# 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.”

Chi-Data:
(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.

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

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

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

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

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.]

Summary

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.”

# Standing ovation for Stan

After 32 years at Williston, Stan Samuelson just taught his last class. What a grand career!

# 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!

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

# Student solutions for the 2014 BC exam – Round 2

Check out the second answer key created by Eton and Evans to the actual #3 from the 2014 BC Calculus exam. You can check out their answer key for #2 right here.

# Stats are everywhere…

…even at the prom!

Mrs. Baldwin received this note from one of her students:

“We did a chi-squared test at the prom table!”

# Microcontrollers and DC Circuits

Here’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.

# Student solutions for the 2014 BC exam

My BC & Multi students are working on creating AP-style grading rubrics for the 2014 BC Calculus Free Response Questions. Check out this AMAZING one created by Eton and Evans!

They did all the work and formatting. #whoa

# BC Calc FRQ Solutions

Many more student screencast solutions of actual BC Calculus free response questions have been added to the Student Screencasts page.

Many more will be added by next year’s class!