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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.
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.
A weighted average is an average that has multiplying factors to give different weights to data at different positions in the sample window. Mathematically, the weighted moving average is the convolution of the data with a fixed weighting function.
Inverse Distance Weighting as a sum of all weighting functions for each sample point. Each function has the value of one of the samples at its sample point and zero at every other sample point. Inverse distance weighting (IDW) is a type of deterministic method for multivariate interpolation with a known scattered set of points.
Kernel average smoother example. The idea of the kernel average smoother is the following. For each data point X 0, choose a constant distance size λ (kernel radius, or window width for p = 1 dimension), and compute a weighted average for all data points that are closer than to X 0 (the closer to X 0 points get higher weights).
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 unbiased weighted estimator of the sample variance can be computed as follows: = = (=) = = (¯). Again, the corresponding standard deviation is the square root of the variance.
The average cost is computed by dividing the total cost of goods available for sale by the total units available for sale. This gives a weighted-average unit cost that is applied to the units in the ending inventory. There are two commonly used average cost methods: Simple weighted-average cost method and perpetual weighted-average cost method. [2]