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E is a weighted average which takes into account both the most optimistic and most pessimistic estimates provided. SD measures the variability or uncertainty in the estimate. In Program Evaluation and Review Techniques the three values are used to fit a PERT distribution for Monte Carlo simulations. The triangular distribution is also commonly used
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 expected value of a random variable is the weighted average of the possible values it might take on, with the weights being the respective probabilities. More generally, the expected value of a function of a random variable is the probability-weighted average of the values the function takes on for each possible value of the random variable.
Smoothing of a noisy sine (blue curve) with a moving average (red curve). In statistics, a moving average (rolling average or running average or moving mean [1] or rolling mean) is a calculation to analyze data points by creating a series of averages of different selections of the full data set.
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. [6] 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 ...
Since the probabilities must satisfy p 1 + ⋅⋅⋅ + p k = 1, it is natural to interpret E[X] as a weighted average of the x i values, with weights given by their probabilities p i. In the special case that all possible outcomes are equiprobable (that is, p 1 = ⋅⋅⋅ = p k), the weighted average is given by the standard average. In the ...
Of those, only Arizona had a larger-than-average shift to the right of 5.8 points, while Nevada's 5.5-point rightward shift was about the same as the weighted average.
Despite its simplicity, the trimean is a remarkably efficient estimator of population mean. More precisely, for a large data set (over 100 points [3]) from a symmetric population, the average of the 18th, 50th, and 82nd percentile is the most efficient 3-point L-estimator, with 88% efficiency. [4]