Idaho's infant death rate went down last year, but the number of babies born to unmarried mothers continued to rise, according to a preliminary report from the Idaho Department of Health and Welfare.

The figures released this week by the department's Division of Health show that 158 children in Idaho died before their first birthday in 1987, compared with 186 the year before and 183 in 1985.The state had an infant death rate of 9.9 for every 1,000 births, down from 11.3 per 1,000 births in 1986 and 10.4 in 1985. The national rate in 1987 was 10 deaths for every 1,000 births.

Dick Schultz, administrator of the Division of Health, said the rough data did not explain the reason for last year's improvement in Idaho. But he said there are indications many babies remain at risk.

In particular, Schultz said he was concerned about the rising number of single mothers and newborns weighing less than 51/2 pounds. Both problems contribute to health problems and death in babies, he said.

The number of babies born out of wedlock was 2,059 last year, up from 1,938 in 1986 and 1,880 in 1985.