To be precise: average weighted population density doesn’t show the density average person experiences. To measure density of average person, we would have to calculate ‘median’ weighted density (i.e. such density level, that 50% of popualtion live in counties with same or higher density and 50% of population in counties with same or lower density)
For hypothetical state where 40% of population lives in dense metro, and 60% are scattered across the rest of the state, average weighted density and density of average person will be very different

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