Section 4.1 Quantifying Uncertainty
Mathematics generally focuses on providing precise answers with absolute certainty. For example, solving an equation generates specific (and non-varying) solutions. Statistics on the other hand deals with providing precise answers to questions when there is uncertainty. It might seem impossible to provide such precise answers but the focus of this text is to show how that can be done so long as the questions are properly posed and the answers properly interpreted.
Indeed, people often make claims about being the biggest, best, most often recommended, etc. One sometimes even believes these claims based upon subjective metrics. In this chapter, we will start by looking at relative frequency and notice several properties regarding relative frequencies as the number of trials increases. We will use these examples to motivate a definition for probability and investigate the resulting consequences of that definition.