Friday, November 8, 2013

An Analysis of Simple Rockets

For one of my statistics projects I chose to analyze a game called SimpleRockets. I wanted to find out the most efficient way to achieve orbit. So I ran numerous tests to figure it out. I measured the height of the rockets apoapsis and the time it took the rocket to reach apoapsis. If the rocket escaped orbit I also measured its escape velocity and the time it took to escape orbit.

I was surprised to find the largest engine was not the most efficient engine. In fact the second smallest engine used with the second largest fuel tank was the best combination to achieve orbit. I attribute this to air resistance in the atmosphere. The larger engines consumed more fuel while they were still in the atmosphere. But the smaller engines had plenty of fuel left after the escaped the atmosphere.

In addition to running tests I was able to look at a bit of the games code. I found all of the different parts values such as mass, fuel consumption, thrust, wet weight, dry weight, and turning ability. I then looked though the planets and found their mass, orbit, and atmospheric density. Seeing these values helped me to come to my conclusion that the atmosphere is responsible for making large ships inefficient.

Thursday, November 7, 2013

Greatest Sport State of the US (currently)

Sports fans around the US each have their own claims on what team is best and which state has the best sports.  Is there a way actually figure out who is the best of the best? I decided to come up with a way to calculate who really is the sports state of america and I displayed this throughout my project.  First, I looked through all 50 states, plus Washington D.C., and took the teams that had at least one MLB, one NFL, and one NBA team and threw out the rest.  I figured this would show the states that were overall the sports state, rather than dominating in one or two types of sports.  This gave me a total of 15 states (Washington D.C. included). I looked at each state and wrote down every MLB, NFL, and NBA team they had. Then I went onto ESPN and found the winning percentages of the past three completed seasons for each individual team.  After that, I calculated the average winning percentage of those three seasons.  If a state had more than one team of the same sport, I then made an average winning percentage for that sport. If they only had one team, I would just use that single team for the sport average.  Finally, I found an average of each sport to show the state's overall winning percentage.

 I displayed all of this in a spreadsheet in Microsoft Excel.
After many calculations I found the top states/teams for each sport 

And last but not least, I determined that Massachusetts is the overall best sports state of the US based upon the last three seasons.  (Meanwhile, we unfortunately have Minnesota in last place) 

Perfect Student

This quarter, Hope and I worked together on a perfect student project.  The idea of this project was to find a way to rank students on their qualities, not just their grades.  We came up with a list of 19 characteristics we found important.  We asked students to rank the importance of each characteristic on a scale of 1-5.  After getting results from the survey we averaged the results to figure out what characteristics were most important.

Results from Survey
We compared our results to what would be the perfect student.  The perfect student would have a score of 5 (light purple).  The average we got shows our ranking out of 5 (dark purple).

Average of the Results we got

Along with finding the most important characteristics, we asked students to rank themselves on a scale of 1-5.  From these rankings, we found the average of their answers to find their ranking.  The top 5 characteristics (trustworthy/honest, respectfulness, responsibility, dedication/hard working, and standing up for what you believe in) were weighted stronger then the other characteristics.  From this we found the maximum, minimum, median, and mean.  

Maximum:    4.32
Minimum:    1.68
Mean:          3.7
Median:       3.84

Even though the class rated themselves, I don't think everyone was completely honest about all of the characteristics.  To continue this project next quarter, we will be ranking people on these characteristics based on what we see -- hopefully the results will be more exact.  We may also ask teachers or other students to rank some students to see how accurate the students ranked themselves.  From this project I figured out what qualities were important to students.  One thing that shocked me was eagerness to learn was on the bottom of the importance ranking.  I thought it would be more important.  I learned that no student thinks they are perfect so if we were to use this ranking over our GPA, the top person would not have a perfect score like the top for GPA could have a 4.0.

Freshman Survey

For my project I decided to take a survey of all the freshmen in school and see what is going through their heads. The questions I chose were because I had been wondering about what the answers were. I wanted to know what the kids in the school thought of the iPads and the lunches, the last questions were just for fun and I wanted to see how the freshmen handled some questions that were not what was to be expected. It took me about a week to come up with the questions, make the survey, send the survey out and get the responses. My first plan was to go to all of the seminar rooms and have the freshmen take it on paper, then I went high-tech and decided to have them take it on their iPad's. I sent the survey out in a email to all of the freshmen in school on Friday and waited over the weekend for the results.

