, is calculated from the variance as follows:
where the variance is a measure of the dispersion, or spread, of a set of values about the mean. When values are close to the mean, the variance is small. When values are widely scattered about the mean, the variance is larger.