The improvement in quarterly earnings of the Student Loan Marketing Association was reported incorrectly in Wednesday's Business section. Its profits increased by 51 percent.

Riggs National Corp., which owns Washington's biggest bank, reported a sharp, 98 percent increase in third-quarter earnings mainly because it made no deduction from income for possible problem loans this year while it took a massive $11.9 million loan loss provision in the third quarter of 1983.

Meanwhile, First Virginia Banks Inc. said its third-quarter profits were $8.8 million (62 cents a share), 15 percent higher than the $7.7 million it earned in the third quarter of 1983, while the Student Loan Marketing Association reported a 17 percent increase in third-quarter earnings to $26.3 million (50 cents) from $17.4 million (37 cents) in the third quarter of last year.

Riggs said profits were $6.8 million (1.13) in the third quarter, compared with $3.4 million (56 cents) in the three months ended Sept. 30, 1983. A spokesman for the bank company said that management took no provision for potential loan losses in the third quarter because the overall health of its loan portfolio is improving and because problem loans are down.

Riggs, with assets of $4.8 billion, said its problem assets -- mainly loans that are not being repaid on time and real estate the bank acquired during foreclosures -- have declined from $32.2 million a year ago to $25.9 million at the end of September. Sources said the bank company's ability to forego any loan loss provision more than offset the squeeze it has faced in recent months because of the large amount of interest-sensitive money market deposit accounts it invested in fixed-rate Treasury securities when interest rates were much lower.

First Virginia, with total assets of $2.6 billion, said it had $10 million in nonperforming assets. The bank company, based in Falls Church, said the third-quarter profits figures were restated to include four banks it acquired during the second three months of 1984.

The Student Loan Marketing Association said its income grew not only because of an increase in business but also because it has developed better ways to protect itself from interest rate risks on the student loans it buys.

American Realty Trust reported third-quarter earnings of $317,359 (14 cents a share), up 80 percent from profits of $175,944 (8 cents) in the same period last year. The Arlington investment trust said its quarterly sales increased to $3.2 million from $2.2 million.

The trust lost $150,217 (7 cents) in the nine months ended June 30, compared with to profits of $1.4 million (62 cents) in the same period the year before. Revenue declined to $6.3 million for the nine-month period, from $10.7 million in the comparable period of a year ago.