Florida joined a few other states last week with a jobless rate that entered double-digit territory for the first time in more than 30 years.

The preliminary unemployment rate in May hit 10.2%, up from 9.7% in April. Some economists are predicting the jobless rate will remain high well into 2011, and some predict the rate could go as high as 10.6%.

And there are other signs of continuing trouble for the not-so sunshine state’s economy.

The Office of Economic and Demographic Research on Monday said Florida’s 67 school districts will experience their third year of declining enrollment in 2009-2010 with the loss of 10,000 students.

Enrollment has declined since the 2006-2007 school year, when districts lost nearly 2,800 students. In 2007-2008, they lost 7,000 students. The peak loss of more than 13,000 was experienced in 2008-2009.

On a bright note Tuesday, the Florida Association of Realtors said the state’s existing home and condominium sales rose in May — the ninth month in a row that sales activity increased in the year-to-year comparison.

Also, for the first time in many months, the statewide median sales price in May for existing homes and condos rose over the previous month’s, the FAR said.

Existing home sales rose 16% last month, with 13,921 homes sold statewide compared to 12,044 sold in May 2008. FAR also reported a 21% rise in statewide sales of existing condos in May.

“The improving sales of existing single-family homes and condos is a trend we have been seeing for several months in Florida. What is new in this month’s data release is that we are seeing evidence of prices beginning to firm,” said Sean Snaith, director for the University of Central Florida’s Institute for Economic Competitiveness. “While one month of data does not a trend make, it is the first green shoot we have seen in some time as far as prices are concerned.”

Florida’s median sales price for existing homes last month was $144,400, compared to $203,800 a year ago. However, the existing home median price in May was higher than in each of the previous four months.

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