Of the one hundred and fifty freshmen only 78 responded. Once the results were in I compiled them and took a random, cluster, convenience and nonrandom samples, then I compared the results to each of the samples and then to the results of the whole survey. The data I got back showed that some of the bad ways of sampling had the most accurate data, however that could have been a fluke: it is possible to get good data with a bad sample, but it is not likely to happen. The point of this survey was to compare the results of all of the different types of samples, and to answer some questions that I had been wondering about for a while. I have not confirmed which is better Xbox or PS 3, so I will need to create further surveys to confirm my results, and why I got the results I did for this survey.

I can now confirm that the freshmen class likes the iPad's overall, and that the freshmen are indifferent about school lunches. Some things I learned from working on this survey are that, freshmen are lazy even when it comes to taking a two minute survey, that even the worst samples can give the most accurate data (but not very often), and I also learned that it takes a lot of work to set up and send out a survey and then compile the results I got back.

Math Survey of the school district

This quarter I had to do a project that was for electives and I had a hard time thinking about what to study. Then Mr. Pethan suggested that I write down ideas about thing that I really disliked and hated. So I wrote down a few thing and then realized that the one thing that I really hated was math. I decided to survey a class from every grade to get a more proper representation of what other kids liked about math or what they didn't like about math.

So first off I had to do a cluster sample and picked one classroom from every grade.  The first thing that I did was make the survey, then I picked all of grades 1st through 8th graders and then I picked 4 math classes in the high school that I was going to survey. After I got the classes figured out I sent emails to the teachers that I wanted to survey there classes and got there permission to do it. Next I set up a date that work for them all to take it and then I went and got it done. Here is Mrs. Fuchstieners 4th grade class results:

Throughout the course of my project I learned that paper copy surveys are really time consuming and fairly boring to go through and look through them all. I have a hunch that most of the elementary and part of the middle school kids that will take my survey will like math while a few of them won't like math. I learned that even when kids are young they are pretty smart people for their age because of some of the answers that these kids give. One of the response that I got was a great one or at least I thought that it was. It said that math needs "To get rid of some words that mean the same things as other". I guess the one main thing that I learned was that even kids in elementary school thinks that math needs to be more fun than what it already was. Over the years math has not only got less fun but more troublesome to the majority of the people. I was talking with my parents and they told me that math has changed so much over the past few years they never even heard of it or would know how to do it anymore. Today even in school I hear even some of the smarter kids say that math isn't what it used to be. So those are the things that I have learned and observed. My point of this project is to see what makes people either like math or hate math. 


In this quarter of statistics, we were assigned to come up with our own projects, whether those projects were improving the course, finding new and interesting data, or some thing else was completely up to you.  The big project that I started was trying to find a way to easily teach the basic concepts of cryptography and how you can use statistics, in addition to some basic math, to crack some elementary ciphers.  I will be the first to admit that when I started out on this project I knew next to nothing about creating or breaking ciphers, so I had to do a lot of research on types of ciphers, how they work, some basic number theory, and the processes you must under go in order to analyze and break the cipher.  As soon I had a good amount of reach done, I started creating a power point to summarize what I'd learned, in hopes of using it teach others.  This power point is, at this point, still a work in progress, and I hope to eventually expand upon it, creating a video series to teach the concepts necessary in cryptography and cryptanalysis.

Through this project I have learned a lot about the applications of statistics and other forms of math.  I think that it is a good thing to be teaching students how math can be used or has been used in the past, other wise they will think is math is just a class you have to take that will never be used beyond an elementary school level, cryptography is good example of this.  Since this project is still a work in progress, I hope to learn and more and add to/expand upon it in order to better teach others, as well as to better myself.

ACL Injuries

Throughout this quarter of Stats class, we have learned many things.  The thing that I did and enjoyed was researching ACL injuries.  This year I have seen many professional athletes go down with torn ACL's. This started to make me wonder and I became interested in how likely it is for an ACL injury to occur.  To find how likely an ACL injury is to occur you can use this graph from BMJ Publsihing group.
To calculate the occurrence of ACL injuries with your team and in real life situations, you need to plug numbers given into an equation of players multiplied by exposures multiplied again by the injury rate above then divided by 1000. The number of ACL injuries that you would expect to see from a hockey team of 40 players who are on the ice 85 times during the season would be about once every 5 seasons or .204. Surprisingly, the Byron Bears did not suffer any ACL injuries to their football team this season. They had a roster of 45 players and the probability of an ACL injury occurring is .445 ACL injuries per season.

