Standard deviation

The standard deviation of a set of values is a measure of how widely the values differ from each other. Specifically, the standard deviation is the square root of the average of the squares of the differences between the data values and their mean. In simple terms, the standard deviation is the distance from the mean within which the vast majority of data exists.

Examples help illustrate this concept. Learning the average height of basketball players us that half are above that height and half are below. Learning the standard deviation of their heights tells us how much opportunity there is for players who are shorter than the average.

Mathematically, the standard deviation of a random variable X is:

<math>\sigma = \sqrt{\operatorname{E}((X-\operatorname{E}(X))^2)} </math> <math>= \sqrt{\operatorname{E}(X^2) - (\operatorname{E}(X))^2}</math>

where the expected value of X is E(X).