Stocks rallied on Tuesday in a volatile session as investors struggled to decipher the Federal Reserve's signals on the economy after a dizzying two-week slide.

The Dow Jones industrial average was up 429.69 points, or 3.97 percent, at 11,239.54, based on the latest figures. The Standard & Poor's 500 Index was up 53.11 points, or 4.74 percent, at 1,172.57. The Nasdaq Composite Index was up 124.83 points, or 5.29 percent, at 2,482.52.

(Reporting by Angela Moon, Editing by Kenneth Barry)