Question: Three great hitters. Three landmarks of baseball achievement are Ty Cobb's batting average of .420 in 1911, Ted Williams's .406 in 1941, and George Brett's .390 in 1980. These batting averages cannot be compared directly because the distribution of major league batting averages has changed over the years. The distributions are quite symmetric and (except for outliers such as Cobb, Williams, and Brett) reasonably Normal. While the mean batting average has been held roughly constant by rule changes and the balance between hitting and pitching, the standard deviation has dropped over time. Here are the facts:
Decade Mean Std. dev.
1910s .266 .0371
1940s .267 .0326
1970s .261 .0317
Compute the standard scores for the batting averages of Cobb, Williams, and Brett to compare how far each stood above his peers.