In MLB, that is Shoeless Joe Jackson of the Cleveland Indians who hit .408 in 1911.
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Rod Carew's best batting average for a season was .388 in 1977 playing for the Minnesota Twins. His career batting average was .328.
the rookie of the year award
For the 2007 regular season, the Red Sox team batting average was .279, which was 5th best in the American League.
The "rookie of the year" award.
Career wise, that would be Tony Gwynn (1982-2001) with a .338 career average. As of the start of the 2008 season, Gwynn ranks 20th all time in MLB career batting average. For a single season, that would be George Brett (1973-1993) with a .390 average in the 1980 season.