Statistics Projects

Juniors in the AP Statistics class had the opportunity, this year, to work on a project in the style of a statistical consultant.  Students used real data from the 50 States and had their choice of variables to examine.  Many of the projects looked at patterns and relationships among various social indicators such as crime, income, education, etc.  We looked for trends and associations using a sophisticated statistical programming language called “R”.  This was an ambitious task, but the students jumped right in and turned in some of their finest work!  Please enjoy the following excerpts from their work.

Ty Lee – Education trends in the 50 States


This histogram visualizes the distribution of the percent of the state population with a bachelor’s degree or higher. Height of boxes indicate the number of states that fall into the range from the left end to the right end. The state with lowest rate was West Virginia, while the highest was District of Columbia. The shape of this histogram seems to indicate that the underlying population is normal; the graph is uni-modal, not skewed, and looks similar to a bell curve.

Cade Zawacki – Statistical Analysis Casts Doubt on a Claim about Gun Violence

“If you look at all the fiascos that have occurred, 99 percent of them have been by Democrats pulling their guns out and shooting people,” Kiehne said. “So I don’t think you have a problem with the Republicans.”

(Does NOT include outliers CO + CT)

(Observed – Expected) ^2 / (Expected)

Blue: 0.2821752532
Red:  0.6195867769   +
Sum: 0.9017620301

Chi-Squared cdf(0.9017620301,e99,1) = 0.3423096854

 With a Chi-Squared value of about 0.902, we can expect to see results like this about 34% of the time – assuming that mass shootings happen randomly in any state. Thus, we cannot conclude that there is a relationship between mass shootings and political affiliation.

Screen Shot 2014-05-28 at 2.38.55 PM

Depicted above: Chi-Squared cdf(0.9017620301,e99,1) = 0.3423096854
(Domain 0<x<2)

[These results suggests that it is highly likely that the political inclinations of the State have no effect on the occurrence or frequency of mass shootings.  This student pointed out that the data limit our conclusions, to a certain degree since we do not have data for the political preferences of individual shooters.]

Norio Chan and Simon Lu – No Significant Difference in Assault Rates in Red and Blue States

Screen Shot 2014-05-28 at 2.39.51 PM

The graph and the results of the t-test show that we cannot reject the null hypothesis of “no difference in assault rates”.  There is no strong evidence to suggest that assault rates are different in blue states and red states.

Gleb Paschenko – Murder Rates Decrease when High School Graduation Rates Increase

Screen Shot 2014-05-28 at 2.40.44 PM

Although some outliers are present, the association seems to follow a moderately strong negative linear pattern.  In states where high school graduation rate is higher, the murder rate per 100,000 is lower.

James Kim – Are Harsher Sentences Associated with Crime Reduction?

Correlation Between Strength of Sentence/Real Execution Rate and Crime Rate

Screen Shot 2014-05-28 at 2.41.30 PM Screen Shot 2014-05-28 at 2.41.39 PM

The very high P-Value suggests that there probably is no relationship between the real execution rate and the murder rate.   [We might be inclined to believe that those states with more severe penalties might see a reduction in crime.  The data was not able to demonstrate that this was the case.]

Emma Lawrence and Sam Atkins – High School Graduation Rates in Red States and Blue State

Screen Shot 2014-05-28 at 2.42.22 PM

If we use a significance level of .1 then we can reject the null hypothesis of no difference in high school graduation rates due to the p-value being less than .1.  There is some evidence to suggest that high school graduation rates are higher in Blue States.  [They are certainly more consistent.]


In a world of uncertainty, the mind looks for deterministic explanations.  Statistics students have learned to talk about uncertainty, supported by quantitative measures, with confidence.  We learned that, too often, our preconceived ideas about a population or claims in the media rest on very little data, indeed.  Students, you have been entrusted with a powerful tool – use it for the good of humankind!

Stats Project

Mrs. Baldwin’s AP Stats classes have been working on several projects. Here’s a peek at one, as described by one of her students:

“This histogram visualizes distribution of percentage of the state population with a bachelor’s degree or higher. Height of boxes indicate the number of states that fall into the range from the left end to the right end of the rectangle. The state with lowest rate was West Virginia, while the highest was District of Columbia. The distribution of this histogram seems to be normal; the graph is uni-modal, not skewed, and looks similar to a bell curve.”


US Math Students of the Trimester – Spring 2014

I am excited to announce a new award, the Upper School Mathematics Students of the Trimester!


Each math faculty member was free to choose whichever student of theirs they thought best exemplified what they are looking for in a model mathematics student. The official description of the award is as follows:

“Awarded to students who exemplify the math department’s core values of competence, confidence, and perseverance while helping their peers realize the relevance and importance of an exceptional mathematical education both for its beauty and for its practical application.”

The following students have been recognized as the Upper School Mathematics Students of the Trimester for Spring 2014.

Please join me in congratulating these outstanding mathematics students!

Cody CavanaghCody Cavanagh – Cody is my student of the trimester because of the way in which he delves into the intricacies of mathematical concepts. Cody completes all of the more straight-forward problems accurately and then spends his time and effort on the most challenging ones. He has consistently shown skill with proofs, with logical thinking, and with making connections. He has had a great year in Geometry in every way!
Marquis FrancoisMarquis Francois – Marquis is one of my most dedicated students. He is always prepared, and his quiet nature belies a strong intellect. I love teaching him, and I can always count on him to fully master the material
Lauren HelmLauren Helm – During T3 Lauren has stepped up her already strong math game. She has been even more laser focused in class, has totally dominated recent topics, and she’s a fantastic driver during small group projects. Her mature yet fun-loving attitude has helped stabilize an energetic class. Her work product has been extraordinarily consistent.
Lanxi KangLanxi Kang – Nancy has excelled in Algebra 2 honors all year. She has thought deeply about each topic that we have covered this year. Each day she has brought the highest level of preparation to class. She has shown a genuine interest in each topic that we have covered and even more importantly a genuine interest in the topic of mathematics in general.
Jasmine Movassaghi

Jasmin Movassaghi – Jasmin has been a B+/ A student all year. More importantly than that is her work ethic and commitment to understanding the concepts. She can always be counted on to take risks to answer questions. As important is that she will not allow the teacher to continue if she is the least bit confused. Putting all that together makes her a pleasure to teach and a great role model for her fellow students.

