Mathematics, 19.03.2021 16:00 harleypage308
Three landmarks of baseballachievement are Ty Cobb’s batting average of 0.420 in 1911,Ted Williams’s 0.406 in 1941, and George Brett’s 0.390in 1980. These batting averages cannot be compared directly becausethe distribution of major league batting averages has changed overthe years. The distributions are quite symmetric and (except foroutliers such as Cobb, Williams, and Brett) reasonably normal. While the mean batting average has been held roughly constant byrule changes and the balance between hitting and pitching, thestandard deviation has dropped over time. Here are the facts:
Decade
Mean
Standard Deviation
1910s
0.266
0.0371
1940s
0.267
0.0326
1970s
0.261
0.0317
Compute the standard units for the batting averages of Cobb, Williams, and Brett to compare how far each stood above his peers. Who is the better player of the three?
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