PHOENIX  Arizona’s jobless rate remained virtually unchanged for the second month in a row.

But that doesn’t necessarily mean the economy is finally stabilizing.

That 9.1 percent seasonally adjusted employment rate for September is the same as August. And it is a tenth of a point less than two months ago.

But Lisa Danka, an assistant deputy director of the Department of Commerce, said Thursday the 10,600 jobs added in September over the prior month is the weakest gain for this time of year seen in two decades.

And when the anticipated seasonal increase in employment of staff at public schools is factored out, the rest of the economy actually was weaker.

Construction employment shed another 900 jobs in September, bringing the yearoveryear losses to 45,800. And that sector of the economy is operating at only 55 percent of what it was at its peak in June 2006.

Another 2,700 jobs were lost in retail trade, half of that in food and beverage stores.

And hotels and restaurants laid off 2,300 workers between August and September. Danka said that relates to continued weakness in tourism.

“We know that folks are not traveling as they did two years ago,’’ she said.

But the weakness is showing up elsewhere.

While the number of people working in public schools is up from August, as would be expected this time of year, there are still 5,700 fewer people with jobs in that sector of the economy. Danka said the overall state economy is a factor here, too.

She said people continue to be thrown out of their homes as they can’t keep up with the mortgage payments.

“People are no longer in those houses,’’ Danka said. “Therefore, children are no longer in those schools.’’

At the same time, schools are not getting the same money they were anticipating, meaning they didn’t hire as many people for the new school year.

A similar pattern shows up at the state university level where employment now is 2,900 less than the same time last year.

Still, Danka said there is a bright side to all of this.

“At least it isn’t jumping,’’ she said of the stable jobless rate. Danka pointed out there have been months in the last year where the figure has jumped a half a point.

Danka warned that even if the economy has hit bottom — an analysis she is not yet making — it is virtually certain that the unemployment rate will increase.

She said the figure is computed through a monthly household survey where adults are asked if they are working and, if not, whether they are looking for employment. If they are not actively out seeking jobs, they don’t count as “unemployed.’’

The data reflects there are “discouraged workers’’ who fit that category: The number of Arizonans who said they were available to work, whether they had jobs or not, has dropped by 13,500 in the last year.

Once the word gets out that companies are hiring again, then people start looking for work. And if they’re surveyed at that point but don’t yet have a job, they join the ranks of the unemployed.

Just The Facts

Seasonally adjusted unemployment rate:

Area / September 09 / August 09 / September 08

United States / 9.8% / 9.7% / 6.2%

Arizona / 9.1% / 9.1% / 6.0%

Phoenix Metro+ / 8.5% / 8.4% / 5.5%

Apache / 15.6% / 14.5% / 11.6%

Cochise / 7.5% / 7.2% / 5.8%

Coconino / 8.3% / 7.7% / 5.8%

Gila / 11.0% / 10.8% / 6.8%

Graham / 15.2% / 15.4% / 6.8%

Greenlee / 21.9% / 22.1% / 4.5%

La Paz / 8.4% / 8.2% / 8.2%

Maricopa / 8.2% / 8.2% / 5.4%

Mohave / 10.6% / 9.7% / 7.5%

Navajo / 15.3% / 14.5% / 10.6%

Pima / 8.2% / 8.1% / 5.6%

Pinal / 11.7% / 11.8% / 7.6%

Santa Cruz / 13.3% / 13.1% / 10.3%

Yavapai / 9.5% / 9.3% / 6.4%

Yuma / 20.7% / 19.0% / 17.7%

+ Phoenix metro includes both Maricopa and Pinal counties

 Source: Arizona Department of Commerce

Employment changes in selected industries

Sector / 1month job change / yearoveryear change / since peak

(negative numbers in parentheses)

Total / 10,600 / (195,800) / (305,300)

Manufacturing / (300) / (13,300) / (27,400)

Mining / (100) / (3,400) / (3,400)

Construction / (900) / (45,800) / (109,800)

Trade, transportation, utilities / (4,200) / (41,000) / (82,900)

Information / (400) / (2,900) / (16,700)

Financial activities / (500) / (10,600) / (22,100)

Professional and business services / (500) / (42,700) / (69,200)

Education and health services / 700 / (3,900) / (4,600)

Leisure and hospitality / (2,400) / (10,900) / (28,600)

Other services / (300) / (5,700) / (9,400)

Government* / 19,500 / (15,600) / (20,800)

* Includes state and local public education

 Source: Arizona Department of Commerce