# No Series: Statistical Analysis to Rank Baseball Players

Math.S.ID.1

Common core State Standards

• Math:  Math
• S:  Statistics and Probability
• ID:  Interpreting Categorical and Quantitative Data
• 1:
Represent data with plots on the real number line (dot plots,
histograms, and box plots).

|
Math.S.ID.2

Common core State Standards

• Math:  Math
• S:  Statistics and Probability
• ID:  Interpreting Categorical and Quantitative Data
• 2:
Use statistics appropriate to the shape of the data distribution to
compare center (median, mean) and spread (interquartile range,
standard deviation) of two or more different data sets.

|
Math.S.ID.3

Common core State Standards

• Math:  Math
• S:  Statistics and Probability
• ID:  Interpreting Categorical and Quantitative Data
• 3:
Interpret differences in shape, center, and spread in the context of
the data sets, accounting for possible effects of extreme data points
(outliers).

## Statistical Analysis to Rank Baseball Players

Lesson Objective: Rank the greatest NY Yankee homerun hitters using statistical analysis
Grades 11-12 / Math / Statistics
Math.S.ID.1 | Math.S.ID.2 | Math.S.ID.3

## Discussion and Supporting Materials

### Thought starters

1. How does letting students define criteria for the greatest homerun hitter enrich the lesson?
2. What statistical analyses allow students to reconcile differences in the data (such as longer careers)?
3. What evidence of understanding is seen in student discussions?

Every time I try to download the supporting materials, I get a connection error. I've tried different browsers. Can someone email them to me? jlking@mpsomaha.org
Recommended (1)
I noticed that he students seemed ready and able to chart,graph and plot the data represented on the table. Also the students really thrived in the pairing and sharing piece of the lesson. The students were able to collect and plug in other data sets. It seems that lesson was well recieved and successful.
Recommended (1)
Having students understand that there is a 'formula' for making informed interpretations with an explanation and reasoning is a great tool. It is not only a relatable subject for students but it also included statistics. I agree that the idea of pairing & sharing is useful for students to gain literacy in a subject such as math because it teaches them that just an answer is not enough but an explanation and clear reasoning is just as important.
Recommended (1)
I was interested to see how students were communicating so fluently and thoughtfully... Their analysis seemed very educational because they were able to debate and interpret their findings validly as a group afterward. All of their input was valued by the teacher too, which seemed to convey how important "disagreement" can be for everyone. I agree Sarah, I loved listening to students discuss their findings! And I agree with you Leena, based on what the students were saying I could tell they were interested in the activity and were learning a great deal.
Recommended (1)
It's one thing for students to know formulas and know how to use them. This segment of the lesson I believe shows an aspect in learning that deals with numerical literacy, being able to make sense of data and make informed interpretation. Can students look at the data in a spreadsheet and notice trends/patterns? Your students were well able. Thank you Ms. Denton.
Recommended (1)

### Transcripts

• TEACHING CHANNEL
INTERVIEW WITH TRUDY DENTON

TRUDY DENTON:
This is our project for today. Who was the greatest Yankee homerun hitter?

