A study by the Congressional Budget Office (CBO) indicates that some families with annual incomes as low as $15,000 -- well below the national median -- would lose money under the Reagan administraton's proposals to cut college student aid. Most of the loss would be in guaranteed student loans.

A typical $15,000 family, according to the study, would end up with $1,180 a year less than under current law to spend on college.

Median family income in 1982 is expected to be about $25,000.

The CBO study, requested by Rep, Dale E. Kildee (D-Mich.), said the student aid that affected families would lose would not be offset by the income tax cuts the president has proposed.

The study did not take into account the president's expected additional request for a tuition tax credit, but the credit is not expected to total more than a few hundred dollars a year and, therefore, would not make up for the losses in college grants and loans.

One portion of the study evaluated how much certain families would lose as a result of proposed cuts in basic educational grants for needy students, guaranteed student loans and school lunches. A typical family was postulated as having two working parents, a child in junion high school and a child in a public college. The study showed:

The family with earnings of $15,000 a year, which now might receive as much as $3,600 in basic college grants and guaranteed student loans, would get about $1,300 a year less (with three-quarters of the cut coming from the amount if could get in a guaranteed loan) and would also lose about $65 in school lunch subsidies.However, it would end up paying $185 less in income taxes.Its net loss would work out to $1,180 a year, the CBO said.

A $25,000 family, now getting $3,150 in basic grants and guaranteed loans, would get $2,400 less under these two programs and also lose $49. in school lunch subsidies. Even after pocketing $415 in income tax savings, it would have $2,012 less to spend on college.

Net loss for the $35,000 family would be $1,824.

The study said the Reagan cuts would not affect every family in the ways shown, because only about one-third eligible for guaranteed loans actually take them.