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Is Capital Punishment a Deterrent? Murder Rates Compared with Execution Rates in Texas, and on a National Level

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Is Capital Punishment a Deterrent? Murder Rates Compared with Execution Rates in Texas, and on a National Level
IB Math Studies IA Is Capital Punishment a Deterrent? | Murder Rates compared with Execution Rates in Texas, and on a National Level |

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The United States of America is one of the only democratic countries that still use capital punishment. This has raised a rather extensive debate, especially over the last 4 decades. I became interested in this issue in 2011 after the controversy surrounding the execution of Troy Davis, and the issue has remained. In my research, one argument in favor of the use of capital punishment has always stood out as the most solid: that it serves as a crime deterrent and will save more lives than we kill. On the other hand, people from the opposing side state that if the death penalty really did act as a deterrent, states that implement it should have much lower murder rates than states that do not, and that is simply not the case. I decided to further investigate the issue by comparing the yearly murder rates and execution rates of the state that has accounted for almost 40% of executions in the country: Texas, and to use Pearson’s Correlation Coefficient to determine if there is any correlation between the two.
Question: What kinds of correlations exist between murder rates and execution rates in Texas?

Variables: Yearly number of executions in Texas. Yearly number of murders per 1000 people in Texas

Hypothesis: There will be no correlation between murder rates and execution rates.

The first thing I did was collect the data. For the state of Texas, I took the total number of murders each year starting in 1977, the year after the reinstatement of the death penalty that resulted from the Supreme Court case of Gregg vs. Georgia. The source I found (http://www.disastercenter.com/crime/txcrime.htm) only accounted for murders up to 2011, as the 2012 murder statistics hadn’t been released yet. I found a yearly record of executions in Texas at
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