Median home prices for existing single-family homes rose in a vast majority of U.S. cities in the third quarter, the National Association of Realtors said. The median price -- the price midway between the highest and lowest prices -- rose in 120 of 149 metropolitan areas, the NAR said Wednesday. \"Housing inventories have been gradually trending down from a record set in the summer of 2007,\" NAR Chief Economist Lawrence Yun said. \"Earlier this year, broad equilibrium began to develop in most areas between home buyers and sellers, which led to a sustained upturn in home prices.\' The national median price in the third quarter for an existing single-family home was $186,100, up 7.6 percent from the third quarter of 2011, when the median price was $173,000, NAR said. Total sales of existing homes rose 3.2 percent to an annual seasonally adjusted rate of 4.68 million, up from 4.54 million in the second quarter and 10.3 percent higher than the third quarter of 2011.