This equation takes in ten data values typically representing normalized decision criteria.  It computes the weighted geometric mean of these input data values. 

The weighted geometric mean is a powerful equation in decision analysis applications, allowing you to weight and combine externally generated values for a set of decision criteria.  This particular equation is limited to 10 input criteria which are assumed to have been normalized. 

Given a set of data,  X = {`x_1, x_2, ... , x_n`}, the corresponding weights are: W = {`w_1, w_2, ... , w_n`}.

If all the weights are set equal, the weighted geometric mean is equivalent to the common geometric mean.

Notes

vCalc has the means to attach an equation, in this case the weighted geometric mean, to columns of data in a data set, so this statistical function can be applied to a much larger data set than ten items.  See  for an example of using the weighted geometric mean on a set of criteria and weights defined in a Data Set.  This alternative version of the weighted geometric mean can take in any number of data elements from a Data Set.

This equation's particular implementation of the weighted geometric mean is intended to primarily be applied to decision analysis questions where the number of decision criteria is relatively small, ten or less.

The weighted geometric mean has the ease-of-use characteristic that any data value whose weight is set to zero will not affect the result.  So, this allows you to do quick what-if analysis where, in addition to trying different combination of data values and weights, you can test "what if I don't consider the n-th criteria at all".

The obvious use in decision support applications is the ability to changes weights representing relative importance of a specific criteria and/or the criteria values themselves and compare the results to another set of weights and criteria values.