Santa Clarita’s unemployment rate ticked up to 6.3 percent in October from 6.2 percent in September, while the nation’s seasonally adjusted jobless rate moved to 7.9 percent over the month from 7.8 percent.

Both rates reflect a full 1-point reduction from October 2011, when 7.3 percent of the SCV workforce and 8.9 percent nationally were  jobless.

The seasonally adjusted county and state rates moved in the opposite direction, improving by 0.1 percent during October.

According to figures Friday from the state Employment Development Department, the biggest job gainer across Los Angeles County during October was the local government sector, which includes public school teachers.

Public education payrolls in L.A. County grew by 22,000 jobs over the month. The gains were partially offset by cutbacks in county government  (down by 1,500 jobs) and city government (down 800).

Private education added 6,300 jobs during the month, with colleges, universities and professional schools accounting for the bulk of the growth (4,500 jobs).

All of L.A. county’s trade sectors posted gains, including etail trade (up 4,900), wholesale trade (up 1,800) and transportation, warehousing, and utilities (up 400). Leisure and hospitality added 2,500 positions, services 600, financial activities 500, and professional and business services 500.

The motion picture and sound recording industries posted the biggest losses, constricting by 3,800 jobs over the month.

Los Angeles County’s adjusted jobless rate fell to 10.5 percent in October from 10.6 percent in September as civilian employment grew by a net of 10,000 jobs and unemployment rolls shrank by 8,000.

California’s seasonally adjusted rate was 10.1 percent in October, versus 10.2 percent in September and 11.5 percent a year ago.