Weighted Geometric Mean (bounded criteria)

Not Reviewed
Equation / Last modified by mike on 2015/07/30 06:58
`barx = `
Weighted Geometric Mean (bounded criteria)
Variable Instructions Datatype
Upper Bound of Inputs Enter the upper bound for the inputs or leave as zero to ignore bound Decimal
Lower Bound of Inputs Enter the lower bound for the inputs or leave as zero to ignore bound Decimal
Criteria 1 Enter the criteria value of the first criteria Decimal
Weight 1 Enter the weight of the first criteria Decimal
Criteria 2 Enter the criteria value of the second criteria Decimal
Weight 2 Enter the weight of the second criteria Decimal
Criteria 3 Enter the criteria value of the third criteria Decimal
Weight 3 Enter the weight of the third criteria Decimal
Criteria 4 Enter the criteria value of the fourth criteria Decimal
Weight 4 Enter the weight of the fourth criteria Decimal
Criteria 5 Enter the criteria value of the fifthcriteria Decimal
Weight 5 Enter the weight of the fifth criteria Decimal
Criteria 6 Enter the criteria value of the sixth criteria Decimal
Weight 6 Enter the weight of the sixth criteria Decimal
Criteria 7 Enter the criteria value of the seventh criteria Decimal
Weight 7 Enter the weight of the seventh criteria Decimal
Criteria 8 Enter the criteria value of the eighth criteria Decimal
Weight 8 Enter the weight of the eighth criteria Decimal
Criteria 9 Enter the criteria value of the ninth criteria Decimal
Weight 9 Enter the weight of the ninth criteria Decimal
Criteria 10 Enter the criteria value of the tenth criteria Decimal
Weight 10 Enter the weight of the tenth criteria Decimal
Rating
ID
MichaelBartmess.Weighted Geometric Mean (bounded criteria)
UUID
0348334b-4e54-11e3-9569-bc764e049c3d

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.