Category:Definitions/Weighted Means
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This category contains definitions related to Weighted Means.
Related results can be found in Category: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:
- $\bar x := \dfrac {w_1 x_1 + w_2 x_2 + \cdots + w_n x_n} {w_1 + w_2 + \cdots + w_n}$
Pages in category "Definitions/Weighted Means"
The following 3 pages are in this category, out of 3 total.