## Baidu Encyclopedia version

Mathematical statistics is a branch of mathematics, divided into descriptive statistics and inferred statistics. Based on probability theory, it studies the statistical regularity of a large number of random phenomena. The task of describing statistics is to collect data, organize, group, prepare the number allocation table, draw the distribution curve of the number of times, and calculate various characteristic indicators to describe the concentration trend of the data distribution, the deviation of the deviation trend and the distribution of the number of times. Inferred statistics are based on the description of statistics, based on the regularity of the sample data, inferring and predicting the population.

## Wikipedia version

Statistical data collection involves research planning, especially with randomized trials designed and planned for surveys using random sampling. Preliminary analysis of the data usually follows the study protocol specified prior to conducting the study. Data from the study can also be analyzed to consider secondary hypotheses inspired by the initial results or to suggest new studies. Secondary analysis of data from planned studies uses tools from data analysis, and the process of doing so is mathematical statistics.

Data analysis is divided into:

Descriptive statistics-describes the statistical data part of the data, that is, the summary data and its typical attributes.

Inferential statistics-the part of the statistical data that draws conclusions from the data (using certain data models): for example, inferential statistics involves selecting a data model, checking whether the data meets the conditions of a particular model, and quantifying the uncertainty involved (for example, using confidence intervals) ).

Although data analysis tools are best suited for randomized data, they are also applicable to other types of data. For example, from natural experiments and observational studies, in this case, the inference depends on the model chosen by the statistician and is therefore subjective.

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