Introduction

In previous chapters, we have described and explored data using descriptive statistics and visual techniques. We have also looked at probability, randomness, and using simulations of random variables to solve problems. The idea of distributions was also examined, which plays a much bigger role later in this chapter.

When looking at applying statistical ideas, there are some important questions to answer concerning methodology. Some examples of these questions could include "how large should I make my sample?" or "how confident can we be in the results?". For this chapter, we will look at how we can apply two of the most important theorems in statistics, starting with their practical implications before moving onto solving common problems using the more useful techniques that are derived from these important ideas.

In this chapter, we will explain what the law of large numbers is and clarify how sample size affects the sample mean. The central...