Comparing cost of living of one state with that of other states
Quality of life matters too. This sometimes appears in the labor economics literature as "compensating differential". So it's probably not enough to weight cost of living by median or average wage unless you can objectively determine that all other factors are identical (e.g, tax structure, quality of transportation networks, population density, greenspace, etc.).

These factors are in general not likely to be pecuniary, so they are usually treated as a residual - if MW/COL in state A is less than MW/COL in state B, then the difference must be due to improved amenities in state A.  This is obviously unsatisfactory, and as a result there's a lot of active literature in this area.  And they will, of course, be highly subjective.