In mathematics, **mean** has several different definitions depending on the context.

In probability and statistics, **mean** and expected value are used synonymously to refer to one measure of the central tendency either of a probability distribution or of the random variable characterized by that distribution. In the case of a discrete probability distribution of a random variable *X*, the mean is equal to the sum over every possible value weighted by the probability of that value; that is, it is computed by taking the product of each possible value *x* of *X* and its probability P(*x*), and then adding all these products together, giving . An analogous formula applies to the case of a continuous probability distribution. Not every probability distribution has a defined mean; see the Cauchy distribution for an example. Moreover, for some distributions the mean is infinite: for example, when the probability of the value is for n = 1, 2, 3, ....

...

Wikipedia

...