Virginia public school students have shown improvement once again, as they have for the past four years, in nationally administered tests measuring achievement in basic skills, but they still fall below the national average in many categories.

Virginia's Department of Education last week released the scores of the standardized tests that were given to 320,000 fourth, sixth, eighth and eleventh graders in 1,723 Virginia schools last fall.

Virginia's fourth graders, who did better overall than students in other grades, got scores above the national average in all subject areas except in mathematics computation.

Richard Boyer, assistant superintendent for program development, said the fourth graders scored higher partly becaused they were the first class required to attend kindergarten classes. Virginia phased-in its statewide compulsory, kindergarten classes over four years beginnings in 1972.

Boyer said another reason for the higher scores is that in recent years Virginia schools, as others across the nation, have been giving more emphasis to instruction in basic skills.

In the three other grades, however, while scores continued to improve over previous years, they did not reach the national average of the 50th percentile in many of the categories measuring such things as reading, science and math computation.

And in three categories, scores of Virginia students were in the 30 to 40 percentile range: Eleventh grade language arts, 38th percentile; eighth grade social studies, 39th percentile; and eleventh grade science, 36th percentile.

Virginia's eleventh graders, however, scored well in math, coming out equal to th national average in the 50th percentile. The 50th percentile is the point at which half of the students tested scored higher and half scored lower.

Besides measuring achievement in the above-mentioned areas, the tests, which are made up and corrected by Science Research Associates, included a Short Test of Educational Ability. Virginia's fourth graders also scored better than their fellow-students on the STEA, ending up in the 49th percentile. Sixgh graders came out in the 47th percentile; eighth graders in the 41st and eleventh graders in the 42nd.

The Education Department says it will have a breakdown of the test scores by school divisions available in about two weeks.

Fairfax County released its scores three weeks ago, revealing that Fairfax students received scores significantly higher than the average state marks.