I would assume you would just find the total budget of a particular district and then divide it by the total number of students. Even at private schools cost is a bit tricky. I teach at a small private school and our tuition does not reflect the cost of actually running the school.
My wife teaches at a large public school. She is a special education teacher. She has 4 students and 3 aides. Her salary is about 50,000 per year, and that doesn’t include benefits which probably run another 15-20 grand. Her aides probably make 30k apiece each. So in her case it costs approximately $125,000 or more to educate 4 children.
I don’t think schools generally count administrative costs when calculating the cost of educating a child.