You're statistics mean absolutely nothing.

"Public school revenue and expenditures vary by school district but Washington DC public schools spend an average of $12,046 per student each year."

Expenditures vary by district and if you look at the median price of houses in each area, you can just about guess where the majority of the funding goes.

I believe that socio-economic class has far more to do with the quality of the neighborhood school. Lets face it, if you have enough money to buy a home in an upscale neighborhood, it doesn't matter what colour your skin might be, you will be given an excellent education in the same school as your neighbor's kids. If you are rich enough, the colour of your skin is not a barrier to anything.

Thats why I think discussion of racial differences is a dead-end. Its your socio-economic class that makes a difference. It all depends on where you can afford to live. Mixed (affordable) housing should be available in every neighborhood and there should be no barriers based on race. This can be planned at the city level and funded by all levels of government. The integration of schools will take care of itself.