ABSTRACT
Statistics is an important use of mathematics in science, and the mathematical power of statistics comes from probability theory. Probability theory is a mathematical theory that has been developed to deal with randomness. This chapter focuses on a kind of statistical reasoning that involves the use of statistics to describe features of data sets to summarize, describe, and display data in a meaningful way. It also focuses on another kind of statistical reasoning that involves the use of statistics to make inferences based on data to draw broader conclusions from data, such as the generalizations and projections. The chapter helps us to give three new examples of situations involving statistical reasoning and describe how statistical reasoning is involved in each. It also helps us to characterize the difference between descriptive and inferential statistics and define probability theory and say how it relates to statistics.
