When using the geometric mean to compare data with different ranges, how do you include a binary piece of data? For instance, if you were comparing 10 companies on 3 categories, with the first category having a range of 1-5, the second having a range of 1-100, and the third being either 0 or 1. All three categories are important, but using the geometric mean will give a value of 0 for the third category.

The geometric mean has no sense for a dichotomous variables coded as 0 or 1. To compare these types of variables across groups, you have to use another method. Comparing proportions using a standard chi-square test may be a good choice.