Note that is a new random variable (it's a function of ). The variance is also denoted as .
A useful formula that follows inmediately from the definition is that

In words, the variance of is the second moment of minus the first moment squared.
The variance of a random variable determines a level of variation of the possible values of around its mean.
However, as this measure is squared, the standard deviation is used instead when one wants to talk about how much
a random variable varies around its expected value.
If we cannot analyze a whole population but we have to take a sample, we define its variance (denoted as ) with
the formula:

where is the aritmetic mean . The value for is an estimator for .
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If the value of the boolean argument <em> total </em> is true, then the variance is computed using the following formula: