Let's say we have N cookies. We are giving the cookies to kids in different schools in different states. Each school has a fixed number of kids. We want a final value of cookies per kid for each state.
Once we have that value, Cs, "cookies per kid" for each state, what is the interpretation of a percentage of total? For example, if we added up all 50 states value (C1 + C2 + C3 + ...) then computed the fractional 'contribution' of each state (C1/(C1 + C2 + C3 + ...) what exactly would that mean?
I argue that it's meaningless, but I'm not sure I can articulate why. Perhaps I am wrong. The premise here is that I have created a normalized count of something and the "percentage contribution of each state" has been requested by management.
The normalization, however, is necessary, since the number of kids from state to state varies and we don't want a high volume of schools in a particular state to skew the numbers.