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Mean

The mean of a set of values [math](x_1, x_2, ..., x_n)[/math] is often represented by [math]\overline{x}[/math]. The calculation of the mean is:

[display]\overline{x} = \mu = {\sum_{i=1}^n x_i \over n}[/display]

The mean may make use of weights (p):

[display]\overline{x} = \mu = {\sum_{i=1}^n x_i p_i \over \sum_{i=1}^n p_i}[/display]

You may want to normalize your weights, which means that their sum will equal 1, with the following:

[display]w_i = {p_i \over {\sum_{j=1}^n p_j}}[/display]

With normalized weights, you can simplify with the following:

[display]\overline{x} = \mu = ...