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The average student grade can be obtained by averaging all the grades, without regard to classes (add all the grades up and divide by the total number of students): ¯ = = Or, this can be accomplished by weighting the class means by the number of students in each class.
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 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 overall grade for the class is then typically weighted so that the final grade represents a stated proportion of different types of work. For example, daily homework may be counted as 50% of the final grade, chapter quizzes may count for 20%, the comprehensive final exam may count for 20%, [1] and a major project may count for the remaining ...
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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.
A power mean serves a non-linear moving average which is shifted towards small signal values for small p and emphasizes big signal values for big p. Given an efficient implementation of a moving arithmetic mean called smooth one can implement a moving power mean according to the following Haskell code.
Algorithms for calculating variance play a major role in computational statistics.A key difficulty in the design of good algorithms for this problem is that formulas for the variance may involve sums of squares, which can lead to numerical instability as well as to arithmetic overflow when dealing with large values.