This equation computes weighted evaluation criteria for a vCalc competition held in Nairobi, Kenya. The judging criteria and their respective weights are input from the data set:

Inputs

Competitor - name of vCalc competition participant

Usage

The competition coordinator adds new records into the dataset containing competitors' score cards (data set: vCalc Competition on ddMMyyyy) for each person or team signed up for the competition.

The competitor (teams') names must be added to the enumerated list of this equations that the user has the pull-down option to see the weighted final score for each competitor.

The competition coordinator must assign the weights to the evaluation criteria as inputs to this equation.  These are weights  for the relative value of each evaluation criteria and are used as the weighting factors in a weighted geometric mean inside this equation.

If any evaluation criteria is not to be considered, it can be assigned a weighting factor of zero.  Generally it is easier to understand the weighting scheme if the weights are all from a standard range (like 1 through 10).  Weights may be real numbers but integer values may be easier to estimate.

Description

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.  The data set is limited only by the number of rows of data provided in the data set.  To simplify the combining function, it is assumed the judging criteria data has been normalized. 

Given a set of judging data,  X = {`X_1, X_2, ... , X_n`}, the corresponding weights are: W = {`W_1, W_2, ... , W_n`}.  This equation computes the resultant weighted geometric mean:

`barx = (prod_"i-1"^N X_i^(W_i))^(1/(sum_"i=1"^10 I_i)), where X = (X_1,X_2, ..., X_N) and  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. 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 the question of "what if I don't consider the n-th criteria at all".

This equation's particular implementation of the weighted geometric mean is intended to to support comparisons of combined criteria that are best combined when normalized. 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.