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Mark"Lajoie batted higher than Hornsby ever did in the 20th century, and a handful of others did as well before that."
I would suggest that it is uncertain who holds the major league baseball single-season batting average record, at least if you count the American Association. According to www.baseball-almanac.com, James "Tip" O'Neill hit .485 in 1887 (275/567), which would make him the record holder. However, according to www.baseball-reference.com, O'Neill batted .435 in 1887 (225/517), which is less than others.