Category:Weighted Means

This category contains results about Weighted Means.
Definitions specific to this category can be found in Definitions/Weighted Means.

Let $S = \sequence {x_1, x_2, \ldots, x_n}$ be a sequence of real numbers.

Let $W$ be a weight function to be applied to the terms of $S$.

The weighted mean of $S$ with respect to $W$ is defined as:

$\bar x := \dfrac {\ds \sum_{i \mathop = 1}^n \map W {x_i} x_i} {\ds \sum_{i \mathop = 1}^n \map W {x_i} }$

This means that elements of $S$ with a larger weight contribute more to the weighted mean than those with a smaller weight.

If we write:

$\forall i: 1 \le i \le n: w_i = \map W {x_i}$

we can write this weighted mean as:

$\bar x := \dfrac {w_1 x_1 + w_2 x_2 + \cdots + w_n x_n} {w_1 + w_2 + \cdots + w_n}$