The state’s seasonally adjusted jobless rate dropped a 10th of a point last month, to 8.2 percent.

Figures from the Department of Administration show Arizona added 30,000 jobs between August and September. Most of those, however, were workers returning to jobs in public schools, community colleges and state universities.

But Aruna Murthy, the agency’s director of economic analysis, said the state also added 5,200 jobs in the private sector. That puts private employment now 53,300 higher than a year ago.

Murthy acknowledged there was a steeper decline in the national unemployment rate. It went down 0.3 percentage points, to 7.8 percent.

She said, though, that appears to be largely a function of unemployed people finding part-time work — and therefore being considered employed — rather than getting full-time jobs.

Big gainers last month include the health care industry, with a sharp hike in employment at medical offices.

Several sectors of the economy posted losses, including construction which shed 1,200 jobs between August and September, with 1,600 jobs lost in retail trade. Murthy said that latter figure appears to reflect layoffs of temporary workers hired for the back-to-school season.

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