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Introduce several popular mathematical statistics methods.
Sampling survey from samples can be divided into probability sampling and non-probability sampling.

Probabilistic sampling methods are divided into simple random sampling, stratified sampling, systematic sampling, cluster sampling and multi-stage sampling.

Non-probabilistic sampling is divided into: convenient sampling. Judgment sampling, quota sampling, snowball sampling.

Simple random sampling is also called pure random sampling. In other words, the survey units are randomly selected from the population, without any grouping, classification, queuing, etc. The characteristics are: the probability of each sample unit being extracted is equal, each unit of the sample is completely independent, and there is no certain correlation and exclusion between them. Simple random sampling is the basis of other sampling forms. This method is usually only used when the difference between the whole units is small and the number is small.

Stratified sampling is suitable for situations with large total amount and large difference. Firstly, the overall units are classified and layered according to their differences or certain characteristics, and then sample units are randomly selected in each class or layer. Stratified sampling is actually a combination of scientific grouping or classification and random principle. Stratified sampling can be divided into equal ratio sampling and unequal ratio sampling, and unequal ratio sampling can be used when the total number of different types is too large. Except for stratification or classification, it is organized in the same way as simple random sampling and equidistant sampling.

Systematic sampling generally queues the signs of massage chairs of all units, and then samples the units at regular intervals. If the population * * * has n units, and the samples drawn from it are n units, dividing the total number of units n by the number of sample units n is the interval distance of equidistant sampling. After giving way, the first group draws one unit immediately, and then draws one unit every k units until N units are drawn.

Cluster sampling refers to selecting several groups (or groups) in a purely random way or by equidistant sampling, and then investigating all units in all selected groups (or groups) one by one.

Multi-stage sampling, which divides multiple sampling procedures into several stages, and then samples step by step to complete the whole sampling process.

Scope of application: there are many overall units and they are widely distributed. It is very difficult to select samples through one sampling, so multi-stage sampling is adopted at this time.

An example of multi-stage sampling

Sampling survey of agricultural output in China.

The sampling method is as follows: firstly draw counties in the province, then draw townships and villages in the county, then draw plots from the drawn townships and villages, and finally draw units from the drawn plots.