In the 1940’s the average professional baseball player’s batting average was 0.2

Question

In the 1940’s the average professional baseball player’s batting average was 0.267 with a standard deviation of .0326. From 1970 to 1980, the average batting average was 0.261 with a standard deviation of .0317. The distribution of major league batting average has changed over the decades but it is quite symmetric each decade. In 1941, a player named Ted Williams had a batting average of 0.406 and in 1980; George Brett’s average was 0.390. Which player had the relatively higher batting average for his peer group: Ted Williams or George Brett?

a) Ted Williams because his average was 0.406 which is higher than Brett’s average of 0.390.

b) Ted Williams because his batting average was 4.26 standard deviations away from his peers while George Brett’s average was only 4.07 standard deviations away from his peers.

c) Ted Williams because his batting average was 4.42 standard deviations away from other players in the 1940’s while George Brett’s average was only 3.92 standard deviations away.

d) George Brett because his batting average was 4.07 standard deviations away from the average for his peers and Ted Williams batting average was 4.26 standard deviations his peers.

e) We can’t compare batting averages from different decades because the equipment has changed.

Explanation / Answer

Z score = (X - mean)/standard deviation

Z score of Ted Williams = (0.406 - 0.267)/0.0326 = 4.263

Z score of George Brett = (0.390 - 0.261)/0.0317 = 4.07

Higher the Z score indicates better batting average. So,

b) Ted Williams because his batting average was 4.26 standard deviations away from his peers while George Brett’s average was only 4.07 standard deviations away from his peers.

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