1998 was a very good year for baseball. The record for the most home runs in a season was broken, not by one player, but by two players. The previous record of 61 home runs was exceeded both by Sammy Sosa and Mark McGwire. These two outstanding players contributed greatly to the revitalization of the game.

Students will take a more in depth look at baseball record breakers. They will use statistics, not just for one year, but over the whole career, to compare some famous players. This data will be analyzed to try to determine who really was the best all-time home run hitter.

The primary audience are students in a statistics class, but this lesson may be used in an Algebra II or Precalculus class also.

Use of the TI-83 calculator is recommended. Students should be familiar with the five-number summary of a data set (minimum, lower quartile, median, upper quartile, maximum) and how to make and interpret box plots.

Internet access; Baseball Statistics Activity Sheet; TI-83 calculator recommended.

To use the Internet to find home-run data for some famous baseball players.

To calculate the five-number summaries of data sets.

To use box plots to compare and contrast different data sets.

To suggest different ways to determine who is the best all-time home run hitter.

In the computer lab, students will search the Internet for the required information and complete the attached Baseball Statistics Activity Sheet. Students will discuss, as a class, their ideas for determining the best all-time home run hitter and what other data they might need to answer this question.

Evaluation.

See points on the Activity Sheet.

Students can find the five-number-summary and make boxplots for the percent of home-runs relative to number of times at bat each of these four players made. They can then compare the players using this criteria.

Students can pick any other sporting record that they want to research. They should use the Internet to find out who the record breakers are and how well they did throughout their careers. They can present their findings on a poster and answer the question, "Who is the greatest all-time ______ ?"

 Teacher Notes.

!!!! Warning !!!! The Web sites given in this lesson may have changed! Before using this lesson with your students, be sure to check if the sites are still working or if you must find another site. Sometimes the sites still have the relevant data but you may need to change the directions to access the data.

To enter data, press STATS > Edit. Clear a list by moving the cursor onto the list name and then pressing CLEAR, then ENTER. Next enter your data.

To make a Boxplot, press 2nd STAT PLOT. Turn on one of the three Plots; choose the boxplot icon (first item in the second row) and enter the list name under Xlist. Freq should be 1. Then press ZOOM and choose 9:ZoomStat. If more than one Plot is turned on, both will be graphed.

You can create a new list by calculation. For example, if you enter the number of home runs in list L₁ and the number of times at bat in list L₂, then you can calculate the percent of home runs in list L₃ by highlighting L₃ and then entering L₁*L₂.

If you need more background about the statistical concepts involved in the lesson, some good sites to check are:

http://davidmlane.com/hyperstat/index.html

http://www.anu.edu.au/nceph/surfstat/surfstat-home/surfstat.html

http://www.math.unb.ca/~maureen/SSCEdCom/basicstats/basicstats.html

http://www.math.unb.ca/~knight/BasicStat/$content.htm

http://www.bbns.org/us/math/ap_stats

http://www.grad.cgs.edu/wise/linksf.shtml

http://www.cvgs.k12.va.us/DIGSTATS

http://www.statsoft.com/textbook/stathome.html

http://www.stats.gla.ac.uk/steps/glossary/index.html

http://www.crpc.rice.edu/CRPC/GT/sboone/Lessons/lptitle.html

http://forum.swarthmore.edu/library/topics/statistics

http://www.psychstat.smsu.edu/introbook/skb00.htm

TI-83 instructions:

http://www.ti.com/calc/docs/act/koehler001.htm

http://www.wku.edu/~neal/manual/ti83.html

The Calculator website at the Mathematics Department of the University of Wisconsin-La Crosse will perform basic statistical calculations. If you do not have access to a simple statistical computer package or calculators with statistics options, your students may access http://www.compute.uwlax.edu/stats_htdocs/newmenu.html to perform statistical computations on-line.

In order to print out just a copy of the student worksheet, highlight this section, then copy and paste it into your word processor. You may then revise the worksheet if you wish.

Activity Sheets.  

1. (4 points) We will use the Internet to look up statistics about Joe DiMaggio, Mickey Mantle, Sammy Sosa and Mark McGwire. Use the site http://www.geocities.com/Colosseum/Arena/3164/dimaggio.html to look up the number of home runs Joe DiMaggio hit each year of his career and enter these numbers in a list in your TI-83. Next look up the number of home runs Mickey Mantle hit each year of his career and enter these numbers in a second list in your TI-83. Use the site http://home.earthlink.net/~tonycap/mmstats.htm

2. (4 points) Find the five-number-summary of each of these two data sets.

3. (2 points) Make side-by-side boxplots of the home run distribution for DiMaggio and Mantle on your calculator and copy them below.

4. (4 points) Use the above boxplots to compare and contrast the home run hitting of DiMaggio and Mantle. What do you notice?

5. (3 points) Do you feel that DiMaggio or Mantle was a better home run hitter? Why?

6. (2 points) List other information that would help you better answer Question #5.

7. (4 points) Use the site http://cbs.sportsline.com/u/baseball/mlb/players to obtain data about Sammy Sosa and Mark McGwire.

8. (4 points) Look up the home run data for Sammy Sosa and Mark McGwire and enter this data in two different lists in your TI-83.

