BOSTON – The Mass. Executive Office of Labor and Workforce Development reported preliminary December 2012 federal estimates show a gain of 7,500 jobs in the state over the month, for a total of 3,263,400 jobs. The December job gain follows a revised loss of 3,200 jobs in November.

According to a news release, the total unemployment rate for December was 6.7 percent, up one-tenth of a percentage point. Over the year, the unemployment rate was down two-tenths of a percentage point from the December 2011 rate of 6.9 percent. The three-month average seasonally adjusted total unemployment rate was 6.7 percent and the six-month average was 6.5 percent.

Compared with December 2011, jobs are up 51,600. Private-sector jobs are up 50,700 with gains in eight of the ten sectors. Professional, Scientific, and Business Services and Trade, Transportation and Utilities had the largest gains. •