Weighted Path Length From The Root
A weight function is a mathematical device used when performing a sum, integral, or average to give some elements more "weight" or influence on the result than other elements in the same set. The result of this application of a weight function is a weighted sum or weighted average. Weight functions occur frequently in statistics and analysis, and are closely related to the concept of a measure. Weight functions can be employed in both discrete and continuous settings. They can be used to construct systems of calculus called "weighted calculus" and "meta-calculus".Jane Grossma''Meta-Calculus: Differential and Integral'' , 1981. Discrete weights General definition In the discrete setting, a weight function w \colon A \to \R^+ is a positive function defined on a discrete set A, which is typically finite or countable. The weight function w(a) := 1 corresponds to the ''unweighted'' situation in which all elements have equal weight. One can then apply this weight to various con ...
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Weighted Average
The weighted arithmetic mean is similar to an ordinary arithmetic mean (the most common type of average), except that instead of each of the data points contributing equally to the final average, some data points contribute more than others. The notion of weighted mean plays a role in descriptive statistics and also occurs in a more general form in several other areas of mathematics. If all the weights are equal, then the weighted mean is the same as the arithmetic mean. While weighted means generally behave in a simil