Black students across the country continue to make substantial gains on the Scholastic Aptitude Test, but average scores overall were unchanged for the third year in a row, the College Board reported yesterday.

In the Washington area, scores on the college entrance examination rose in four major public school systems -- the District, Alexandria, and Fairfax and Montgomery counties. But average scores fell again in Prince George's County and showed no change in Arlington.

"Holding ground is better than losing ground," said Education Secretary William J. Bennett in commenting on the national report. "But that's not terribly encouraging . . . . We've gotten a lot of education reforms in place, but this {education} thing is not fixed yet. We've stalled."

Bennett added that the test gains by blacks were "good news." The average score for blacks rose six points during the last two years and 41 points during the past decade in the combined verbal and mathematical parts of the examination.

During the decade, the average score of white students fell one point in the verbal section and was unchanged in mathematics. The difference in scores between blacks and whites is 208 points on the combined score of the test, compared with a 250-point-gap a decade ago.

For all of last spring's seniors who took the test, the average verbal score fell one point to 430, while the average mathematics score rose one point to 476, compared with the scores of seniors a year earlier.

After a massive decline for years, national averages reached a low point in 1980 and 1981. They have risen since then by six points in verbal and 10 points in mathematics, but the recovery is far less than the slide of 54 points in verbal and 36 points in mathematics from 1963 to 1980.

The SAT is the nation's most widely used college entrance examination and was taken last year by almost 1.1 million students, about 38 percent of the nation's high school graduates. The number taking the two-hour, multiple-choice test rose by 8 percent, far more than the estimated 2 percent rise in graduates.

Donald M. Stewart, College Board president, said the stable scores were a positive development because "greater numbers of test takers usually mean lower averages." Robert Cameron, the board's executive director for research and development, urged "patience in looking for major improvements."

During the last two years, Cameron noted, the number of blacks taking the SAT rose by 25 percent. No racial data was issued in 1986 because of changes in a questionnaire.

Locally, D.C. public schools reported a six-point gain on the verbal part of the test and a three-point gain in mathematics. The proportion of graduates taking the examination rose from 34 percent in 1986 to 41 percent last spring. At 713 points, the combined score is still the lowest in the area, but it has risen by 19 points during the last two years and by 36 points in the decade.

A perfect score on each half of the test is 800 points; the minimum is 200.

Meanwhile, Montgomery scores remained the highest among area school systems at 988, followed by Fairfax at 980. Both districts reported increases in the proportion of students taking the examination -- up to 86 percent in Fairfax and 74 percent in Montgomery.

Arlington County continued to rank third with scores unchanged at 967.

The average for Alexandria reached 942, rising nine points this year and 50 points during the last decade, the largest increase for any school system in the area.

The average in Prince George's County continued to slide, dropping seven points to 826 after a 13-point decline last year. The decline over 10 years has been 47 points, the area's steepest.

Brian Porter, the school spokesman, said Prince George's schools are trying to enroll more students in algebra, a crucial subject covered in the SAT, and have adopted a plan for SAT preparation.