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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'').
[[category:statistics]]
[[category:probability]]
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'').
[[category:statistics]]
[[category:probability]]