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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 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]
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.
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]
For normally distributed random variables inverse-variance weighted averages can also be derived as the maximum likelihood estimate for the true value. Furthermore, from a Bayesian perspective the posterior distribution for the true value given normally distributed observations and a flat prior is a normal distribution with the inverse-variance weighted average as a mean and variance ().
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 unbiased weighted estimator of the sample variance can be computed as follows: = = (=) = = (¯). Again, the corresponding standard deviation is the square root of the variance.
c = cost of capital, or the weighted average cost of capital (WACC). NOPAT is profits derived from a company's operations after cash taxes but before financing costs and non-cash bookkeeping entries. It is the total pool of profits available to provide a cash return to those who provide capital to the firm.