9. Find the five-number summary for each data set in #8. (4 points)

10. (2 points) Make side-by-side boxplots of the home run distributions for Sosa and McGwire on your calculator and copy them below..

11. (4 points) Use the above boxplots to compare and contrast the home run hitting of Sosa and McGwire. What do you notice?

12. (3 points) Do you feel Sosa or McGwire is a better home run hitter? Why?

13. (4 points) If you had to pick one of the four above mentioned baseball players as the all-time greatest, who would it be and why?

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1. (4 points) We will use the Internet to look up statistics about Joe DiMaggio, Mickey Mantle, Sammy Sosa and Mark McGwire. Use the site http://www.geocities.com/Colosseum/Arena/3164/dimaggio.html to look up the number of home runs Joe DiMaggio hit each year of his career and write these numbers below. Next look up the number of home runs Mickey Mantle hit each year of his career and write these numbers below. Use the site http://home.earthlink.net/~tonycap/mmstats.htm

Joe DiMaggio

Mickey Mantle

2. (4 points) Find the five-number-summary of each of these two data sets.

3. (2 points) Make side-by-side boxplots of the home run distribution for DiMaggio and Mickey Mantle below.

4. (4 points) Use the above boxplots to compare and contrast the home run hitting of DiMaggio and Mantle. What do you notice?

5. (3 points) Do you feel that DiMaggio or Mantle was a better home run hitter? Why?

6. (2 points) List other information that would help you better answer Question #5.

7. (4 points) Use the site http://cbs.sportsline.com/u/baseball/mlb/players to obtain data about Sammy Sosa and Mark McGwire.

8. (4 points) Look up the home run data for Sammy Sosa and Mark McGwire write this data below.

Sammy Sosa

Mark McGwire

9. (4 points) Find the five-number summary for each data set in #9.

1o. (2 points) Make side-by-side boxplots of the home run distributions for Sosa and McGwire.

11. (4 points) Use the above boxplots to compare and contrast the home run hitting of Sosa and McGwire. What do you notice?

12. (3 points) Do you feel Sosa or McGwire is a better home run hitter? Why?

 13. (4 points) If you had to pick one of the four above mentioned baseball players as the all-time greatest, who would it be and why?

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1. (4 points) We will use the Internet to look up statistics about Joe DiMaggio, Mickey Mantle, Sammy Sosa and Mark McGwire. Use the site http://www.geocities.com/Colosseum/Arena/3164/dimaggio.html to look up the number of home runs Joe DiMaggio hit each year of his career and enter these numbers in a list in your TI-83. Next look up the number of home runs Mickey Mantle hit each year of his career and enter these numbers in a second list in your TI-83. Use the site http://home.earthlink.net/~tonycap/mmstats.htm

Joe DiMaggio: 29, 46, 32, 30, 31, 39, 21, 25, 20, 39, 14, 32, 12

Mickey Mantle: 13, 23, 21, 27, 37, 52, 34, 42, 31, 40, 54, 30, 15, 35, 19, 23, 22, 18

2. (4 points) Find the five-number-summary of each of these two data sets.

3. (2 points) Make side-by-side boxplots of the home run distribution for DiMaggio and Mantle on your calculator.

4. (4 points) Use the above boxplots to compare and contrast the home run hitting of DiMaggio and Mantle. What do you notice?

Mantle’s "box" is slightly larger and his maximum is quite a bit larger. Otherwise, the boxplots are very similar.

5. (3 points) Do you feel that DiMaggio or Mantle was a better home run hitter? Why?

Except for the one time Mantle hit 54, he was the about the same as DiMaggio.

6. (2 points) List other information that would help you better answer Question #5.

How many times DiMaggio and Mantle were at bat. If Mantle were at bat a lot more times than DiMaggio, then his record is not comparable to DiMaggio’s.

7. (4 points) Use the site http://cbs.sportsline.com/u/baseball/mlb/players to obtain data about Sammy Sosa and Mark McGwire.

8. (4 points) Look up the home run data for Sammy Sosa and Mark McGwire and enter this data in two different lists in your TI-83.

Sosa: 1, 3, 15, 10, 8, 33, 25, 36, 40, 36, 66

McGwire: 3, 49, 32, 33, 39, 22, 42, 9, 9, 39, 52, 58, 70

9. (4 points) Find the five-number summary for each data set in #8.

10. (2 points) Make side-by-side boxplots of the home run distributions for Sosa and McGwire on your calculator.

11. (4 points) Use the above boxplots to compare and contrast the home run hitting of Sosa and McGwire. What do you notice?

McGuire’s "box" is quite a bit to the right of Sosa’s. His median is also much larger. However, the spreads are about the same.

12. (3 points) Do you feel Sosa or McGwire is a better home run hitter? Why?

McGwire, because his median is quite a bit larger than Sosa’s median and McGuire’s "box" is much more to the right of Sosa’s.

13. (4 points) If you had to pick one of the four above mentioned baseball players as the all-time greatest, who would it be and why?

I would pick McGuire since his boxplot is the farthest to the right and his median is the largest. However, bats and balls have changed since Mantle and DiMaggio’s times and if McGuire and Sosa had used the equipment that Mantle and DiMaggio had, maybe their records would not be so high.