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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Here is A graph relating AP Free response question Number vs. Chapter in the 5^{th} 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:

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

Other observations:

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.**“Probability, served three ways:”****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.

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(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…]]>

Hi Friends: this is a great article articulating how one statistics teacher has been thinking about “data science.” As a teacher of AP Statistics, Sports Research, and Computer Science Principles, I found this presentation very helpful. Enjoy!

(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 its powers and limitations, is key to good citizenship. It’s how the 21st century finds its way. Also, there are lots of jobs—good jobs—where “data scientist” is the title.

So there ought to be data science *education*. But what should we teach, and how should we teach it?

Let me address the second question first. There are at least three approaches to take:

- students use data tools (i.e., pre-data-science)
- students use data science data products
- students do data science

I think all three are important, but let’s focus on the third choice. It has a problem: students in school aren’t ready to do “real” data science. At least not in 2017. So I will…

View original post 1,430 more words

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Source: The Lesson of Grace in Teaching

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

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**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.

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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!

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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!

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