Throughout this process I learned some very interesting things, whether it be about the ACL or how often of an occurrence ACL injuries are. I also talked to my friends dad who is a general surgeon and he was talking to me about the ACL and other ligaments of the knee. That was very good for me as I was able to understand what I was researching more in depth. This project also took some time to complete. I was also more interested because of the injury that Adrian Peterson suffered a couple years ago. I wanted to know the chances that a football team will have players with an ACL injury. For a pro football team that does not make the playoffs, the number of ACL tears per season would be 1.602, obviously some teams might have more than others just depending on other factors that go into it. Being able to put these numbers and predictions into real life situations is what I enjoyed most about this project. I am excited to see at the end of the season how many injuries teams have as by those calculations, there should be around 51 ACL tears. Through 7 weeks there were 38 ACL tears, which would surpass the expected number of 51. This could be due to multiple things including the high speed in the pros and the physicality of the game. I had a lot of fun working on this project and learned many cool things!

Teacher's Expectations

I worked on a group project on what high school seniors are expected to accomplish vs. what high school seniors are capable of accomplishing.  I did the teacher's perspective for surveying.  These were the average results of 16 randomly selected teachers:

How many hrs. seniors should spend on ALL homework in one week?
How many hours of work should a senior do a week?

How many hours of sleep should a senior get each week?

How many hours on extracurriculars (sports, volunteer, music) a week?

How many hrs. should a senior have a week of free time?
avg. hours/week15.816.456.213.813.7

As you can tell from the table above, seniors are expected to be quite productive in a week with only 168 hours.  Here is the work I did to show that there are not enough hours in a week based on teacher perspective.  (I rounded to the nearest hour since students will vary anyways). 

Hours in a week 168
Homework hrs. -16
Work hrs. -16
Sleep hrs. -56
Extracurricular hrs. -14
"Free time" hrs -14
School hrs. -35

This leaves us with 17 hours in a week and we have to include prep time (amount of time to get ready) in a day which is about 7 hours in a week.  Leaving us with 10 hours!  Then you need to eat which is about 1.5 hours a day leaving us with NEGATIVE 0.5 hours in a week!  That does not include our transportation from Point A to Point B during a week-long time period.

I tried to work mostly on what teachers expected from us while Manda got the students perspective.  First we took all the different departments of teachers and did an SRS to get teachers to survey from each department.   We were going to survey 20 teachers, but we had 4 teachers as undercoverage because they weren't in the building while we surveyed.  After we asked all the teachers the survey questions, I made a table with the data.  I found the average hours per week for each question (the first table above).  Then I included school, eating, and prep time to get the results.

I learned that to take a decent survey you need to be very specific on the questions you ask, how you ask them, and who you ask.  It all needs to be worked out so you try to not have bias.  It's difficult to survey when you know what you want the results to be!

The point of this survey was to prove that as a senior in high school, a lot is expected from us!  Of course, every senior is different and results may vary from senior to senior.

Wednesday, November 6, 2013

Jacob Ostreng

In the first quarter of stats I did a few projects. The main project that I worked on was my Class Improvement Project. The goal of this project was to try to figure out why a lot of people got a bad grade on the module six test (hypothesis testing), and how to fix that. I started off by entering the test data into spreadsheet, figuring out what people struggled with, and how to teach that. For the most part students struggled with what a p-value was and how to explain it in context. I then researched different ways and methods to teach p-value and used the information I learned to make a short presentation explaining what a p-value is. The other part of the test that students did poorly on was remembering when to use symbols, such as mu and p-hat. So I made a review of Module 4 to help refresh their memory.

I learned how to explain information better, and figured out how to analyze data better. I think that the process that I went through to figure out what students struggled with worked well, but probably was not the most efficient. If I had more time to work on this project I would like to try to teach students, who have worked through Module 5 in this stats program, how to use p-value using the presentation that I created. I would then analyze their test data with the test data of my class. However, p-value is only part of Module 6 so they would still have to learn the rest of module 6 before taking the test. The most difficult part of this project was trying to remember why it was that I did not understand p-value and how it was that I learned what it was. If I remembered what it was that finally made p-value "click" then it would have saved me a lot of time and effort.

