What sort of political districts are we talking about? Congressional, state senate, state house, city/ward?
I suppose it doesn't matter; only in the smallest communities is one census block going to consist of one township council seat, for instance.
I think what you might be asking is "Of the dozens/hundreds of census blocks in a political district, which one is the most typical?" But then you're not asking that at all.
You're asking for a rough estimate for the demographics of each political district.
Census.gov has much of that already done for you - but then that's probably where you got your input data.