Weighted Geometric Mean (bounded criteria)

Not Reviewed
Equation / Last modified by mike on 2015/07/30 06:58
`barx = `
MichaelBartmess.Weighted Geometric Mean (bounded criteria)

This equation takes in ten data values typically representing normalized criteria.  It computes the weighted geometric mean of the 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 to the specified range.  A corresponding equation will be created that can take in any number of data elements from a data set.

Given a set of data, these data being the criteria when applied in a decision analysis context, 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.

Note:  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.  This 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 upper and lower bound for the range of the inputs is used to check that the user input value is not outside an expected range.  If you wish to ignore bounds on the range of the input criteria values, simply leave both upper and lower bound set at the default 0 value.

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 you test "what if I don't consider the sixth criteria at all.

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