Black Men and Prison Recidivism

Today, we continued our discussion of Statistics and we were introduced to "measures of dispersion." Measures of dispersion indicate the extent to which values are spread around a central value. We took a closer look at mean. The measures of dispersion for mean are mean deviation, variance and standard deviation. Mean deviation is simply the mean of the absolute values of the differences between the data values and the mean (kind of like you're finding the mean of the mean.) Variance is the square of the mean deviation, and standard deviation is the square root of the variance.

In an effort to keep math "real-world" applicable, I decided to use measures of dispersion on something I'm interested in, and that is the rate of recidivism of Black males in New York State. Recidivism is the rate at which incarcerated individuals return to prison.

Above is a chart regarding the amount of prisoners in adult private prisons between the years 1987-2001. Clearly the overall trend of prisoners has since grown since the late '80s. Are these rates justified? And where are African-Americans in these numbers? This is the question I set out to answer using mean deviation, variance and standard deviation.

How Often do We Eat: An Introduction to Frequency Tables

In our Statistics class this week, we discussed the basic principles of Statistics, which included measures of central tendency: mean, median, mode and range. We started our unit off discussing how to find the mean, how  to create a frequency table, how to find the mean from a frequency table and then how to create a histogram and find probabilities from said histograms. To understand the idea behind these objectives, Ms. Saint-Preux polled the entire class on the following question, "How often do we eat?"

First, we polled the class to get our raw data. We then created a frequency table based on our results. From there, we calculated the average of how often our class eats. Ends up our class eats, on average, 8 hours a day!

On the next day, we discussed creating a histogram. We took the basic information of the hourly increments and our frequency to create our histogram. The results are shown here below.

Did You Know...?

...that if you leave answers blank on the SATs you will have a better chance of getting a higher score on the exam than if you guessed on every single question?

(Introductory Paragraph)

My name is Ms. Saint-Preux and I am here to convince you that when taking the SAT it is better to either eliminate at least one answer choice and then guess, rather than guessing on each question.

(Background Information)

The SAT is a standardized exam that primarily 11th graders must take in order to fulfill the requirements for attending a 4-year college and/or university. It used to be out of a score of 1600, but recently it has been changed to a total score of 2400. It includes a Math, Writing and Critical Reading section. The entire test takes about 3 -4 hours to complete. 

The SAT penalizes the test taker for guessing. If you get one question correct, you receive one point. If you leave a question blank, you get 0 points--in other words nothing happens to your score. But if you get a question wrong, you get 1/4 of a point off. For example, if you answer 3 questions, and you guess on 2 of them and get them wrong, you receive .5 points. Yet, if you leave two questions blank, and get one right, you receive and remain with 1 point! In addition, if you can eliminate at least one question from the four multiple choice, you increase your chance of getting the right answer from 25% to 50%. 

(Steps/Calculations)