Possible Solutions, 2015 AP Statistics free response questions, Draft 2

Hi Colleagues!   Thanks for the edit suggestions.  Most edits were typos and cleaning up details.  Here is draft #2:  Possible Solutions 2015 AP FRQ

I welcome any critiques, alternate solutions, questions or criticism.

Posted in Uncategorized | 3 Comments

Possible Solutions to 2015 AP Statistics Exam questions, draft 1

Hi Colleagues! 


Well, here’s my first draft of possible solutions. 

You can access the questions here at AP Central.

Disclaimer: I construct these as a service for both students and teachers to start discussions. There is nothing “official” about these solutions. I certainly can’t even guarantee that they are correct. They probably have typos and errors. If you catch some, let me know! But if they generate discussion and help others, then I’ve succeeded.

The link to my solutions is here: Possible Solutions 2015 AP FRQ

Thoughts about the questions:

#1. Part a was straightforward. Part b  will require students to construct a pretty sophisticated criterion for preferring either company. It will be interesting to see how “convincing” students’ arguments need to be.

#2. A great, simple question that will require precise communication of how confidence intervals work.  I like how students must explain  why a lack of evidence for  claim does not imply evidence that its negation is true.

#3.  This should, hopefully, be a slam dunk for kids. This is a good indicator of whether your students are understanding the formulas you use, or simply mimicking things that were done in previous problems.

#4. A straight up inference test for the difference in two population proportions.  I anticipate students not being specific enough in stating that volunteers were randomly assigned to treatments. 

#5.  Again a great litmus test to see if students understand the tools they use. This seems almost too simple for  #5.

#6. I think that this was a great, challenging problem. It’s a great problem to use in teaching sampling distributions in the future. It requires students to consider the distribution of a population, the distribution from a sample from that population, and  the distribution of the sampling distribution of the sample means.  I especially like how the oft-ignored requirement of simple random sampling comes to the surface here.  I worry that too many students will overlook the questions posed and write something that is simplistic and irrelevant.

Posted in Uncategorized | 11 Comments

2015 AP Statistics questions released! Stay Tuned.

Hi colleagues,  The questions were just released. You can get them here!

Upon first glance, many of them seem very simple, but I can see that students will need a high level or precision in their language to give convincing, thorough responses.  #6 was accessible, but takes a lot of thinking about what you are seeing. I can see why some students might think it was “really easy.”  I worry that they may have read those questions too superficially.   But if the questions force students to read, write and think, it’s a good thing.  See you soon!

Posted in Uncategorized | Leave a comment

Stay Tuned: My attempts at 2015 AP Statistics Free Response solutions coming soon!

Hi Colleagues,

It’s time to dust off this blog!  It’s been a VERY busy year, and most of my work / correspondence has happened off-site.  But I am looking forward to reviving my blog this summer.

To get me off to a good start, I will continue my annual tradition. I will “walk the plank” and submit a set of responses to the free response section of the 2015 AP Statistics Test.

You can see what I did in previous years: here in 2014  and here in 2013 .

A few comments:

1.  I am NOT, in any way, claiming that these solutions are exemplary. or “what the college board expects.”  I am a teacher of AP Statistcs since 1997, and these are my version of “good ” solutions.

2.  My solutions will go up about 24 hours AFTER the College board officially releases the Free Respsonse questions to the public at AP Central’s Statistics Exam Page. 

3. Please ask questions, critique, make corrections, or suggest different, better, or more interesting responses. This is intended to start dialogue.

See you soon!

Posted in Uncategorized | 4 Comments

2014 FR questions, AP Statsitics Exam. MY REVISED first attempt at solutions.

Hi all: I just worked through the 2014 AP Statistics Free response questions, which are publicly available here. 

My attempts at solutions can be found here .  

Possible Free response solutions 2014 frq,  Second Draft!

Those were my first attempt.  Thanks to Corey Andreasen, Pat Humphrey and others who caught some errors!

Again, these are simply attempts at solutions, and they probably still have errors… so tear them apart! I invite corrections, critiques, questions, and commentary.

I look forward to the dialogue.

If they provide a starting point for further dialogue about the questions, then I have succeeded.

UPDATE: Thanks to Corey Andreasen for his on-point comments.

I agree with his critiques, but I also want to think more about 4a:  Is there more to a complete solution than simply “means are pulled up by unusually high incomes, and medians aren’t?”

Posted in Uncategorized | Tagged | 25 Comments

Stay Tuned: attempts at solutions, 2014 AP Statistics Free Response coming soon !

Hi all!

this Friday, about 180,000 students will take the AP Statistics exam.  Typically,  the College Board releases Free Response questions to the public 48 hours after the administration of the exam.  As soon as I can access the questions and work through the problems, I will post a first attempt at solutions for people to read, discuss, and critique.

Best of luck to your students, if you’re an AP Stats teacher!  Best of luck if you are taking the exam!

Posted in Uncategorized | Tagged , | 5 Comments

SSAC 14: What does it take to call a strike?

Difference between P(strike|S) and P(Strike|not S) for four different counts in baseball

Difference between P(strike|S) and P(Strike|not S) for four different counts in baseball

Have you ever thought that umpires are a bit too willing to call strikes when the count is 3-0?  Or, perhaps, you’ve noticed that umpires rarely call strikes when the count is 0-2?  In this very clear paper,  Etan Green and David Daniels  from Stanford University use Pitch f/x data to answer questions about how the  count (number of balls and strikes against a batter) help predict the chances that an umpire calls a ball/strike on the next pitch.

I was impressed with how the researchers wrote and presented so that everybody can understand their work.  This paper is easy to understand and share with students in high-school, in my opinion.  It simply takes a baseline understanding of the rules of baseball, basic probability ideas, and reading three-dimensional graphs.   

How are umpires biased?

  •  3 balls:   P(called strike) rises by about 10 per
    centage points above what happens overall.
  • 2 strikes:  P (called strike)  reduces by as much as 20 percentage points below what happens overall.
  • Last pitch called strike:  P (strike) reduced by  as much as 15 percentage points.

Is this isolated to a subset of umpires?  

Let’s look at the 50% contour line of calling

a strike overall, When looking at pitches after 2 strikes,  this contour contracts.  The area between these contours is called a “band of reversal:”  We found  a lack of bias emerging for pitches called after a ball.  But the ENTIRE distribution of strike thresholds is above zero for pitches after two strikes.  IN short, EVERY UMPIRE IS BIASED.


Every umpire shows bias for certain ball counts.

Posted in Uncategorized | Tagged , , , , , | Leave a comment