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There are several investigation methods in mathematical statistics.
Census: the work of investigating all units in the statistical population to collect statistical data. It is a one-time comprehensive survey specially organized for a specific purpose.

Sampling survey: refers to an investigation method that selects some units from all the units of the research object for investigation and analysis, and infers the quantitative characteristics of the whole population based on the quantitative characteristics of these units.

Comprehensive survey: refers to a statistical survey method in which the national statistical system and various business departments make unified arrangements from top to bottom and provide information from bottom to top, so as to obtain systematic and comprehensive basic statistical data on a regular basis.

Focus survey: it refers to an incomplete survey method in which some key units are selected from all the respondents to conduct surveys in order to obtain statistical data. Because the key units account for only a small part of all the respondents, and the number of survey marks accounts for a large proportion in the whole, the statistical data obtained from the survey of these key units can reflect the basic trend of social and economic phenomena.

Typical investigation: According to the purpose and requirements of the investigation, on the basis of preliminary analysis of the respondents, a few representative typical units are consciously selected for in-depth and detailed investigation and study.