WASHINGTON – Sales of existing homes rose 5 percent in December, a trade group said Friday, as another tough year in the U.S. housing market came to a positive close.

The National Association of Realtors, which last month said it had overstated sales data by 14 percent from 2007 onwards, said December sales rose to a seasonally adjusted annual rate of 4.61 million.

November sales were revised down to 4.39 million, from an initially reported 4.42 million.

Economists polled by MarketWatch had expected sales at a 4.7 million-sale clip in December.

Lawrence Yun, the NAR’s chief economist, said lower mortgage rates, improved job conditions and rising rents have helped lift sales figures, although he noted that December 2010 also was strong before petering out later.

For all of 2011, sales edged up 1.7 percent to 4.26 million — compared to the 2005 peak of 7.08 million.

Median sales prices in December fell 2.5 percent from the same period of 2010 to $164,500.

Inventories — generally low in the winter months — fell 9.2 percent to 2.38 million, the lowest since March 2005, which represents 6.2 months of supply. The months of supply of inventory were the lowest inventory since April 2006.

Distressed sales accounted for 32 percent of sales, up from 29 percent in November.

Data also suggested continued tough financing conditions, something the Federal Reserve lamented in a recent white paper on the housing market.

All-cash transactions represented 31 percent of purchases, up from 28 percent in November, and first-time buyers accounted for 31 percent of all transactions, down from 35 percent in November.