Possible Solutions: 2017 AP Statistics Free Response Questions

Hi Colleagues,

After the AP Statistics Exam questions have been released, I put out my own solutions and invite feedback, other approaches, and questions.

Nothing official in these solutions: I have taught AP Statistics for 21 years, and I have graded multiple times. Based in this experience, I put forth the solutions you see here.

Possible Solutions 2017 AP FRQ (First Draft)

I got a bit delayed with putting these out this year, but I did enjoy myself this weekend, so that’s good.  Workouts, friends, and rest are truly essential components of my days anymore. If you are a teacher, don’t underestimate their impact on your own health and well being.  Our profession sometimes glamorizes the false benefits of being the  “overworked martyr.”  I certainly perpetuated this in the past.  Trying to turn over a new leaf in recent years.

Thanks to Amy Crum for her solutions – I checked my own answers with hers before posting them.

Thoughts about the problems:

1: The Wolves problem.  (Basics of linear regression and scatterplots)  Haha!  I LOVE the idea of simply asking what the heck “linear” and “strong” and “positive” mean in this context. I predict that many students will not respond substantively to these questions (You know-  linear means it’s linear!)

2. Water and Soft Drinks. (one sample z-interval for a proportion)  Cool context:  there may be some issues with students correctly describing  the population of interest and the sample of interest in correct context. A common error for my students is to mis-understand the context, and then say something totally incorrect at the end of the problem.

3.  Melons.  (normal models, conditional probability) Great probability problem.  I like the subtle twist on conditional probability in part c).

4.  Pottery.  (making conclusions from boxplots, complex context) Another good,  challenging problem with exploratory data analysis. Students will need to articulate which numbers from which parts of which box-plot(s) are providing evidence for their conclusions.

5.   The Schizophrenia problem. Straight up simple chi-squared test.  I wonder if students will be expected to describe the association after completing the test, or if completing the test is enough.

6.  (Sampling with/ without replacement,  tree diagram probability).  This seemed like a shorter investigative task than in the past.  I wonder what will suffice as “complete” reasoning/ work for each part.  I especially wonder whether student swill be able to “transfer the lesson learned”  from parts (a) and (b) to part (c) without additional work to confirm that this difference  carries through to more complex situations.

 

 

 

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AP Statistics Exam, Free Response Questions: Any patterns?

The free response questions for the AP Statistics exam are sometimes hard to predict.  What trends do exist?

Here is A graph relating AP Free response question Number vs.  Chapter in the  5th Edition of The Practice of Statistics.

1:           Exploring Data (single variable, quantitative)
2:           Modeling Distributions of Data  (z-scores, percentiles, normal model)
3:           Describing Relationships
4:           Collecting Data
5:           Probability, the basics
6:           Random Variables, the binomial and geometric distribution.
7:           Sampling Distributions
8:           Inference: Confidence Intervals, 1 variable.
9:           Significance Tests, 1 variable.
10:         Inference for two groups
11:         Inference for categorical data
12:         Inference for regression

Here’s a graph of the relationship. Here are a few trends I observe:

  1. Question 1 tends to be exploratory data analysis OR an easier test about inference.
  2. Question 2 seems to feature probability OR sampling/ experimental design
  3. Question 3 seems to feature probability OR sampling/ experimental design
  4. Question 4 seems to feature an inference procedure often, but not always
  5. Question 5 seems to feature an inference procedure often, but not always.
  6. Question 6 always is a mixed bag, bot often involves some reasoning regarding inference.

Other observations:

  • “Probability, served three ways:”  Probability questions are often, but not always, three-parters that take a single scenario and then “serve up” questions involving three different techniques in probability.
  • Two sample t  vs Matched Pairs t questions are common.
  • Inference for regression, when addressed, is done pretty lightly, and often in question 6.  There are often many other parts to question 6 that are not about inference for regression.

chapter vs FR_question_number

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Smelling Like Data Science

This gallery contains 12 photos.

Originally posted on A Best-Case Scenario:
(Adapted from a panel after-dinner talk for the in the opening session to DSET 2017) Nobody knows what data science is, but it permeates our lives, and it’s increasingly clear that understanding data science, and…

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The Lesson of Grace in Teaching

Yes, I’ve started a new blog.  The platform here at WordPress seems to be nicer and more versatile.  I’ll be blogging here from now on. However, my first blog post was at Blogger, becau…

Source: The Lesson of Grace in Teaching

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My Possible Solutions: 2016 AP Statistics Free Response Questions

Possible responses to the 2016 AP Statistics Free Resposne questions, draft #1.

You can access the questions here.

Note: 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.

My first draft: possible solutions, APStatistics FR 2016

Please read, critique, and suggest fixes!

Reflection:

I think that these very accessible questions are attempting to give students a chance to explain their reasoning and thinking with appropriate specificity.  I suspect that students can easily falter in the following ways:

#1:  I wonder if we’ll see students failing to be appropriately specific in using measures of center/ spread. I can see kids giving incorrect values for IQR, and not using range as something much more accessible. I can also see the rubric penalize for not quantifying the amount of increase of the mean.  It possible, so students should probably quantify the increase.

#2.  I wonder if we’ll see students not being appropriately nuanced in explaining the effect of the ads on preference.

#3.   I wonder if we’ll see students not identifying the variables correctly – they will probably identify summary statistics instead.

#4. I wonder if we’ll see students not showing mathematical pathways, and giving a surface-level explanation of part c)

#5. I wonder if we’ll see students not explaining thoroughly enough WHY np and n(1-p) must be greater than 10.

#6. I wonder if we’ll see students not being focused enough in answering the specific question posed in each part.

 

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PDEs Course Design (Part 5): Inclusion and Excellence

Source: PDEs Course Design (Part 5): Inclusion and Excellence

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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.

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