The number of traditional, middle-income black families with a husband, wife, and children living together has dropped sharply in the District of Columbia over the last decade, according to a new U.S. Census report. The change leaves the city's black population increasingly dominated by single adults and female-headed households whose incomes tend to be lower.

Many of the black families appear to be moving to the suburbs, the report indicates, where the total black population reached 347,000 in 1977, more than double what it had been in 1970.

Overall, about 43 percent of all blacks in the Washington area lived in the suburbs in 1977, compared to just 24 percent when the decade began.

The new report, based on a survey taken in 1977, shows that the number of traditional black households in the city declined from 77,900 in 1970 to 55,000 seven years later -- a decrease of 29 percent.

In 1977, the report said, these traditional families made up just a third of all black households in the city.

Over the same period, the number of intact black families rose by 32,200 in the suburbs, reaching 60,500 in 1977 and forming the dominant group in the suburbs' booming black population.

"Middle-class black families with kids are the ones who are leaving the District," said George W. Grier, a demographer who analyzed the new census data in a report issued today by the Greater Washington Research Center.

"We don't have the exact data on why," he continued. "But a lot of it has to do with the schools. They're also looking for a more modern house, and they're attracted to the suburban lifestyle. . . . It's a replay of the white suburban migration of the past. The motives are the same."

According to the new population estimates, which Grier and his wife Eunice prepared from the census data, the number of whites in the suburbs rose by just 1.4 percent over seven years -- a drastic slowdown from the boom of the 1960s.

Indeed, blacks accounted for 69 percent of all population growth in the suburbs in the 1970s. By 1977 they made up about 15 percent of suburban residents, compared to just 8 percent in 1970.

The new report contains no data on the black population of different suburbs. Earlier estimates, prepared by state health departments in Maryland and Virginia, indicate that the greatest growth has been in Prince George's county. But, there were also sizeable increases in Montgomery and Fairfax, although the estimated numbers involved there were much smaller than in Prince George's.

Within Washington the number of both blacks and whites declined proportionately from 1970 to 1977 and the city's population remained about 71 percent black.

However, because of the loss of middle-income black families, median household income rose much less in the city than it did in the suburbs. In 1977 it was just two-thirds of the area-wide average. The city's share of the area's poorest households -- those earning less than 5,000 a year -- actually rose from 49 to 52 percent.

Grier said that with the surge of housing renovation on the fringes of downtown, the District appears to be attracting a large group of prosperous whites. But since many of them are relatively young, their incomes are not as high, he said, as the middle-class black families -- most headed by husbands in their mid-30s -- who are moving to the suburbs.

During the 1950s and 1960s, Grier said, Washington lost most of its middle-class family-oriented whites. It now appears to be losing a similar group of blacks, he said, and "is increasingly becoming the home of the singles, the rich, and the poor.

"The same thing is happening in a lot of other cities," he added. "It already happened in Manhattan. But Washington clearly is ahead of the pack."

Although the average income of blacks in the suburbs is still lower than whites, the new census report indicates that black suburbanites have made sharper gains since 1970 than any group in the area, including suburban whites and both blacks and whites in the city.

In 1977 the median household income of suburban blacks was about 39 percent higher than that of blacks in the District, a gap that had widened substantially since the start of the decade.

In their report the Griers also make the following points:

Growth for the entire Washington metropolitan area slowed drastically after 1974, principally because of a low birth rate and the net loss of population to counties on the metropolitan fringe.

The number of households is growing much more rapidly than the number of people, as the youth wave of the late 1960s moves into the 25-34 age bracket where most new household formation occurs.

The area's Asian population climbed from about 32,000 in 1970 to 55,000 in 1974 to 94,000 in 1977, principally because of refugees from Vietnam.

Owner-occupied housing increased far more rapidly than rental units throughout the area. For the first time it accounts for a slight majority of all housing units.

In the District, the number of rental apartments actually fell by 7 percent from 1970 to 1977. The decline in rental units occupied by whites was 20 percent compared to just a 3 percent drop in those occupied by blacks. Grier said this apparently occurred because condominium conversions were more widespread in white neighborhoods.

The number of children under age 5 in the metropolitan area dropped by 52,500 from 1974 to 1977, compared to a drop of 16,700 in the previous four years. When these children reach school age, the report calculated that the area will need 580 fewer classrooms.

Despite steep increases in the price of gasoline, the number of cars continued to increase more rapidly than the number of people. By 1977, there was an average of 1.5 cars for each area household. About 13.6 percent of the households own no car at all.

Grier said the increase in cars is explained by the shift of population to the suburbs and the rise in the number of women who are working and need a car to get their jobs.