Simpson's Paradox, Derek -vs- David:Averaging across categories can be misleading but this can be resolved with weighted averages.

In baseball, thebatting averageis defined as the number of hits divided by the number of times at bat. Below is a table for the batting average for two different players for two different years.

The number in parentheses gives the number of times at bat for each player for each year.Batting Average(# of times at bat)19951996Derek0.249(55times at bat)0.315(585times at bat)David0.254(415times at bat)0.322(145times at bat)

(a) What are the averages of the two batting averages for Derek(x_Derek)

and David(x_David)?

DoNOTuse a weighted average, just take the mean of 1995 and 1996 batting averages.Round your answers to 3 decimal places.

x_Derek

=x_David

=

(b) Who had the higher average batting average using the non-weighted average?

Derek

David

(c) Using a weighted average, calculate the average batting averages for Derek(x_Derek)

and David(x_David).

Round your answers to 3 decimal places.x_Derek

=x_David

=

(d) Who had the higher average batting average using the weighted average?

Derek

David

(e) What caused the discrepancy in average batting averages?

Derek's higher average occurred with more times at bat (585).

David's higher average occurred with fewer times at bat (145).

Derek's lower batting average was based on a small number of times at bat (55).

All of these contributed to the discrepancy.