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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 ...
A weighted average, or weighted mean, is an average in which some data points count more heavily than others in that they are given more weight in the calculation. [5] For example, the arithmetic mean of 3 {\displaystyle 3} and 5 {\displaystyle 5} is 3 + 5 2 = 4 {\displaystyle {\frac {3+5}{2}}=4} , or equivalently 3 ⋅ 1 2 + 5 ⋅ 1 2 = 4 ...
It is a measure used to evaluate the performance of regression or forecasting models. It is a variant of MAPE in which the mean absolute percent errors is treated as a weighted arithmetic mean. Most commonly the absolute percent errors are weighted by the actuals (e.g. in case of sales forecasting, errors are weighted by sales volume). [3]
Inverse-variance weighting. In statistics, inverse-variance weighting is a method of aggregating two or more random variables to minimize the variance of the weighted average. Each random variable is weighted in inverse proportion to its variance (i.e., proportional to its precision). Given a sequence of independent observations yi with ...
The weighted harmonic mean is the preferable method for averaging multiples, such as the price–earnings ratio (P/E). If these ratios are averaged using a weighted arithmetic mean, high data points are given greater weights than low data points. The weighted harmonic mean, on the other hand, correctly weights each data point. [14]
In survey methodology, the design effect (generally denoted as , , or ) is a measure of the expected impact of a sampling design on the variance of an estimator for some parameter of a population. It is calculated as the ratio of the variance of an estimator based on a sample from an (often) complex sampling design, to the variance of an ...
Inverse distance weighting (IDW) is a type of deterministic method for multivariate interpolation with a known scattered set of points. The assigned values to unknown points are calculated with a weighted average of the values available at the known points. This method can also be used to create spatial weights matrices in spatial ...
The earliest reference to a similar formula appears to be Armstrong (1985, p. 348), where it is called "adjusted MAPE" and is defined without the absolute values in the denominator. It was later discussed, modified, and re-proposed by Flores (1986).