What is the study of mathematical probabilities, distributions and deviations?

Statistics. Statistics is a branch of mathematics which is the scientific study of mathematical values pertaining to qualitative descriptions and transcribe them into quantifying values such as the descriptive statistics and infuses these quantities in the field of inferential statistics. In these two categories involve probabilities, distribution and deviations which are mainly compositions of the descriptive statistics. Inferential statistics will involve comparison and variation of the given values. Methods are t-test, analysis of variance, and two-way analysis of variance and other methods.