Gleb PashchenkoGleb Pashchenko – Gleb is our first ever double award winner! From one teacher: Gleb has done impressive work in AP statistics this year. He has come to understand the underlying principles of statistical analysis. In this course, students learn the language of a statistician and practice interpreting results with quantified measures of uncertainty. Gleb has been a model for this practice and consistently demonstrates his desire to improve his knowledge and skills. From another teacher: Gleb has excelled in all aspects of this course. He has had perfect test scores and regularly submits outstanding quality coding projects. Gleb’s attention to detail is superb and he is a joy to have in class.
Ryan PatenaudeRyan Patenaude – Ryan is an outstanding math student and has done well all year in pre-calculus. Ryan always answers difficult questions during class, completes his work with thoughtfulness and effort, and helps his classmates frequently.
Taylor PotaskyTaylor Potasky – She has been consistently at the top of the class. She works very hard and is always focused and on task. she is one of the most likeable people in the school.
Alexis RyanAlexis Ryan – Alexis is always engaged and works hard. She has been particularly responsible about staying on top of her work when she has been away from school for outside commitments. She is helpful to the others in the class and helps to keep a fun and positive atmosphere in class.
Evan StarkEvan Stark – Evan has been a very consistent student all year long. This trimester, he has been nearly flawless on all of his assessments. In class, he is always well focused and engaged in our discussions. He has been a leader, and has helped the class move forward on a daily basis.
Lindsay WhippleLindsay Whipple – Lindsay has been a diligent worker in every aspect of Geometry. Always focused and on task in class, Lindsay enjoys a challenge. She has battled through the demanding questions of the third trimester by drawing on previously learned concepts while looking for new ways to solve a problem. Her work is accurate and she has learned from the few mistakes she has made this semester. I commend her determination to be her best!


Past students of the trimester can be found right here: Fall 2013, Winter 2014

Microcontrollers and DC Circuits

TedHere’s some great info put together by Mr. Matthias, the teacher who will be leading the charge in the classroom next year for one of Williston’s brand new courses, Microcontrollers and DC Circuits.

1. What topics will this class be covering?
The basic principles of microcontroller design and simple DC electrical circuits will be introduced. Topics of voltage, current, resistance, capacitance, induction, Ohm’s Law, and breadboard prototyping will be covered. In addition, students will use their Java/C++ programming knowledge to write programs for the Arduino microprocessor and use these programs to control the behavior of their DC circuits. Online circuit design software will also help students test and document circuit designs before building them.

2. How is this class different from the other classes taught at Williston?
The two major areas of knowledge presented in this course are computer programming an direct current electricity. Classes already exist for students to learn computer programming in the Math Department (e.g.; Engineering & Robotics, Advanced Programming and AP Computer Science, Video Game Design) and the Science Department offers topics in electricity (e.g.; AP Physics 2, AP Physics C). What makes the Microcontrollers and DC Circuits course unique is the way it integrates topics from BOTH departments into a single, hands-on experience. The topics presented in Microcontrollers and DC Circuits form the basics of a STEM-based (Science, Technology, Engineering and Mathematics) education.

3. Why do you think it is an important class to offer?
Microcontrollers and DC Circuits expands the School’s STEM offerings for students interested in studying electronics, computer engineering, or electrical engineering at the college/university level. It also presents topics that can be somewhat abstract (programming theory, current/voltage/resistance, etc.) and makes them concrete through experimentation in a hands-on experience.

4. Why should students take this class? What type of student do you think this class will appeal to?
Certainly, any student who has an interest in computer programming or engineering will find that this course will augment their level of preparation for studying engineering at the college/university level. In addition, a student who has had taken the computer programming classes at Williston will be able to use and expand their programming knowledge to build and program DC circuits that perform many different functions.

5. What prerequisites are required for a student to take this class?
Prospective students must have competed both Engineering & Robotics I and II, or Advanced Programming in Java and receive approval from the Math Department.

6. Is there anything else students should know or other things about this class you would like students considering this class to know?
Microcontrollers and DC Circuits is designed for knowledge mastery through a fun, engaging and experiment-based experience. Student will each have their own microcontroller (Arduino), a prototyping “breadboard”, and a kit of electrical components. In addition, software to program the Arduino will be installed on the students’ Surface.

Also, for those students who anticipate taking AP Physics 2 or AP Physics C, Microcontrollers and DC Circuits will prepare them in advance for the topics in the Electricity unit of both courses.

7. Have you taught any other similar topics before? If not, has there been/ do you anticipate there being a learning curve for you as a teacher when preparing the material?
I have taught the skills necessary for the computer programming aspect of Microcontrollers and DC Circuits. I have also been an amateur electronics hobbyist for the last 52 years. I will be blending my teaching experience in computer programming with my knowledge of DC electronics, and will frame both in a curriculum I am developing with the generous help awarded to me by a Williston Summer Grant. As part of the grant, I will be attending a week-long workshop for educators taught by secondary school electronics curriculum developers.