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Poverty remained virtually unchanged in 1988, with 31.9 million poor people in the nation, but the inflation-adjusted per capita income of Americans rose a sharp 1.7 percent to an all-time high of $13,120, the Census Bureau said Wednesday.

The bureau, in its annual report on poverty and income statistics - this one for the last year of the Reagan administration - found that despite the long and continuing economic recovery from the 1982 recession, little headway is being made in the effort to end poverty."Both the number of poor and (the) poverty rate have declined since 1983, the recent peak in these figures, but both remain above their 1978 levels, the recent low point," the report said.

The report also noted that median household income in 1988 was $27,230, unchanged in real terms from 1987. And for the first time since 1982, median family income did not increase, staying at $32,190 in 1988.

Household income includes a variety of living arrangements, including unrelated individuals.

Per capita income divides all the income of the nation by the total population.

On poverty, the bureau said that overall about 53 percent of poor families were maintained by single women; for poor black families, 75.6 percent were maintained by women with no spouse present, while for whites the comparable figure was 43.5 percent.

Half of the nation's poor in 1988 were either children under 18 (39.5 percent) or those over age 65 (10.9 percent). The rate of children in poverty showed some improvement, dropping from 20.5 percent in 1987 to 19.7 in 1988 but did not change significantly for the elderly, the report said.

Nor were there any statistically significant changes among the poverty rates for various ethnic groups, with the white poverty rate at 10.1 percent, the black rate at 31.6 percent, the Hispanic rate at 26.8 percent and persons of other races, primarily Asians, at 20 percent.

Regionally, the only significant change was in the Midwest, where the poverty rate dropped by 1 percentage point, to 11.5 percent, and the number of people in poverty fell by 600,000.

The Northeast continued to have the lowest poverty rate, 10.2 percent, while the South had the highest, 16.2 percent. The rate in the West was 12.7 percent.

The poverty rate for families was 10.4 percent, unchanged from 1987. It was lowest for married couple families, at 5.6 percent. About 33.5 percent of families headed by a woman without a husband were poor as were 11.8 percent of families headed by a male with no wife present.