Standard deviation
From Conservapedia
| This article/section deals with mathematical concepts appropriate for a student in late high school or early university. |
Standard deviation is a measure in statistics of the dispersion of a set of values (represented as X). It is defined as the square root of the variance of these values, where variance is defined as
![\sigma^2 = \operatorname{E}[(X-\operatorname{E}[X])^2] = \operatorname{E}[X^2] - (\operatorname{E}[X])^2](images/math/a/a/a/aaaa43abfad7d330dd949fe18a21350b.png)
where the expected value of X is E(X).
Thus the standard deviation is
![\sigma = \sqrt{\operatorname{E}[(X-\operatorname{E}[X])^2]} = \sqrt{\operatorname{E}[X^2] - (\operatorname{E}[X])^2}](images/math/0/a/a/0aa016b9a1bd18f25ebd00f822912559.png)
The formula for standard deviation must not be confused with the formula
(where 
is the sample mean).
which is the formula for a point estimate of the true standard deviation from a sample size of n. As such this statistical estimator itself has a variance which, as the formula indicates, decreases as the sample size increases.
