Question

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

In baseball, the batting average is 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)

1995 1996

Derek 0.249 (45 times at bat) 0.315 (585 times at bat)

David 0.254 (405 times at bat) 0.320 (145 times at bat)

(a) What are the averages of the two batting averages for Derek (xDerek) and David (xDavid)? Do NOT use a weighted average, just take the mean of 1995 and 1996 batting averages. Round your answers to 3 decimal places.

xDerek =

xDavid =

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

(c) Using a weighted average, calculate the average batting averages for Derek (xDerek)  and David (xDavid).  Round your answers to 3 decimal places.

xDerek =

xDavid =

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

(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 (45).

All of these contributed to the discrepancy.

Answer 1

a)

	1995	1996	Average
Derek	0.249	0.315	0.282
David	0.254	0.32	0.287

b) David has highest batting average than derek from above method.

c)

			Number of times bat	Number of hits	Total hits =1995 hits+1996 hits	Total bats =1995 bat+1996 bat	Total hit/total bat
	1995	1996	1995	1996					Average
Derek	0.249	0.315	45	585	11.205	184.275	195.48	630	0.310
David	0.254	0.32	405	145	102.87	46.4	149.27	550	0.271

d)

Derek has highest batting average than david from weighted average method.

e) Option D

All of these contributed to the discrepancy.

Please revert back in case of any doubt.

Please upvote. Thanks in advance.