I doubt the actual number of private schools is as relevant as the fact that private schools educate less than 10% of students and that the average private school is much smaller than an average public one.
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I was curious about how many schools are in the US.
From Wikipedia entry ("Education in the United States"):
In 2010, there were 3,823,142 teachers in public, charter, private, and
Catholic elementary and secondary schools. They taught a total of
55,203,000 students, who attended one of 132,656 schools.
5,072,451 students attended 33,740 private elementary and secondary
schools in 2007
So private schools make up about 25% of the total.