TEACHING CHANNEL
INTERVIEW WITH TRUDY DENTON

TRUDY DENTON:
This is our project for today. Who was the greatest Yankee homerun hitter?
(interview)
I'm Trudy Denton. I teach at Staples High School in Westport, Connecticut.
(class)
You’re asked to create a baseball dream team for your fantasy baseball league. The last spot you have to fill has to include a great homerun hitter. So what I want you to do is study the following homerun records for these four New York Yankee greats. Which player is the greatest homerun hitter? Why did you choose this player? And in order to come to your conclusion, you might want to use graphs and statistics to support your choice. Then, after you identify the greatest, you need to rank the four players and describe your rational for the ranking.
(interview)
How can you look at this data and decide who's the best homerun hitter? The point of the lesson really was to give students the experience in comparing and analyzing distributions using graphical displays.
STUDENT 1:
Which kind of graph do you want to make first? Do you want to make a box plot or a...?
STUDENT 2:
Yeah, I think a stacked box plot would be good.
TRUDY DENTON:
They were given the task of putting the data into box plots, observing what the data told them, both in terms of the shape of the data, the center of the data, how spread was it, or is there anything unusual, and we also asked them to make a decision about what they saw. In other words, who was the greatest homerun hitter? What makes you think that they're the greatest hitter, and to use what they observed from their analysis to draw that conclusion.
STUDENT 3:
Isn’t kind of unfair that Roger Maris was around for like six years, and Lou Gehrig did it for like, double that length?
TRUDY DENTON:
OK. So, what does that mean? How do you reconcile that?
STUDENT 1:
Either Babe Ruth or...
STUDENT 2:
What about Mickey Mantle, it looks like.
TRUDY DENTON:
Sports is just full of readily accessible data, and the figures, the names that we used -- Babe Ruth, Mickey Mantle, Roger Maris, Lou Gehrig -- are icons, American heroes that most people have heard of. It’s a relatively familiar set of numbers for them to access and to deal with.
STUDENT 4:
I think the most important thing is how Gehrig went to zero. So that means some years he just didn't hit any.
TRUDY DENTON:
I find the pairing and the sharing a really great strategy. They sit every day in pairs. When they can share with another student, you see evidence of their having made the learning their own, and that's when it sticks. It’s not just a process of memorization.
(class)
How we doing here, guys? We’re getting close? A couple more minutes to tie it up.
(interview)
Last year we had the benefit of acquiring the statistical software to use. They get to see the results very quickly, rather than inputting numbers by hand.
(class)
OK. Are we good? Are we ready to share? OK. Who wants to go first?
STUDENT 5:
We said Babe Ruth was undoubtedly the first person, because he has the smallest range, the most consistent, and his mean is the highest.
STUDENT 6:
Definitely Mickey Mantle for second, because his standard deviation is just slightly higher than Babe Ruth's.
TRUDY DENTON:
Usually the first two players are pretty straightforward and everybody agrees. They wrestle with that third and fourth place.
STUDENT 7:
Not only did Maris only play seven seasons, but other than his one great season he was rather average.
STUDENT 8:
Lou Gehrig also had like a smaller range, even considering the fact that he had a couple seasons where had zero homeruns, or one. There's an even greater variance in the way that Roger played and that shows, like his sixth season was like eight homeruns, and his second had 61, so he's like a huge, he's kind of all across the board.
TRUDY DENTON:
So they kind of get to that, that the player with the consistency is probably one that you want. They get that things like illness and health impact someone's performance.
(class)
All of you identified the fact that Lou Gehrig had a couple of seasons where, for health reasons, or at the beginning of the career, he wasn't as productive. If you were to strip away those seasons, he would be up there in terms of productivity and performance with...
(interview)
They’ve kind of done this more structured analysis as a group, and we've talked about it. Now I’m asking them, OK, go out and get some real data.
(class)
You guys have a task. Over the next 15 minutes here and all of tomorrow, you're gonna find three related data sets.
(interview)
The activity is actually completely transferrable to other data sets, and it's really just a matter of researching what a particular group of students' interests might be.
(class)
Check college. The NCAA keeps really good statistics for all sports. What have you guys got?
STUDENT 7:
Something with NFL quarterbacks.
TRUDY DENTON:
NFL quarterbacks, OK. If you want to enter data into Fathom, it has to be in a spreadsheet format.
(interview)
We’re fortunate to have the software. I think it's a wonderful tool to have. But this whole lesson, and this whole approach, can be replicated using a graphing calculator. Even a teacher doesn't have a smart board in their classroom, they can do an overhead projector with the graphing calculator screen on top, and the kids could even share what's on their graph. So there's a number of ways to adapt this lesson for a lot of different situations. You could even modify this lesson for middle school and make it appropriate for them. There’s a lot of flexibility with this kind of thing, and you can adapt it and make it as sophisticated as you need it. Or, you can even ratchet down the sophistication and make it applicable to a wide range of ages and ability levels.
(class)
All right, see if that works. It’s either not going to recognize it or it'll work. And it worked. What do you know. So now you have your range and your RQR for each one. See what that, see if that supports what you were thinking about.

* * *END OF AUDIO* * *
* * *END OF TRANSCRIPT* * *

### School Details

Staples High School
70 North Avenue
Westport CT 06880
Population: 1885

Data Provided By:

Trudy Denton

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