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The weighted mean in this case is: ¯ = ¯ (=), (where the order of the matrix–vector product is not commutative), in terms of the covariance of the weighted mean: ¯ = (=), For example, consider the weighted mean of the point [1 0] with high variance in the second component and [0 1] with high variance in the first component.
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 ...
The lower weighted median is 2 with partition sums of 0.25 and 0.5, and the upper weighted median is 3 with partition sums of 0.5 and 0.25. These partitions each satisfy their respective special condition and the general condition. It is ideal to introduce a new pivot by taking the mean of the upper and lower weighted medians when they exist.
The Marshall-Edgeworth index, credited to Marshall (1887) and Edgeworth (1925), [11] is a weighted relative of current period to base period sets of prices. This index uses the arithmetic average of the current and based period quantities for weighting. It is considered a pseudo-superlative formula and is symmetric. [12]
The second form above illustrates that the logarithm of the geometric mean is the weighted arithmetic mean of the logarithms of the individual values. If all the weights are equal, the weighted geometric mean simplifies to the ordinary unweighted geometric mean. [1]
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]
For example, if two thirds of the sample was used for the first measurement and one third for the second and final measurement, then one might weight the first measurement twice that of the second.
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]
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