Statistics
Winter Math Reflection- First Semester
1. A clear explanation of the problem/skill/concept that anyone could understand
My class recently completed a mini-project that entailed researching a subject of our choice, and choosing another topic that related to it. When we chose our two topics, we then worked towards finding correlations between the two things. My essential question for this project was, "Is there a correlation between capital punishment and murder rates per state?". I chose this subject because I was interested in learning whether or not the most common argument for the death penalty (that it helps deter homicides) was a valid claim or not. To find this correlation, I compared murder rates per state and the amount of inmates on death row per state. The final product of this project was supposed to be a paper written in technical form that throughoughly explained the steps that we took when finding our correlation. Interestingly, the problem that I ran into during this project did not emerge in the math (like I had expected), but instead it appeared during the process of (trying) to write the paper.
2. Evidence of the process you went through to solve/master/understand it
I experienced significant struggles trying to write the paper in a technical format. For whatever reason, I was not able to clearly explain my ideas and process. I finally realized that to get the most possible out of the project, I was going to need to advocate to change the format of my final product. Fortunately, my teacher was willing to let me turn my project into a Power Point presentation, and verbally explain what I did throughout the course of the project. Being able to verbally analyze topics helps my understanding of the subject at hand. I am able to go into deeper explanations and hear my thought process as I talk through my topic. Being able to transfer my skill of verbal analyses to a math concept is the major factor in what led to my success and understanding of the math concepts during the Correlation project.
3. Proof that you completely understand the ideas discussed
Unfortunately, I still need to learn the basics of being able to write in a technical statistical form. However, I feel very confident in my understanding of how correlations work and how they can essentially be applied to almost anything. To find the correlation between the two subjects of my initial question, I needed to apply the equation specific to correlations to the data that I found during my research. The correlation equation is, T=R×√(N-2)÷(1-R²). I have listed what each symbol in the equation represents, and in turn written out my numbers that were calculated. The symbols are: N= Data Sets, R= Correlation, R^2= Correlation Squared, and T= Significance. The numbers that I used in the calculation were: N=50 (# of states used), R= -.01, R^2= 1e-4 (.0001), and T=-.01x√(50-2)÷(1-(1e-4)).
After going through this process and getting the final answer, all that I have to do to find a correlation is understand that for a correlation to have any significance there would have to be a minimum of a 3.84 correlation. If it is around 6.63, it can be determined that there is an undeniable correlation between the two subjects and anything between 3.84 - 6.63 should be recalculated to ensure whether or not there is a correlation.
When I conducted the calculation using my numbers, I resulted in a -0.01 correlation which signifies that there is absolutely no chance that capital punishments deter homicides.
4. A general discussion of how this problem frame you work in math looking forward, both towards next semester and beyond. Good place for self reflection- what are you talented at and how will you maximize those gifts? What is a challenge and how will you account for that?
The Correlation Mini-Project helped me hone in on a unique skill set that I plan on utilizing in a potential future career. I hope to pursue a career involving human rights, international affairs, or international diplomacy. All of these fields require a high amount of literary fluency, as well as being able to look at statistics and being able to verbalize their significance. This project revealed that if necessary, I have the ability to talk through statistical reasoning and what it signifies. It has created an unequivocal skill that can be carried on throughout my future. Even though I will be able to apply the skill of verbal reasoning to a wide variety of things, I will have to tackle the challenge of having a difficulty writing technically by continuously practicing and taking as many opportunities as I can to work on it. Not only was this project was a great way for me to research a subject that I am interested in, but I learned how to work with challenging aspects of a project and turn them around in a beneficial way.
My class recently completed a mini-project that entailed researching a subject of our choice, and choosing another topic that related to it. When we chose our two topics, we then worked towards finding correlations between the two things. My essential question for this project was, "Is there a correlation between capital punishment and murder rates per state?". I chose this subject because I was interested in learning whether or not the most common argument for the death penalty (that it helps deter homicides) was a valid claim or not. To find this correlation, I compared murder rates per state and the amount of inmates on death row per state. The final product of this project was supposed to be a paper written in technical form that throughoughly explained the steps that we took when finding our correlation. Interestingly, the problem that I ran into during this project did not emerge in the math (like I had expected), but instead it appeared during the process of (trying) to write the paper.
2. Evidence of the process you went through to solve/master/understand it
I experienced significant struggles trying to write the paper in a technical format. For whatever reason, I was not able to clearly explain my ideas and process. I finally realized that to get the most possible out of the project, I was going to need to advocate to change the format of my final product. Fortunately, my teacher was willing to let me turn my project into a Power Point presentation, and verbally explain what I did throughout the course of the project. Being able to verbally analyze topics helps my understanding of the subject at hand. I am able to go into deeper explanations and hear my thought process as I talk through my topic. Being able to transfer my skill of verbal analyses to a math concept is the major factor in what led to my success and understanding of the math concepts during the Correlation project.
3. Proof that you completely understand the ideas discussed
Unfortunately, I still need to learn the basics of being able to write in a technical statistical form. However, I feel very confident in my understanding of how correlations work and how they can essentially be applied to almost anything. To find the correlation between the two subjects of my initial question, I needed to apply the equation specific to correlations to the data that I found during my research. The correlation equation is, T=R×√(N-2)÷(1-R²). I have listed what each symbol in the equation represents, and in turn written out my numbers that were calculated. The symbols are: N= Data Sets, R= Correlation, R^2= Correlation Squared, and T= Significance. The numbers that I used in the calculation were: N=50 (# of states used), R= -.01, R^2= 1e-4 (.0001), and T=-.01x√(50-2)÷(1-(1e-4)).
After going through this process and getting the final answer, all that I have to do to find a correlation is understand that for a correlation to have any significance there would have to be a minimum of a 3.84 correlation. If it is around 6.63, it can be determined that there is an undeniable correlation between the two subjects and anything between 3.84 - 6.63 should be recalculated to ensure whether or not there is a correlation.
When I conducted the calculation using my numbers, I resulted in a -0.01 correlation which signifies that there is absolutely no chance that capital punishments deter homicides.
4. A general discussion of how this problem frame you work in math looking forward, both towards next semester and beyond. Good place for self reflection- what are you talented at and how will you maximize those gifts? What is a challenge and how will you account for that?
The Correlation Mini-Project helped me hone in on a unique skill set that I plan on utilizing in a potential future career. I hope to pursue a career involving human rights, international affairs, or international diplomacy. All of these fields require a high amount of literary fluency, as well as being able to look at statistics and being able to verbalize their significance. This project revealed that if necessary, I have the ability to talk through statistical reasoning and what it signifies. It has created an unequivocal skill that can be carried on throughout my future. Even though I will be able to apply the skill of verbal reasoning to a wide variety of things, I will have to tackle the challenge of having a difficulty writing technically by continuously practicing and taking as many opportunities as I can to work on it. Not only was this project was a great way for me to research a subject that I am interested in, but I learned how to work with challenging aspects of a project and turn them around in a beneficial way.