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Mathematical statistics uses probability theory and other branches of mathematics to study statistics from a purely mathematical standpoint.

Mathematical statistics is the subject of mathematics that 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 in face of the involved uncertainty.

Mathematical statistics is the theoretical basis for many practices in applied statistics.

See also Edit


  • Borovkov, A. A. (1999). Mathematical Statistics. Taylor & Francis.
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