Overall I think that I did very well on this project and obtained very good results. I created a different explanation of what a p-value is then what Mr. Pethan originally taught us. I think that more data needs to be obtained to figure out if this new approach to p-value actually helps students understand p-value better.

This is the Presentation that I made

The Most Dangerous Place to Live

For our project we found out the most dangerous state to live in America. We collected data on different topics that could make a place dangerous. We made a graph of each category and then made a graph of all of the factors combined. We made z-scores out of the data we found to make a ranking system. We choose 8 different factors that made the state dangerous. We choose murders, heart disease, pneumonia, lung cancer, traffic accidents, earthquakes, tornadoes, and hurricanes. We used per 100,000 people in each state for murders, heart disease, pneumonia, lung cancer, and traffic. For earthquakes, tornadoes, and hurricanes we based it off per square mile.  We made graphs for each individual factor and made a mega graph showing exactly what state was the most dangerous. The scores helped us rank each factor and showed how important it was. We found out that Louisiana was the most dangerous state and Utah was the safest state. It seemed like the southern states were more dangerous. They were in hurricane range and also could have tornadoes. They also had a high rate for heart disease because they were the more overweight states.

I learned a lot about America from this project. I know where I want to live when I'm older. What to look for and avoid when I find a place to live. Avoid places that allow smoking and avoid fast food. I learned how to make a graph. It turned out to be very easy. I remembered how to make z-scores from our data. It seemed like the south east was the worst overall because they had a lot of heart diseases, tornadoes, and hurricanes. There health wasn't the greatest and heart disease was caused from all the bad food they tend to eat. Minnesota and Utah were the safest mainly because they had no real threats. They both don't have a lot of huge cities and little natural disasters. Healthy life styles will also lower the chances for diseases.

If I did this project differently I would add more categories to make our mega graph even more accurate. If we had more time we could do it by city not state to make it even more exact.

S-curves and normal

One of my projects that I did was about smartphones being sold over the years. I thought that this was one of the best projects I have done. I made this project into a video and put it on YouTube. This graph below is a graph I created which tells me the number of total phones sold between the years of 2008 and 2013.
I also talked about market penetration for Android. Market penetration is the extent to which a product is recognized and bought by customers in a particular market.  Duopoly which is a situation in which 2 suppliers dominate the market for a commodity or service.  I also mention a little bit about The Diffusion of Innovations Theory.

This video below explains the video that I made out this project.:

This graph shows smartphone sales\

These are the sources:

Most Dangerous Place to Live Project

For the project I worked on with Buster, Dan and Joe, we made a map of the worst place to live in the U.S by state.  First we researched things that kill people, like murders, and lung disease. Then we made individual maps for each category, which were murders, heart disease, lung cancer, influenza/phenomena, traffic deaths, hurricanes, and earthquakes. After we made all the graphs, we created a z-score for each factor and then used these z-scores to create a ranking formula, which allowed us to create one big "Mega Graph", that showed the most dangerous and most safest states in the U.S.

This project taught me a lot of things, and by far the most beneficial thing that this project taught me was how to create info graphic maps using hard data. Creating the maps was actually pretty easy because of the the Google spreadsheets, which was  a lot more efficient than excel, because we could all be typing in data at the same time. The Piktochart website we used was also something new that none of us had used before, but once we figured it out it too was easy and very helpful to use. This project helped teach me how to make something decently interesting out of boring statistical data about traffic deaths, hurricanes, earthquakes, etc. This project also taught me how to work better in a group, because this is one of the first group projects that we've had to come up with things on our own and decide what we want to do, usually the teacher will tell you exactly what they want. This new approach really challenged us to actually think and be creative, which seems like one of the main goals of this class.

I thought that our project turned out well, but if I had to improve it, I would of tried to get even more death factors included. I would want everything big or small to be considered when deciding on what factors to use, like air quality, crime rates in general, proximity to nuclear reactors. Also I thought our maps could of looked more detailed, because the shading of the colors told you what the most dangerous and safest places were with ease, but trying to tell the difference of states in the middle was hard to do. We couldn't really find anything better, so we just used Google spreadsheets. It would of also been nice if we could of included some sort of interface with our info graphics, like being able to click on each individual state and having important information pop about relating to our death factors, but we had no idea how to do that.

