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But the question of what that means in an unemployment rate is a little less certain.

On paper, the state Office of Economic Opportunity puts the seasonally adjusted jobless rate for September at 6.7%. That follows a 5.9% figure for August and 10.7% the month before.

What’s causing these wild swings is not the number of people working. It’s the number of people not working but reportedly looking.

The way the state figures it, another 151,727 people joined the workforce between August and September. That includes both those working — a figure that did not change markedly — and those who said they are looking.

But the month before the workforce figure dropped 151,220.

So what’s going on? More to the point, are these swings real?

Doug Walls, the agency’s research administrator, says blame COVID-19.

Not the virus itself. But he said that the pandemic has resulted in some issues with the surveys of households that determine the size of the workforce along with other factors.

It starts with what Walls said is “the volatility that’s come from the COVID-19 pandemic.�

“One thing that we’re hearing from the U.S. Bureau of Labor Statistics and the Department of Labor is that there are challenges that the Local Area Unemployment Statistics are going through and the LAUS program is experiencing associated with the impacts of COVID-19 on the workforce movement,â€� he said. That, Walls said, is complicated by the fact that these numbers are based on a survey of just 1,400 ÃÛèÖÖ±²¥ households.

So some big month-to-month changes in who is employed, who is not and who is looking — all pieces of determining the jobless rate — can play havoc with the statistics.

“It is a challenge to parse out whether those are actual changes in the economy or those are due to the large swings and large changes in the workforce because of COVID,� he said.

So can the numbers now being released for September be counted on as reliable? And was that 5.9% rate for August — the one that led Gov. Doug Ducey to crow about the recovery — accurate?

“Fair points,� Walls conceded. “This is something the BLS is working to address.�

But making true comparisons month over month may be difficult.

Walls said BLS used some “modified methodology� in coming up with the September figures in an effort to address some of the drastic changes in the numbers.

Still, Walls said he believes the September numbers are accurate enough.

“They’re not making dramatic changes to the methodology or approach,� he said. “The month-to-month comparisons are still justifiable.�

At least for the time being.

Walls pointed out that there is a “benchmarking� process where the numbers are reexamined at the end of the year, opening the door to retroactive adjustments to the figures now being released. But those revised and presumably more accurate numbers won’t be available until March.

A clearer picture of the ÃÛèÖÖ±²¥ employment situation may come from a separate survey of employers.

It starts with that addition of 30,200 jobs. But fully a third of those were in public education, people who are not on annual contracts like food service workers and janitors who are returning to schools.

Private sector employment is up 19,400 month-over-month.

But the state is still far from being out of the woods.

Employment by private companies is still 85,500 below where it was the same time a year ago.

There were continued gains in wholesale and retail trade. In fact, Walls says that sector of the economy actually has regained all the jobs lost since February.

All that, however, has been more than offset by losses elsewhere.

Leading that column is the state’s leisure and hospitality industry.

It has shed 56,000 jobs in the past year, with another 24,300 lost in professional and business services.