The Pell grant program for needy college students made an estimated $649 million worth of errors in the 1982-83 school year through administrative mistakes and inaccurate applications, according to a study by the General Accounting Office.

The GAO report said new Education Department rules designed to strengthen the program's validation procedures caused delays in awarding grants and may have cost schools more to implement than they achieved in savings. The error rate climbed despite the new procedures, the report said.

Although the department has tried to address the problem, the GAO report said, "The department's management problems hinder effective action; the lack of policy on error and fragmentation within the Office of Student Financial Assistance has led to confused responsibilities for identifying and acting on error."

The errors occurred because students misreported their family income and also because institutions made mistakes in calculating the students' grants. Both the GAO and department officials said the errors were not deliberate, but merely human mistakes that occurred in dealing with the program's complicated forms and eligibility formulas.

Most of the $649 million in error was in the form of grants that were larger than students were eligible to receive. But that figure also includes a sizable amount for students who did not receive as much as they should have.

In the 1982-83 school year, the GAO said, 42 percent of the students received more money than they should have, while 21 percent did not receive enough. The average overpayment was $444 that year, and the average underpayment was $259, the study found.

More than 2.5 million students received grants averaging $959 that year, for a total of $2.4 billion.

An Education Department official in charge of the program said the problems cited by the GAO were well known, and have been the subject of at least three department quality-control reports.

But the official, C. Ronald Kimberling, assistant secretary for postsecondary education, said that most of the problems are being addressed and that the GAO's findings could be outdated.

"We're aware of a significant amount of error," said Kimberling. "It's not just blowing smoke to say there are some serious errors in the program."

But, he said, "We feel that our most recent efforts are moving to correct that."

The grant program, named after Sen. Claiborne Pell (R-R.I.), is aimed at low-income college students.

The program awards grants as small as $50 and as large as $1,800, based on eligibility formulas that consider a student's family income.

The program is administered by a central processor, a private firm under contract to the Education Department that computerizes information on the students' applications and checks the applications for internal consistency.

Because the amount of the awards are based on students' financial needs, much of the information must be validated. The GAO report said that the biggest error was attributed to students who misreported their family's income, but that the problem had been largely corrected through tougher validation procedures.

Congressional aides said that when the Pell grant program is extended later this year, as part of the reauthorization of all federal higher education programs, Congress is likely to give schools more discretion to correct problems when they arise.

Now, applications with errors must be sent back to the central processor, which often means additional delays.