Below is the culmination of all of our work, which is a map of the most dangerous states to live in. The darker the shade of red, the more dangerous the state is.

Perfect Student

Everyone has their own description of what the perfect student is. It varies from person to person. Taylor and I created a survey to figure out how close our sample, which happened to be students from statistics class who took the survey. There were 29 students who participated in the survey. We picked out 19 characteristics that we felt were the most important. We also chose the ones that we believed were the most important and that the class would find the most important too.  The order of most important in the class is below.

Here shows what Taylor and I thought was the most important compared to our sample.

We took the highlighted characteristics and weighed them in our formula because those were the ones that the class cons
We found that most of the class ranked themselves in the 3-4 out of 5 range. The graph below displays the average responses from the samples along with the perfect student score.

This is how our sample measured up against the perfect student. Out of 190 points possible our sample received 154.2414 points all together.

This survey was really fun to put together but there are some flaws. Since people did put themselves mostly in the 3-4 range out of 5, it makes the data not too accurate. People tend to think that they are better then they actually are. Next Quarter we plan on doing this survey again while having teachers and peers assess the students along with themselves.

Perfect Person

I wanted to come up with a project to find what makes someone The Perfect Person/Students.  I watched videos online and read comments left by other people to see what they believe makes the perfect person.  I then researched what characteristics would be a good list and then trimmed them down to get a exact list.
First, I came up with three categories to put all of my characteristics under.  Those categories were Society, Economy, and Future Family.  After I got my categories, I started to make a list of key characteristics that I thought would be important.  We put each characteristic into the three categories that we created.  Once we had a list of characteristics, we decided to find a way to measure every characteristic and get a number for each one.  Then I found pictures and made a slideshow on Haiku Deck on my iPad.  I then later created note cards and shared my project with the class.

This was my economy slide.  The characteristics that I put under economy were smarts, independent, efficient, and fixing your mistakes, growing/improving.  I put how to measure these on my note card and shared it to the class.

I learned that you can basically use statistics with everything.  You can find ways to measure characteristics using numbers.  I learned how to classify things based on how important they are to make someone the perfect person.  There are many ways people can describe a perfect person but I believe that I came up with some of the most important ones.  I struggled with this project a little bit because it wasn't easy to actually come up with an exact list to share under each category.  There were so many options to choose from that I had to think about what ones meant the most.  I think that the research was the most tough spot as I said before that there were so many different options.  This was a very different and weird question to deal with.  I had to deal with new factors every time that I read something new during my research.  I could have done this project the whole quarter and I still would be working right now.  I had to deal with it and just come up with a list that I thought was correct.  I believe that this would be a good project to do with like 5-6 people so you could find more information and then put all of them together to make one big project.

Tuesday, November 5, 2013

The Most Dangerous States

To do our project, we gathered data for 8 different categories. Those categories were; Heart Disease, Murder, Lung Cancer, Traffic Accidents, Influenza/Pneumonia (all per 100,000 people) and number of earthquakes, tornados, and hurricanes per state. For each category we made a separate graphs by taking the data and inserting them into Google Spreadsheets. Once we had all of our individual graphs, we put them on the website This site helped us design a page to let us display each graph in its own unique way. Once we had all the individual graphs done we then made our one big Mega Graph. In this graph, we inserted all of our data onto another Google Spreadsheet. We made a z-score for each individual category and then made a ranking formula by adding all of the z-scores together. We used this ranking formula to find out the least and most dangerous states to live in. We then took that spreadsheet data, and just like before, made into a graph so we could easily see which ones were better or worse. (The darker the color, the more dangerous the state.) We also listed the states in order from the most dangerous to the least dangerous so you could easily see which ones were more dangerous than others.

I learned a lot from doing this project. For one thing, when we started this, we had no idea what were going to do to show our information. Then as we gained more and more data we had the idea of using a colorful map to display our information. We had no idea how we could do this but luckily Mr.Pethan worked his magic and messed around with Google Spreadsheets and found a way to do it. This was my first time ever using Google Spreadsheets and it was actually pretty easy to use with the help of Mr.Pethan. Using the Piktochart website was also something new. None of us had ever used it before and we had to figure out how to use it from scratch. I also learned a thing about working together because it was hard to get all of our information together. We all did our own parts and had to find ways to get it all together on one computer, and eventually we all had to get it on the same website which was harder than it seemed.

