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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 ...
The lower weighted median is 2 with partition sums of 0.49 and 0.5, and the upper weighted median is 3 with partition sums of 0.5 and 0.25. In the case of working with integers or non-interval measures, the lower weighted median would be accepted since it is the lower weight of the pair and therefore keeps the partitions most equal. However, it ...
In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first moment) is a generalization of the weighted average. Informally, the expected value is the arithmetic mean of the possible values a random variable can take, weighted by the ...
In statistics, a moving average ( rolling average or running average or moving mean[ 1] or rolling mean) is a calculation to analyze data points by creating a series of averages of different selections of the full data set. Variations include: simple, cumulative, or weighted forms. Mathematically, a moving average is a type of convolution.
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 ...
Definition. The arithmetic mean of a set of observed data is equal to the sum of the numerical values of each observation, divided by the total number of observations. Symbolically, for a data set consisting of the values , the arithmetic mean is defined by the formula: [ 2] (For an explanation of the summation operator, see summation .)
Generalized mean. Plot of several generalized means . In mathematics, generalized means (or power mean or Hölder mean from Otto Hölder) [ 1] are a family of functions for aggregating sets of numbers. These include as special cases the Pythagorean means ( arithmetic, geometric, and harmonic means ).
The generalized mean, also known as the power mean or Hölder mean, is an abstraction of the quadratic, arithmetic, geometric, and harmonic means. It is defined for a set of n positive numbers xi by. [ 1] By choosing different values for the parameter m, the following types of means are obtained: maximum of. quadratic mean.