Standard Deviation
Standard Deviation is a statistical measure that quantifies the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range.
Definition[edit | edit source]
The standard deviation of a random variable, statistical population, data set, or probability distribution is the square root of its variance. It is algebraically simpler, though in practice less robust, than the average absolute deviation. A useful property of the standard deviation is that, unlike the variance, it is expressed in the same units as the data. Note, however, that for measurements with percentage as the unit, the standard deviation will have percentage points as the unit.
Calculation[edit | edit source]
In the case of a parametric family of distributions, the standard deviation can be expressed in terms of the parameters. For example, for a normal distribution, the standard deviation is the square root of the (non-central) second moment, or the square root of the variance.
Applications[edit | edit source]
The standard deviation is often used in statistics and the natural sciences to measure the amount of variation or dispersion of a set of values.
See also[edit | edit source]
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