Sales of existing homes rose in January by the largest amount in two years, raising hopes that the worst of the severe slump in housing may be coming to an end. Median home prices, however, fell for a sixth straight month.

The National Association of Realtors reported Tuesday that sales of previously owned homes rose by 3 percent last month, the biggest one-month increase since a 3.3 percent increase in January 2005, a time when housing was roaring toward the peak of its five-year boom.

The median price of an existing home sold in January dropped to $210,600, a decline of 3.1 percent from a year ago. It marked the sixth straight month that the median price has been down compared with a year ago. The January decline was the third-biggest drop in history.

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