(CBS Moneywatch) College price tags are meaningless. Why? Because most families don't pay the published bill, as a new federal report shows.

Students of all income levels routinely receive price cuts when they head off to college, according to statistics just released by the U.S. Department of Education.

Average cost of attendance

To fully appreciate the size of those discounts, you need to know the average cost of attendance (tuition, room/board, books/supplies) for students going to the three types of four-year institutions:

- Public colleges and universities: $17,563

- Private nonprofit colleges and universities: $33,969

- Private, for-profit colleges and universities: $27,854

Average grants/scholarships

The biggest grants come from private, nonprofit institutions, which have to remain financially competitive with public universities. Here are the average annual grants or scholarships (free money) that students receive at the three types of institutions:

- Public schools: $6,593

- Private non-profit schools: $14,200

- Private, for-profit schools: $5,317

Average net prices

After grants and scholarships are deducted, private for-profit schools are the most expensive. Here are the average net prices after the discounts are applied:

- Public institutions: $10,971

- Private non-profit schools: $19,770

- Private for-profit schools: $22,537

Bottom Line

Never shop for schools simply by looking at their published prices. Instead use a college's net price calculator to determine what the institution will cost your family.