### Purpose

To explore data sets and statistics in baseball.

### Context

At the middle-school level, students can build on previous experience to delve into statistics in greater detail. Students should be focused on the entire process, including formulating key questions; collecting and organizing data; representing the data using graphs and summary statistics; analyzing the data; making conjectures; and communicating statistical information in a meaningful and convincing way.

In this lesson, students will use baseball data available on the Internet to develop an understanding of the different ways in which data can be analyzed. First, they will practice selecting data to perform calculations in response to pre-formulated questions. Then they will use the data to formulate and answer their own questions.

### Motivation

Distribute a copy of the 500 Homer-Club chart.

Then ask these questions:

- Which player took the most number of at bats to hit 500 home runs?
- Which player took the least number of at bats to hit 500 home runs?

Review the concepts of mean, median, and mode. Then ask each student to calculate the mean, median, and mode using the CNN/SI data in the following columns: total number of home runs, age of player, and total number of at bats.

### Development

Have students use their Baseball Stats student esheet to go to MLB No-Hitters, on the ESPN website. Tell them that they will use information from this site to answer questions about baseball statistics. They should use the data from 1970 to the present.

Students should answer these questions:

- What is the average score of the no-hitters pitched since 1970?
- Which scores appear most often in the data?
- What is the mean, median, and mode?
- Which year had most no hitters?
- Which League has had most no hitters?
- What is the ratio of perfect games to no-hitters?

After students have answered the questions, have the class discuss the data. Ask students to draw some conclusions from the data table and have the group provide feedback as to whether or not the conclusion can be supported by the data. Ask if they can make any predictions about future no-hitters based on the data.

Divide the class into groups and assign one of the problems below to each group. These problems are based on statistical information about Minor League teams. Tell each group that they will report their findings to the rest of the class, including the method used to solve the problem. Pass out the Baseball Stats student sheet for each student to fill out as he/she is working with the group.

Students will use data found in Stats on the MiLB.com site. You can have students copy the data from the website, or you can print out the charts from the page and give copies to each group. The student esheet will direct students to the site.

Have groups answer these questions:

- Which Pacific Coast League team had the best batting average in 1998?
- Which Pacific Coast League team had the best batting average in 1997?
- Which Pacific Coast League team had the best batting average in 1996?
- Which International League team had the best batting average in 1998?
- Which International League team had the best batting average in 1997?
- Which International League team had the best batting average in 1996?
- Which American Association League team had the best batting average in 1997?
- Which American Association League team had the best batting average in 1996?

There are at least two methods that the groups might use to figure out the batting averages for the teams. One method is to add all of the batting averages in the first column and divide by the number of players. Another method would be to add all of the hits (in the 4th column) and all of the at-bats (in the 2nd column) and divide the total number of hits by the total number of at-bats.

After students have calculated their answers and presented the information, have each group select one team and calculate the team batting average using the other method. Then, compare the results. Ask the class to discuss which method of computing the average would be most accurate and why. Also, ask the class to discuss whether the data from previous years would still be applicable.

Finally, have students use their student esheet to go to the Minor League Archives site again. Working in groups again, students will select data from the website and devise questions that they think can be answered using the data. Each group should then solve their problems and write the answers on a separate sheet of paper. Then, the groups should exchange and solve each other's problems.

### Assessment

First, have the original groups compare their solutions to the problems to those of the other group. Each group should evaluate the solution, and if it is different from their own, explain if it is a better answer or if it is merely a different form of the same answer.

Second, have each student write a one paragraph response to the following problem: If a batter has a .400 batting average and gets a hit the first time at bat in a game, what are the odds of his getting a hit in his second at bat? His third? His fourth? Will this change depending on which part of the season it is?

### Extensions

The Chance Database website contains materials designed help teach a college-level Chance course or a more standard introductory probability or statistics course. This site contains interesting background information for teachers, but also contains links to datasets that you can adapt for middle school lessons.

The Data and Story Library is an online library of data files and stories that illustrate the use of basic statistics methods.

ESPN.com is a good source for more statistical data about a variety of sports including football, tennis, golf, soccer, and so on.

Census Bureau Population Topics and Household Economic Topics contains surveys, reports, and tables on a wide variety of topics.