Nevada’s unemployment rate dropped to its lowest level in 3 1/2 years in October — a seasonally adjusted 11.5 percent and a 10.9 percent unadjusted.That is a decrease of more than 2 percent from a year ago.The highest unemployment remains in the Las Vegas reporting area — 11.1 percent. But that is 0.4 percentage points lower than the previous month.Reno-Sparks and Carson City reported a 0.2 percentage points decline to 10.6 percent to 10.7 percent respectively in October.For all of those jurisdictions, those are the lowest October percentages since 2008.“October’s unemployment rate is the lowest rate since May of 2009,” said Gov. Brian Sandoval. “While this news is welcome, our state’s unemployment rate remains at a high level and continues to indicate the need for sustained economic diversification and private sector job growth.”For October, Chief Economist Bill Anderson of the Department of Employment, Training and Rehabilitation said a gain of 2,500 positions is expected in October but that preliminary estimates show a gain of 4,700 jobs this October. He said for most of the year, private sector payrolls produced the gains — a total of 11,100 more than the same 10 month period of 2011.But Anderson said this year, public payrolls are showing signs of leveling off after an extended period of decline even as the private sector began recovering.In Carson City, where the labor market is heavily reliant on governmental jobs, total public employment ticked up slightly adding about 100 workers for a total of 9,900 jobs. It was the first increase in more than a year.“All things considered, available information suggests that Nevada’s labor market has been on the mend since right around the beginning of 2011,” Anderson said.Statewide, the total labor force still is down from a year ago by about 15,000 workers. But it’s up some 7,800 from September to 1.37 million.According to the monthly report issued by DETR, there are about 150,000 looking for work in Nevada — a reduction of 34,000 from a year ago.In Carson City, 3,000 in a workforce of 27,600 are without jobs. The only reported change from September was the roughly 100 hires by local public employers.Reno-Sparks reported 23,600 unemployed in a workforce of 223,100 and Las Vegas 109,800 jobless out of 985,100 workers.In contrast to the other reporting areas, Churchill County’s unemployment rate increased a tenth to 9 percent in October. That translates to 1,200 jobless in a poll of 13,390 workers.Douglas County held steady at 11.4 percent with 2,450 seeking work in a labor force of 21,400. But that is Douglas’s lowest unemployment rate this year.Lyon County, which through the recession has had Nevada’s highest unemployment rate, reported its lowest rate in well over a year at 14 percent. Lyon started the calendar year at 17.8 percent but has been steadily improving for the past 10 months. For October, Lyon had 3,160 out of work in a labor force of 22,520.