Last month marked the best September for Massachusetts single-family homes sales since 2005, according to the latest report by The Warren Group, publisher of Banker & Tradesman. A total of 4,358 single-family homes sold in Massachusetts in September, a 16 percent increase from 3,739 sales in September 2012. Sales also increased in the third quarter - rising to 16,097 from 13,957 during the same period in 2012. Year-to-date sales are up by 12 percent at 37,757, compared to 35,590 during the same period a year ago. "Despite rising interest rates, home sales have remained high this year, particularly booming in the third quarter," said The Warren Group CEO Timothy M. Warren Jr. "Median prices continue their upward surge with a 16 percent gain. These data show that there continues to be strong demand and a shortage of supply. Twenty six communities are now above their pre-crash high for median price and others are closing in on previous highs. "The median price of single-family homes rose almost 16 percent to $323,625 in September, up from $280,000 a year earlier. Third quarter median prices also increased - rising 15 percent to $340,000 from $300,000 in the third quarter 2012. The median price for homes sold January through September was $325,000, up 12 percent from $289,900 in the prior year.In September, condominium sales statewide rose 12.5 percent to 1,800, up from 1,608 a year ago. Condo sales in the third quarter increased more than 9 percent to 6,615, compared to 6,056 during the third quarter 2012.