The pilot of the Cessna 177B stated that he was attempting to land on runway 3R, a 2,150-foot-long, 28-foot-wide, asphalt runway. During the approach, the pilot noted that the windsock was favoring runway 3R, with a left crosswind approximately 15 degrees from the center of the airplane. While on a short final approach, the pilot then observed the windsock indicating no wind, but favoring a direction across the runway. The pilot continued his approach at 60 knots, with full flap extension. He flared the airplane over the first one-third of the runway, but the airplane floated and touched down between 500 to 700 feet from the end of the runway. The pilot was unable to stop the airplane on the runway. It traveled off the end of the runway and struck muddy terrain. During the impact, the left wing, including a left wing rib sustained damage. Examination of the airplane by a Federal Aviation Administration inspector did not reveal any preimpact mechanical malfunctions, nor did the pilot report any. The reported wind at an airport located approximately 15 miles north of the accident site, about 31 minutes before the accident, was from 160 degrees at 4 knots. The reported wind at the same site about 29 minutes after the accident was from 160 degrees at 6 knots.