The tutorial summarizes the theoretical material and provides examples of solving practical problems in the following sections: linear algebra, probability theory, methods for evaluating and testing hypotheses, the principal component method, regression and cluster analysis using a free statistical data processing system and R programming. The appendices to this manual contain information on the installation and use of the R system, as well as listings of programs that can be used in the educational process. The textbook is intended for students studying in the direction of "Applied Informatics," the program of which provides for the study of modern means and methods of computational statistics.