The Census Bureau said yesterday that the number of people living below the government's official poverty line rose last year to 34.4 million, or 15 percent of the population--more than one American in seven.

It was the highest national poverty rate since 1965 and the fourth consecutive annual increase.

The bureau also reported yesterday that median family income in 1982 was $23,433, down 1.4 percent from 1981 when adjusted for inflation.

The decline in median family purchasing power and increase in poverty were mainly reflections of the recession and increase in unemployment. While inflation receded last year, incomes receded more.

"Another contributing factor," the bureau noted, "may have been the tightening of eligibility standards for certain government aid programs, such as Aid to Families with Dependent Children." Last year was the first in which the poverty figures reflected the domestic spending cuts President Reagan has pushed through Congress.

The 1982 poverty figure was up a full percentage point from the year before, when there were 31.8 million people below the cutoff, 14 percent of the population.

The poverty line, which is adjusted each year for inflation, was $9,862 last year for a family of four, somewhat higher for larger families and lower for smaller ones.

Conservatives long have complained that the poverty figures exaggerate the number of poor in America because they are based on cash income only and fail to account for such non-cash or in-kind benefits as Medicare, Medicaid, food stamps and housing subsidies for the poor.

Medicaid is now the largest federal welfare program, food stamps the second largest, and in-kind benefits of all kinds totaled $72.5 billion in 1980. Previous Census studies have shown that the poverty rate goes down as much as two-fifths if non-cash benefits are counted.

The overall poverty figures mask tremendous differences within the population as a whole. The census report shows that:

While the national proportion of people in poverty was 15 percent, the figure for the aged, 65 and over, was only 14.6 percent, down from the 15.3 percent for this age group recorded in 1981. The bureau said the receipt of automatic cost-of-living increases by retired people living on Social Security and other public programs was a factor.

The proportion in poverty was enormously higher for blacks (35.6 percent) and Hispanics (29.9 percent) than for whites (12 percent), although all three groups were up over 1981.

Families headed by a female householder with no husband present had the highest group rate--36.3 percent--and for female-headed non-white families with several children, the poverty ratios mounted to 70 and 80 percent.

For children under 18, the poverty ratio was 21.7 percent.

In central cities 19.9 percent of people were in poverty, compared with 9.3 percent in suburban areas and 17.8 percent in rural and other areas. The rate was 22.1 percent for people living on farms.

The South remains the poorest section, with 18.1 percent of its people in poverty, compared with 13.3 percent in the Midwest, 13 percent in the Northeast and 14.1 percent in the West.

Median income for male workers 15 and over was $13,950, for women it was $5,890, or 42 percent of what the men make. However, these figures include people who do not work full-time. For people working full-time all year long, the male median income was $21,660 and the female $13,660, a ratio of about 63 percent.

In 1959, the overall national poverty rate was 22.4 percent; in 1965 it was 17.3 percent, the last time it has reached at least 15 percent. Then, as a result both of national prosperity and larger government cash income programs, the poverty ratio dropped to 11 to 12 percent in the mid-1970s. Since 1978 it has risen steadily, reflecting the poor performance of the economy in recent years.