The cost per student at the University of the District of Columbia is higher than average public college costs in any state except Alaska, according to the National Center for Education Statistics.

UDC's relatively high costs--$9,760 per student in 198l--probably reflect high staffing levels, high salaries and small classes, said Thomas Snyder, the NCES researcher who compiled the cost data.

"It's hard to know completely what's going on there," said Snyder. "But no matter how you look at it, the costs are high."

Snyder said 1981 is the most recent year for which comparable data is available from colleges across the country.

Shortly before he resigned last week, UDC president Benjamin H. Alexander complained in a report that the university was burdened with "excess and unneeded" administrators, but he said his efforts to cut back had been thwarted by the board of trustees.

Alexander suggested later that the administrative staff could be cut "by at least 30 percent and that's conservative." He said many staff members are unneeded holdovers from the three public colleges that merged to form UDC in 1977--Federal City College, D.C. Teachers College and Washington Technical Institute.

Ronald H. Brown, chairman of the UDC trustees, said Alexander's report was "self-serving" and noted that the city legislation creating the university gave strong protections to existing employes.

"I wouldn't dispute any of the data, but before you make these comparisons you have to remember that the university came from three separate, full-blown institutions," board vice chairman Estelle Taylor said of Snyder's findings about UDC's expenditures. "The people who came were protected in their jobs, and that makes it extremely difficult to deal with any overlapping."

According to the D.C. budget office, the number of faculty, administrative, and clerical jobs at UDC has dropped by about 6.5 percent over the past five years, mostly through attrition.

Several efforts by former UDC president Lisle Carter to reduce staff were blocked by lawsuits and arbitration rulings that the layoffs were not conducted properly.

UDC is the only public college in Washington and gives two-year, four-year, and master's degrees, making it the equivalent, under one administrative roof, of many state college systems. It now has a budget of $72 million, 570 full-time faculty members, and about 1,000 other employes. Last fall's enrollment was 14,115, but since about two-thirds of its students attend part-time, UDC had a full-time equivalent enrollment of 8,598.

Snyder said his agency, a part of the U.S. Department of Education, does not collect data on college staffing. But he said its budget data shows that UDC spends a relatively high proportion of funds on administration--18.9 percent, compared to a nationwide average of 11.7 percent at public colleges around the country without significant doctoral and professional programs.

The cost comparisons indicate that operating expenses at UDC were more than double the average $4,572 cost per student at such colleges nationwide. They were also higher than the $7,604 average costs at public research universities, whose scientific and medical programs generally boost expenses.

In the comparison of public colleges in the different states, Snyder said Alaska's very high cost--$15,622 per student--probably reflects exceptionally high living costs and the small size of its schools. After the $9,760 cost in the District, the states that come next are Wyoming, $7,563; Vermont, $7,156; and New Mexico, $6,739. Maryland ranks 39th, with costs per student of $4,766, and Virginia 42nd, with costs averaging $4,731.

Urban colleges with large remedial programs, such as UDC, generally have higher-than-average costs, said Paul Brinkman of the National Center for Higher Education Management Systems in Colorado, which analyzes college cost data.

However, he noted that UDC's costs are still far above other schools in this group. For example, at City College of New York, the cost per student was $6,632; at Morgan State in Baltimore, $5,463; and at Chicago State University, $5,841.

Alexander was president of Chicago State for 7 1/2 years before his stormy 10-month term at UDC.