Education Secretary Lauro F. Cavazos yesterday urged every college in the nation to clarify its educational mission and cut administrative costs in order to hold down tuition charges, which rose faster than inflation in the last decade.

Despite those increases, Cavazos said, a college education remains affordable to qualified students, and cost-cutting on campus could keep it that way in the 1990s. He cited a College Board finding that almost half of all college students pay less than $2,000 a year in tuition and fees.

The secretary criticized news media for focusing on tuition charges at the most expensive schools while 80 percent of students attend two-year or four-year public colleges where tuition averages $1,800. The average is $9,400 at private four-year colleges.

"We need to be sure. . . that future increases do not make college unattainable," Cavazos told reporters. "Colleges and universities need not -- and must not -- try to do everything. Instead, each institution must determine its mission and make the necessary tradeoffs."

Cavazos, a former president of Texas Tech University, said he would even suggest that colleges eliminate entire academic departments if they are tangential to a school's central mission and the courses are available at nearby institutions.

Another possibility for cost-cutting, he said, would be for neighboring colleges to consolidate libraries.

A new Education Department brochure, "Tough Choices: A Guide to Administrative Cost Management in Colleges and Universities," states that colleges often can trim administrative costs by 10 to 20 per- cent.

The 47-page brochure, being sent to every college president in the country, cites examples of unnamed colleges that found savings in student registration, academic advising, library and housekeeping budg- ets.

Cavazos praised a new report on Howard University that recommended closing or consolidating several academic programs in health, nursing, pharmacy, "human ecology" and education. "That's exactly what I'm talking about, and those are tough choices they are going to make there," he said.

The Education Department was venturing into the realm of college budgeting, he said, because of its mandate to ensure wide opportunity to attend college.

Cavazos said federal student aid has increased 23 percent beyond inflation since 1980. His aides said the growth, mostly in loans, did not keep pace with tuition increases that averaged about 8 percent a year in the 1980s -- well beyond inflation levels.

A number of large universities have embarked on large-scale efforts to cut administrative costs that have grown rapidly in recent years, including Stanford University, Cornell University and Washington University in St. Louis. Washington, for instance, decided to drop its sociology department and dental school.

But Richard F. Rosser, president of the National Institute of Independent Colleges and Universities, said large private universities have a greater capacity for savings than small, liberal arts schools.

"We find that most of our private colleges are already cut down to the bone," Rosser said. "Frankly, I think it would be difficult at most of our institutions to make significant savings. If anything, we're underadministered. We don't have enough people."

Rosser said what is needed is more federal and state aid to students as well as more encouragement for parents to save for college.

Leonard L. Haynes III, assistant secretary for post-secondary education, acknowledged that the department last year scrapped a printed brochure on student aid in favor of a stapled fact sheet. "We went to the fact sheet because of the {brochure's} cost. . . That was a tough choice we had to make," he said.