# Chance ( Math 5 ) Syllabus

Course description:

In this course, we will use current events, guest lectures, and personal experiences, to examine fundamental statistical and probabilistic concepts as they appear in daily life. By the end of the course, you will be able to critically analyze the statistics you come across in your day-to-day life. Throughout the course, you will produce and analyze statistical information of your own. You will also evaluate other students' analyses.

We may view statistics as the organization and analysis of data. The following quantity would be an example of a statistic: the percentage of people in the US who own a pinball machine. There are several useful statistical ideas which we will explore in this course, including the average, the standard error, and the correlation coefficient. Sometimes a statistic is best understood with a picture as opposed to a number, and we will study such visual aids including: the histogram, the scatter plot, and the regression line.

Probability may be viewed as an attempt to understand randomness. For example, one might use probability to make sense of the following question: If you chose a person in the US at random, what is the chance that they own a pinball machine? We will explore several probabilistic concepts, including that of model, expected value, variance, confidence intervals, along with certain explicit models including the binomial model, normal distributions, and the models which arise in various gambling situations.

Many of the issues explored in Chance lie at the intersection of statistics and probability. For example, you might interview 1,000 US citizens and ask them "Do you own a pinball machine?" and then collect the following statistic: the percentage of these 1,000 people who own a pinball machine. Suppose 8% of those interviewed answered yes. With what right do you have to claim that 8% of the US population owns a pinball machine? To answer this, one has to understand how to give a statistic meaning with probability, which can be quite a tricky business. Information will be presented to you in this form throughout your life, and it is likely that you will make decisions based on such information. The primary goal of this course to help you better understand such information, allowing you to make more educated decisions in situations where statistics arise.