If I could do this project again or improve it in any way, I think I would find more categories of scenarios that make a state dangerous and get more specific and precise data. I liked how Google Spreadsheets made it easy to make the United States graphs so I would definitely use that again if I had to. Using Piktochart went pretty well but at first it was hard to find out how to use it and it was hard to find different ways to make it more creative. Also when we were searching about ways to possibly display our information, we found a website that allowed you to scan over every state to get more specific information about that particular subject. If we could have found a way to do that or had more tools to make something like that I feel it would have added a lot to our project.

Skeptical Stats

        If you have seen David McCandless' TED Talk, you know that he is known for his bright and fun graphs. When I watched this video, one graph in particular caught my eye; "Peak Break-up Times" on Facebook. At first, I wanted to scrape statuses from Facebook and create a similar graph, a graph that showed the common times for a relationship to begin. However, the more I researched data scrapers and tried to get one going, the less confident I became in my venture. My teacher showed me the site "", and I began to think that perhaps David McCandless' data and graph were not totally accurate, so I decided to pick apart his graph and give other reasons for why someone might be posting "broke up" or "break up" in their Facebook status. I tore apart the graph from left to right, explaining that on Valentine's Day, someone might not be posting about a significant other that broke up with them, but could say: "My boyfriend broke up my night of studying by taking me to dinner and a movie". The peaks leading up to spring vacation, summer vacation, and Christmas vacation, could all have a similar reason, too. Who wouldn't post about "taking a break up at the cabin" over summer break? Or post a question on Facebook about whether Joseph broke up with Mary when he found out she was pregnant? And what David McCandless claims as the "safe day", or Christmas, could really just be a decrease in status updates, or more posts about what people are doing with their families instead of a depressing relationship status change. Overall, it was a fun project to do! I didn't have to be serious and calculate a ton of numbers, but use my imagination and think outside the box!

Small Town Utopia

          We all have our own biases about how the town that we live in is the best, but is there really a clear winner? That is the question I set out to answer in my project. Although there are many towns I could have put in my sample, I just used the small suburbs around Rochester. These suburbs included Byron, Kasson, Stewartville, Triton, and Pine Island. I chose six categories to rank each town on. Three of these categories were educationally based, and the other three were just having to do with the town. The six categories were MCA math scores, MCA reading scores, college readiness, average house value, houses per 1000 people, and crime rates. I chose these because I thought they were all pretty important to making a town great. I was hoping that I could collect numerical data for each category and using those numbers, rank each town. The academic data was the easiest to find. I was able to get that data easily all off of one website and then make graphs and compare them. The other three categories were a little bit more difficult because I had to find websites that had information for all of the towns on them so that I could be consistent. I found that certain websites had slightly different numbers for the categories, so if I used data for one town from one website, I needed to keep that same website for all of the other towns. I created graphs for all of the categories and used a z-score in order to rank the average house values.
            Although I thought it would be relatively easy to find all of the data and compare, it was harder than I thought. I think that the data that I chose provided a minimal undercoverage and nonresponse. This is because the categories that I chose weren't based off of surveys, it was strict city data. One bias that could have occurred was on the houses on the market. The website I used wasn't a specific real estate agency, but it could have been biased to one, making sure that more of those agencies' houses were showing up. I also learned that it was harder to rank the towns than I thought. It was easy when it came to academics because it was already in percent. I had to use z-scores and find the standard deviation for the house values, which is something I learned in stats. It was fun to be able to actually apply that to something that I was doing on my own. When looking at my graphs, it was interesting to see that the math test scores were a lot more varied than the reading test scores. All of the towns were in the 78%-88% when it came to the reading tests, while in math, the scores varied from 45%-74%. It makes me curious as to why it is that way, but that might be a project for another time. I learned that the area around Rochester is a pretty safe place when it comes to crime. All of the towns had the same crime rate, which was the same as the average crime rate of Minnesota. While looking at the amount of houses on the market, it made me wonder why certain towns would have more or less houses for sale. Is it because people are trying to get out? Is it because everyone is trying to move there, or no one wants to leave? Maybe there's a higher demand in some towns versus others. Again, that's not something I ever found out, but this project spurred more questions that I would sometime be interested in finding the answer to.

These are a couple of the graphs and the stats that I used for my project.