General population and sample

A set of homogeneous objects is often investigated with respect to some characteristic characterizing them, measured quantitatively or qualitatively.

For example, if there is a batch of parts, the quantity can be a quantitative feature in accordance with GOST, and quality - the standard of the part.

If necessary, their testing for compliance with standards is sometimes resorted to a continuous survey, but in practice this is extremely rare. For example, if the general population contains a large number of studied objects, it is practically impossible to conduct a continuous survey. In this case, a certain number of objects (elements) are selected from the whole population and examined. Thus, there is a general and selective aggregate.

General name the aggregate of all objects that are subject to examination or study. The general population, as a rule, contains a finite number of elements, but if it is too large, then in order to simplify the mathematical calculations it is allowed that the whole aggregate consists of an infinite number of objects.

A sample or a selective collection is a part of the selected elements from the whole collection. The sample can be repeated or repetitionless. In the first case, it is returned to the general population, in the second case, not. In practice, random sampling is often used.

The totality and sample should be related to each other by representativeness. To put it differently, in order to be able to confidently determine the characteristics of the entire population in terms of the characteristics of the sample, it is necessary that the sampling elements represent them as accurately as possible. In other words, the sample should be representative (representative).

The sample will be more or less representative if it is produced randomly from a very large number of the whole population. This can be stated on the basis of the so-called law of large numbers. In this case, all elements have an equal probability of getting into the sample.

There are different options for selection. All these methods can in principle be divided into two versions:

• Variant 1. Elements are selected when the general population is not divided into parts. To this variant it is possible to carry simple random repeated and repetitionless selection.
• Option 2. The general population is divided into parts and selected elements are selected. This includes typical, mechanical and serial selection.

A simple random selection is a selection in which the elements are extracted one by one from the whole collection in a random way.

Typical - a selection, in which the elements are selected not from the whole set, but from all of its "typical" parts.

Mechanical is a selection when the entire population is divided into a number of groups equal to the number of elements that should be in the sample, and accordingly one element is selected from each group. For example, if you want to select 25% of the parts made by the machine, then select every fourth detail, and if you want to select 4% of the parts, then select every twenty-fifth detail, and so on. At the same time, it must be said that sometimes mechanical selection may not provide sufficient representative sampling.

Serial is a selection in which elements are selected from the whole set of "series" subjected to continuous research, and not one at a time. For example, when parts are manufactured by a large number of machine-tools, a continuous survey is conducted only for the production of several machines. Serial selection is used if the test feature has insignificant variability in different series.

In order to reduce the error, mathematical and statistical methods of estimating the general population using a sample are used. And selective control can be either single-stage or multi-stage, which increases the reliability of the survey.