Mathematical statistics deals with gaining information from data. In practice, data often contain some randomness or uncertainty. Statistics handles such data using methods of probability theory.
Statistics is divided into:
descriptive statistics - the part of mathematical statistics that describes data, i.e. summarises the data and their typical properties
inferential statistics - the part of mathematical statistics that draws conclusions from data, i.e. checks whether the data fulfill some condition and gives guarantees on the involved uncertainty.
Mathematical statistics is the theoretical basis for many practices in applied statistics.
References
Borovkov, A. A. (1999). Mathematical Statistics. Taylor & Francis.
