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Extended data statistics is a comprehensive science that infers the nature of the measured object and even predicts the future of the object by searching, sorting, analyzing and describing the data. Statistics uses a lot of professional knowledge in mathematics and other disciplines, and its application covers almost all fields of social science and natural science.

Based on the study of social and economic problems, statistics has experienced at least three stages of development in the development process of more than two thousand years: city-state politics, political arithmetic and statistical analysis science.

"Mathematical Statistics" is not a new discipline independent of statistics. To be exact, it is the general name of all the new methods of collecting and analyzing data formed in the third development stage of statistics. Probability theory is the theoretical basis of mathematical statistics, but it belongs to mathematics rather than statistics.