$6k for white pupil in NY $5k for black pupil in NY
$3k for white pupil in Ohio $2k for black pupil in Ohio
Clearly that's more money for white pupils regardless of location
Now imagine that there's 60 black students in NY and 10 in Ohio, but 10 white students in NY and 60 in Ohio
That means total funding is 320k for 70 black pupils and 240k for 70 white students
So you can spin the figures to say that black pupils get more funding, but the truth is the opposite.
For example, if District X pays better than neighboring district Z, District X will most likely have greater chance of hiring teachers in both districts, letting them choose the most qualified. Resulting in the school with higher salaries naturally getting more teacher candidates to choose from.
While some expenditures might not have a direct impact on student educations, they still have some effect. Another one would be - a school investing in a new Air conditioning and filtration system, students are probably going to have an easier time learning when they don't have to worry about being too hot or too cold in their classrooms.