The weighted mean of a discrete set of numbers {x_1, x_2, ..., x_n} with weights {w_1, w_2, ..., w_n} is given by 〈x〉 = sum_(i = 1)^n w_i x_i, where each weight w_i is a nonnegative real number and sum_(i = 1)^n w_i = 1. For a continuous set of numbers x(t) parameterized by the variable t defined over the set T and a weight distribution w(t) also defined over T with w(t) nonnegative for all t element T and integral_T w(t) d t = 1, the weighted mean of x is given by 〈x〉 = integral_T w(t) x(t) d t.
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