Dispersion Indexes, Variance, and Standard Deviation

A pdf or cdf is determined only approximately by any location index. For practical purposes it is sufficient to know the value of one location index—e.g., the mean—together with a measure indicating how the probability density is distributed around the chosen location index. There are several such measures called dispersion indexes. The dispersion index most commonly used and the only one to be discussed here is the variance V(x) and its square root, which is called the standard deviation a. 

It is assumed that fix) satisfies Eq. 2.16 or 2.17 and Ai is a large number. It is worth noting that the variance is nothing more than the average of ix — mY. The variance of a linear function of x, a + bx, is 

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