Think of all the educational programs that have been generated over the years, each with its own qualifications and rules. Reagan tried to fix it with block grants for a reason. The oversight often costs more than the amount that gets to beneficiaries.
I think it should be each Principal's duty to report these averages in his or her school to the school board or whomever they are responsible to. Then, anyone with a lick of sense can look at the reports and see if there are any inequities.
My point was refuting newzjunkey's "there can't be too much oversight," not that there shouldn't be any. Best to keep it local.
I doubt the teachers' salaries are where the inequities lie.
Unless they are non-union, temps, or unaccredited (IMO, accreditation is a monopoly barrier to entry). Remember, an unemployed engineer won't be accredited, but would be far more qualified to teach math than most accredited high school teachers.
Also, building maintenance would factor in. If you have ever seen a NYC school, you will know what I mean.
Charter schools often don't own their facilities, but, once again, special building codes governing schools often turn into horrendously expensive traps: new construction being too costly to attempt, so the old stuff that is deteriorated to the point of dangerous remains in use.
Teachers need to be accredited. Not everyone who has knowledge of a subject is qualified to teach it. Also, the old saying that those who can DO and those who can't TEACH should never be the rule in this country or even an option.