Simpson's Paradox, Jeter -vs- Justice: In baseball, the batting average (BA) is defined as the quotient of hits divided by the times at bat. Below is a table for the 1995 and 1996 batting averages for Derek Jeter and David Justice. Who has the better batting average? Try a straight average of the two years and a weighted average based on the number of times at bat. You should get contradictory results.
Player BA - 1995 BA - 1996
Derek Jeter .250 (48 times at bat) .314 (582 times at bat)
David Justice .253 (411 times at bat) .321 (140 times at bat)
(a) Looking within each category of year, which player had a better batting average?
(b) Using a weighted average across both years, calculate the mean batting average for each player. Which player had a better batting average?
(c) Why did Derek Jeter fair so well using the weighted average?