# PBS Teachers™

Activity III: Batting Averages and More (Grades 7-10)

Standards

* These standards have been adopted and are based on the information from Principals and Standards for School Mathematics: Discussion Draft, October l998, National Council of Teachers of Mathematics.

Objectives

• set up and solve a system of equations
• apply their understanding of percentages and their calculation
• set up a spreadsheet and do calculations using columns
• reason from data

Activity3

A. The following data is for eleven of the greatest hitters in the baseball hall of fame.

 Player Games At Bats Hits Batting Average (BA) Runs Batted In (RBI) Home Runs Hank Aaron 3298 12364 3771 0.305 2297 755 Rod Carew 2469 9315 3053 0.328 1015 92 Ty Cobb 3034 11429 4191 0.367 1961 118 Lou Gehrig 2164 8001 2721 0.34 1990 493 Rogers Hornsby 2259 8173 2930 0.358 1584 301 Reggie Jackson 2820 9864 2584 0.262 1702 563 Mickey Mantle 2401 8102 2415 0.298 1509 536 Willie Mays 2992 10881 3283 0.302 1903 660 Stan Musial 3026 10972 3630 0.331 1951 475 Babe Ruth 2503 8399 2873 0.342 2211 714 Ted Williams 2292 7706 2654 0.344 1839 521

1. Place this data in a spreadsheet using either a computer or in a graphing calculator. Determine the percentage of home runs per games, the percentage of home runs per at bat, and the home runs per hit.

2. Rank these eleven players in descending order of the ratio of home runs per game.

3. Rank these eleven players in descending order of the ratio of home runs per at bat.

4. Rank these eleven players in descending order of the ratio of home runs per hit.

5. Based on all of the data, make an argument that Babe Ruth is the best hitter in baseball history.

6. Based on all of the data, make an argument that one of these eleven is the number two greatest hitter in baseball history.

7. Make a statistically based argument that Henry Aaron is the greatest home run hitter of all time.
B. The morning edition of the daily newspaper reported that Mark McGwire had a batting average of .350. After the Saturday night game in which McGuire had 3 hits in 5 times at bat, his new batting average was reported to be .352. Determine the number of at bats and hits McGwire had prior to the Saturday night game.

C. At different times in the season, when Mark McGuire had 3 hits for 5 times at bat, his batting average jumped from .350 to.366, from .350 to .358, and from .350 to .355. Explain why the increase is not the same amount each time.