Earlier quoted context omitted.
You continue to shift terms, so it makes it more difficult to pin you down. My math is pretty solid - socio-economic classes are defined by values in intervals . So guessing the average income for each race would be guessing what interval? It would be guessing middle class for each race! Remember, you stated the proposition that, 'race is a good class indicator' - thus, we don't care about variance in the interval ca…
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The "set of classes" means nothing. If you're trying to predict someone's behavior, distinguishing someone who makes $59,999 from someone who makes $60,000 makes no sense. If it helps, pretend I said "socioeconomic status" every time I said "class". They're interchangeable to me, though the latter indeed implies discrete groups.
With that said, if you think living on $55,530 is anything like living on $34,218, you're just wrong. How can multiplying one's income by 1.6 not have a massive effect on their life?
That's ignoring the decreasing marginal utility of a dollar as incomes rise. The poverty threshold for a family of four is $22,025. Black households have a "surplus" income of $12,193. White households have a surplus income of $33,505. The average white family will find itself in a situation where theft is attractive far less often than the average black family.
"Not substantial"? Consider my mind boggled.