The Foundation Center keeps Forms 990 for every non-profit organization which files with the IRS. It is fairly easy to see how much the school reported as income and expenses as well as a wealth of other data. Note that it is frankly impossible to compare apples to apples when it comes to private schools. Even their accounting and reporting varies from school to school. But a review of the data paints the same picture: costs are rising.
Another fact to consider is that tuition charged by a school does not completely offset expenses. That is why you will see your tuition bill filled with additional charges for technology, communications, laundry, athletics, uniforms and so on. These sundries, as the more bespoke schools style them, vary from school to school.