# Introductory Statistics

MAT 3280: Introduction to Statistics [4 credit hours]

Course Description: An introduction to statistics (non-Calculus based). Frequency distributions; their graphic and tabular representations; measures of central tendency, of dispersion and of correlation; sampling; elementary probability theory; linear regression, the Central Limit Theorem.

Prerequisite: Algebra II

Many students in majors that involve the analysis of data are required to take a course in Elementary or Introductory Statistics. These "lower Statistics" courses often fall into one of these catagory descriptions:

• MiniTab™ or Excel™-based Statistics Courses
These courses tend to be centered around the philosophy: "here is a big set of data, and here's how you run it through MiniTab or Excel to spit out some answers". The number of formulas in these types of courses is staggering, with a multitude of notations that can make your head spin. Some refer to these courses as "food processor" Statistics: put the numbers in, press a button, and voilà! - result soup.
• "Understanding"-type Statistics Courses
These types of courses tend to be focused on the task of interpreting statistical language and concepts into social science, business, and "real world" situations. Often these courses are overwhelmed with often confusing (and unexplained) notation, like

While a practical appreciation for statistical language and usage is often achieved in these courses, it is at the expense of a mathematical, experimental, and empirical approach to the discipline of statistics, thus a limited understanding.
• TI-Graphing Calculator-based Statistics Courses
These courses tend to follow a more investigatory approach to the academic discipline of statistics. Although the TI-Graphing Calculators will do many statistical computations, it is cumbersome (but not impossible) to operate with large data sets on these calculators, and are limited by computational power as well as the tiny screen and poor resolution. Similar to Precalculus courses based upon the TI-Graphing Calculators, these course mix a (usually) healthy portion of hand computations with small amounts of calculator computations, glued together with learning about the interpretations of statistical usage and language in "real world" applications.
• No Technology-based "Talk" Statistics Courses
These courses often have more reading and interpretive explanations, learning the "language" of Statistics in application to social science, humanities, and business usage, with little or none of the computational portion of the subject. The goal here is usually to become familiar with the vocabulary of statistics, so that the student may read textbooks and reports using these terms, and be able to understand the stated interpretative results.

## Experimentation-Based Empirical Statistics

Our Introductory Statistics course takes a more ambitious approach to any of these standard course models described above. Our curriculum tenets are:
Utilizing the powerful computer algebra and graphing software LiveMath™, serious numerical and graphing experiments are the gateway to the establishment of statistical concepts.
• More Numbers, Less Words
Using the adapted curriculum Statistics&LiveMath from the more advanced calculus-based Prob/Stat&LiveMath and Prob/Stat&Mathematica from the MathEverywhere team, the focus of the curriculum is on data, numerical experiments, and graphical presentations. Words are kept to a minimum, as are endless lists of (unexplained) statistical notations that usually accompany long, drawn-out narratives.
• The Power of Random Numbers
As Probability and Statistics is concerned with the study of making sense of seemingly random data, the usage of random number-based experiments is key to an empirical approach to the subject. "Let's generate another random set of data, and see if our previous conclusions still hold" is a staple of the curriculum.
• Bridge From Computer To Paper/Pencil Computations
While a computer is essential to an empirical study of statistics and probability, one must also have basic manual skills away from the computer.
• Liberal Arts Philosophy
Rather than training a student in the language of statisticians, we believe in the liberal arts philosophy that a core understanding of the concepts of probability and statistics will easily lend itself to the applied task of interpretations of statistical language to the social science, humanities, business, and "real world" topics. As such, our curriculum often starts with "Here is a random data set - let's investigate it", rather than "25 people were asked which restaurant they go to each week, and how many times they go to it. Here are the results. Let's analyze this study."