That's quite correct, but it's two fold. Even if you have funding from the state and feda (which we do get to offset this effect), the home lives of these kids are generally much worse than middle and upper neighborhoods, which also brings down the mean. We're talking pollution, 80 hour work weeks, higher incarceration, etc. it all brings down the mean.
Then the feds have the gall to REDUCE funding if schools can't bring themselves to by the bootstraps? It's awful. That said, Obama admin did help a little in this regard, since at least they did listen to the educational research on this.