What is Statistics?

Statistics is fundamentally about data, how to collect data, how to analyze data, and how to use data to make inferences and draw conclusions about the real world. Furthermore, statistics is an applied field with a wide range of practical applications. In fact, the scientific method relies on statistics to the point that it is impossible to do science without stats.

In the context of MATH 204 Introduction to Statistics, we will not do much in the way of data collection. However, we will discuss some important ideas regarding best practices in data collection and we will work with data that has been collected for us. We will certainly spend a lot of time analyzing data and drawing conclusions from data and our data analyses.

The data that one typically analyzes using statistics or statistical methods have some common features that we will take a moment to point out now:

1. The data is “structured” in the sense that it has an underlying order to it. This will be explained in greater detail in the early lectures of the course.
2. The data is typically a “sample” in that it is but a minor representation of all of the data one could possibly collect.

The second point is important because a collection of sample data should often be random which introduces uncertainty. We will spend a lot of time talking about sampling and the uncertainties associated with doing so. The most effective set of tools for dealing with uncertainty come from probability theory. Thus, we will spend some time in this course to develop an understanding of a small number of essential concepts from probability. Probability will form the backbone of the body of statistical knowledge we develop in this course.

Applied Statistics and Computing

You do not necessarily have to be strong in mathematics, for example, algebra and calculus in order to develop a solid understanding of statistics. Abstract mathematics provides one avenue by which to approach statistics, but actually working with data and seeing real examples is another. However, if one is to learn statistics by working with data and while avoiding the use of advanced mathematics, which is what we do in this course, then it is best to make extensive use of computing power. Thus, in this course, we will exploit the power of the R statistical computing environment and the interface to R provided by RStudio. These can both be accessed via a web browser by using RStudio Cloud.

By the end of this course, you will be able to understand the significance of the following plot:

Furthermore, you will have developed the skills and learned the tools necessary to make such a plot for yourself.

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