WASHINGTON (AP) _ Students whose parents closely monitor their activities tend to get the highest grades in school, and those with both parents in the home also score better, a new study shows.

The National Center for Education Statistics drew those conclusions Friday from a study of information gathered in 1980 and 1982 from 58,000 high school students.

Sophomores were asked to what extent their parents or guardians monitored their activities - that is, knew where their children were and what they were doing.

''The overwhelming majority of 'A' students (88 percent) also indicated the highest degree of parental supervision,'' the center said. ''Fewer 'B' students indicated that their parents knew of their activities (81 percent).''

Some 72 percent of the ''C'' students and only 61 percent of the ''D'' students said their parents monitored what they did closely.

''Teachers and other educators frequently cite the importance of parental involvement to learning,'' the center said in a report on the study.

''A two-parent family may have an advantage over a one-parent family in this,'' it said. Eighty percent of the ''A'' students lived in a household with both parents. Among the ''B'' students, 71 percent did; ''C'' students, 64 percent and ''D'' students 60 percent.

''Exactly 75 percent of the students who said they earned mostly 'A.'' grades reported that they talked with their mothers or fathers every day or almost every day,'' the report said. The percentage fell to 67 percent for the ''B'' students, 59 percent of the ''C'' students and only 45 percent of the ''D'' students.

All of the students, regardless of grades, were more likely to talk about school with their mothers than their fathers.

''Some 92 percent of the 'A' students reported that their mothers kept close track of their performance, compared to the 85 percent who reported their fathers did so,'' it said. ''Of the 'B' students, 89 percent said their mothers kept close track of their performance and 79 percent said their fathers did.

''Of the 'C' students, 84 percent said their mothers and 69 percent said their fathers kept up with their progress. And of the 'D' students, the corresponding figures were 80 percent for mothers and 64 percent for the fathers.''

Among the ''A'' students, 25 percent reported their parents attended PTA meetings at least once in a while; the ''B'' students reported 22 percent; ''C'' students 20 percent and ''D'' students 15 percent.