This textbook develops an application-oriented approach to the mathematical theory of data and randomness, starting from everyday phenomena and extending into the axiomatic theory of probability. It is primarily aimed at students of mathematics education, but it also serves as a meaningful introduction to stochastic concepts for other mathematics students. In the chapter "Descriptive Statistics," concepts of data reduction and presentation are developed. The construction of "Probability Theory" begins with typical examples, with a detailed presentation of the historical and substantive development of the concept of probability. These two areas are brought together in the chapter "Inferential Statistics." The book concludes with a look at the application of stochastic methods in the empirical sciences.