Overpayments in the $11 billion federal-state welfare program for mothers and children have dropped to 7.1 percent, lowest national rate in history, according to Secretary of Health, Education and Welfare Joseph A. Califano Jr. The reduction from the previous 8.1 percent figures will save $1000 million a year.

The overpayment rate is the percentage of outlays wasted on ineligible persons or on excess payments to eligible persons.

The District of Columbia, Maryland and Virginia all improved. In the six months ending Oct. 1, 1978, the District rate dropped from 13.5 percent to 10.2. The District now has the fifth worst record instead of second worst. Illinois has the worst, 14.7 percent.

Maryland dropped from 13.2 percent to 11.4 percent, giving it the Third worst record, and Virginia dropped from 6.9 to 6.

In another report on outlays for the poor, Sen. Harrison A. Williams (D-N.J.) released a study showing that the United States spends $6.3 billion annually on education and training programs for youth in the 14 to 22 age bracket.

Williams said he applauded the fact the three-quarters of it goes to low-income people. But he deplored the fact that about four-fifths goes to aid college or high-school students and only a fifth to help high school graduates and dropouts train for jobs.

The study, prepared by the Congressional Budget Office, shows that for those in the lowest income bracket, the per capita federal outlay for college student is $1,943 a year where only $399 is spent on training a high school dropout.

"I am startled at the disparity in the levels of support given these youths who do not go on to a college or a university," Williams said.

Williams said the low per-capita spending on high school dropouts is unfortunate because these youths have "the greatest difficulty entering and remaining in the labor force. They form the hard-core unemployed."

Califano's report that the welfare overpayment rate is down represents the culmination of a long campaign to save money by cutting welfare waste. Six years ago the rate in the program of Aid to Families with Dependent Children was 16.5 percent. In a program as large as AFDC - about $11 billion iin U.S. and state outlays annually - a rate of 16.5 percent means a waste of $1.65 biliion a year. A reduction to 7.1 percent means $710 million is wasted.

Califano also announced that defaults on the guaranteed student loan program are dropping and the default backlog should be eliminated within 18 months.

But he said the students default on direct loans, administered by colleges, have risen to 841,000 and the amount in default is over $700 million. He said colleges which do not try to collect on the loans will be penalized by loss of federal funds for the new loans. The penalties will total $100 million for 1,260 schools in 1978-80 school year, he said.