Question

the following table shows the number of hits (h), number of at - bats (ab), and batting average (avg = h/ab) for major leaguers derek jeter and david justice in 1995 and 1996. complete parts a through d.

player	1995			1996
jeter	12	48	.250	183	582	.314
justice	104	411	.253	45	140	.321

a. which player had the higher batting average in both 1995 and 1996?
david justice
derek jeter
b. compute the batting average for each player for the two years combined.
derek jeter had a batting average of 0.310. david justice had a batting average of 0.270.
(round to three decimal places as needed.)
c. which player had the higher combined batting average for 1995 and 1996?
derek jeter
david justice
d. briefly explain why the results might seem surprising or paradoxical.
when the two seasons are taken separately, the data show that david justice is the better hitter in both seasons. when the two seasons are taken together, the data show that
derek jeter is the better hitter overall.
both hitters have equal batting averages.
david justice is the better hitter overall.

Explanation:

Step1: Analyze part a

Compare the 1995 and 1996 AVG of Jeter and Justice. In 1995, Justice's AVG is .253 and Jeter's is .250. In 1996, Justice's AVG is .321 and Jeter's is .314. So Justice has a higher AVG in both years.

Step2: Analyze part b

For Jeter, total hits $H = 12 + 183=195$, total at - bats $AB=48 + 582 = 630$. Batting average $AVG=\frac{195}{630}\approx0.310$. For Justice, total hits $H = 104+45 = 149$, total at - bats $AB=411 + 140=551$. Batting average $AVG=\frac{149}{551}\approx0.270$.

Step3: Analyze part c

Since Jeter's combined AVG is 0.310 and Justice's is 0.270, Jeter has the higher combined AVG.

Step4: Analyze part d

When the two seasons are taken separately, Justice has a higher AVG in each season. But when combined, Jeter has a higher AVG because the number of at - bats in each season is weighted differently. Jeter had many more at - bats in 1996 (a year with a relatively high AVG for him) compared to 1995, while Justice had a much larger number of at - bats in 1995 (a year with a relatively lower AVG for him compared to 1996).

Answer:

a. David Justice
b. Derek Jeter: 0.310, David Justice: 0.270
c. Derek Jeter
d. Derek Jeter is the better hitter overall.