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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 arithmetic mean (sometimes called the "unweighted average" or "equally weighted average") can be interpreted as a special case of a weighted average in which all weights are equal to the same number (in the above example and in a situation with numbers being averaged).
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.
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. Variations include: simple, cumulative, or weighted forms. Mathematically, a moving average is a type of convolution.
Informally, the expected value is the mean of the possible values a random variable can take, weighted by the probability of those outcomes. Since it is obtained through arithmetic, the expected value sometimes may not even be included in the sample data set; it is not the value you would "expect" to get in reality.
For p = 0 we set it equal to the geometric mean ... Furthermore, for a sequence of positive weights w i we define the weighted power mean as [2] ...
The fund is equally weighted across 11 sectors and each holding is equally weighted within each sector. 5-year returns (annualized): 8.9 percent. Expense ratio: 0.20 percent.
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]