Question

In the mid-1990s, one of the main debates in Major League Baseball was whether Derek Jeter or David Justice was a better baseball player. One key metric in this debate was their respective batting averages, calculated as the number of hits divided by number of at-bats. The following information is available regarding their batting averages in the years 1995 and 1996:

	1995		1996		Combined
Player	Number of Hits	Number of At-Bats	Number of Hits	Number of At-Bats	Number of Hits	Number of At-Bats
Derek Jeter	12	48	183	582	195	630
David Justice	104	411	45	140	149	551

1. Looking at the years 1995 and 1996 individually, who has a higher batting average?

2. Look at the two years combined, who has a higher batting average?

3. Compare your answers to parts a and b. What phenomena is at play here, and why does it occur?

Answer 1

Requireenta: Year Derek jeter 1995 12/48 = 0.250 1996 183/582 = 0.314 David justice 104/411 = 0.253 45/140 = 0.321 The above table shows that David justice had a slightly higher batiing average than derek jeter in the year 1995 ( 25.3% > 25.0%) and in 1996 (32.1% >31.4%) Requirement b: If we combine the data for the two years, then Derek jeter David justice 195/630 = 0.310 149/551 = 0.270 Jeter By the above calculations, it is clear that derek jeter has higher batting average 31.0% than david justce's batting average of 27.0%.

Requirement c: If we compare the answers to parts a and b, there was a contrasting result. Eventhough david justice had higher average for the two years individually but has less batting average than when data is combined for two years. This is mainly due to the fact that the two years do not carry same weight when data is combined.. David justice's had most number of at bats in the year 1995 and for that year he had an average of 25.3% Whereas, Derek jeter had most number of at bats in the year 1996 and for that year he had an average of 31.4% The season with most number of at bats is what making biggest influence on the overall batting numbers Because of that derek jetter is ahead of david jsutice.