I know the formulas for standardizing, normalizing, and mean normalizing (if we take the wikipedia's definition for these terms). What I want to do is to normalize to a set value. For example, if I live in Peoria, IL where the cost of living index is 1.04, then how do I normalize to 20 other cities' cost of livings (87.9, 93.9, 113, 158.3)?
Essentially, I want to know if a dollar goes so far in the area that I am used to, how much will a dollar go in the cities I might want to move to. Is this just standardizing to a z score?