Based on probability theory, it studies the statistical laws of a large number of random phenomena. The task of descriptive statistics is to collect data, sort out and group them, compile a frequency distribution table, draw a frequency distribution curve and calculate various characteristic indexes to describe the concentration trend, deviation trend and skewness of data frequency distribution.
Inference statistics is based on descriptive statistics, and infers and predicts the population according to the regularity summarized by sample data.
The links of mathematical statistics mainly include:
1, model selection and establishment. In mathematical statistics, a model refers to some assumptions about the studied population, which usually specifies a certain type of population distribution. The establishment of the model should be based on probability knowledge, professional knowledge of the studied problem, past experience and samples (data) extracted from the population.
2. Data collection. There are three ways: comprehensive observation, sampling observation and arranging specific experiments. Comprehensive observation, also known as general survey, refers to observing each individual in the group and determining the required indicators. Sampling observation, also known as spot check, refers to extracting a part from the population and measuring its related index values.
Arrange specific experiments to collect data, which should be representative and easy to analyze.
3. data collation. The purpose is to extract useful information contained in the data. One form is to make an appropriate chart, such as a scatter chart, to reflect the general rules or general trends implied in the data. The other form is to calculate some numerical features to describe some aspects of the sample, such as simple descriptive statistics such as sample mean and sample variance.
4. Statistical inference. It refers to drawing some conclusions about the population distribution according to the population model and the samples taken from the population. The collection and arrangement of data is the necessary preparation for statistical inference, which is the main task of mathematical statistics.
5. Statistical prediction. The object of statistical prediction is the value of a random variable at a certain time in the future, or the value that will be taken when observing the variable under certain conditions.
6. Statistical decision-making. An action plan based on statistical inference or prediction and considering the consequences of actions (expressed in the form of economic losses).