NEW YORK — COLLEGE undergraduates are paying an average tuition increase ranging from 6 to 13 percent above last year's costs, according to a recent survey by the College Board.The annual survey, which is based on responses from 78 percent of the nation's colleges and universities, shows that, on average, a four-year private college student is paying $10,017 for tuition and fees, up 7 percent from last year. At public institutions, a four-year in-state student is paying $2,137, up 12 percent. At two-year private colleges, the average tuition and fees is $5,290, up 6 percent, and at public two-year colleges it is $1,022, up 13 percent. "Although we haven't seen double-digit increases for public institutions since 1983, many people expected them this year because of the widely publicized cuts in state budgets," says Donald Stewart, president of the College Board. Public institutions report that they charge out-of-state students an average of $3,309 a year for a four-year education and $2,396 for two-year matriculation. Based on the survey, the College Board estimates that room and board, transportation, and personal expenses run from $4,913 for a student who lives at home and commutes to a two-year public college to $16,292 for a student in a dormitory at a four-year private institution. The Board notes that in the 1990-91 college year, $28 billion in scholarships, grants, loans, and other forms of financial aid helped about half of all college students pay for their education, up 4 percent from 1989-90.