a statistical observation in which only a selected part, not all elements, of the totality under study (called the universe in this case) are researched.

The selected elements of the totality (the sample) will rep-resent the totality with acceptable precision if two conditions are met: the sample must be sufficiently large to manifest the regularities extant in the general totality and the elements of the sample must be selected objectively, independently of the will of the researcher so that each element has an equal chance of being selected or these chances will be known to the researcher. These conditions are established by the mathematical theory of sampling method, based on a series of the most important theorems of probability theory, which altogether form the so-called law of large numbers. Only if these conditions are observed is it objectively possible to evaluate the precision of the sample survey on the basis of the data selected. The precision of the survey is measured with the aid of the average error of selection, the magnitude of which is directly proportional to the degree of variation of the characteristics under study and inversely proportional to the size of the sample. It is possible to produce a sample survey more rapidly and less expensively than an all-around survey, and the results obtained are essentially equal in accuracy and not infrequently are superior, because a sample survey can be more thorough. In socioeconomic research, a basis for the sample is necessary for selection in most cases—that is, a list or enumeration of the units from which the sample will be taken. Local objects such as houses, populated areas, or regions may be conveniently selected from a map. Also, certain preliminary information on the nature of the totality under study is useful for correct calculation of the size of the sample. The representative quality of the sample is ensured not only by size but also by strict observation of scientifically established rules of selection, which guarantee its objectivity. The techniques of selection are extremely varied. In socioeconomic research, systematic (mechanical) selection is widespread—that is, the selection, using a fixed interval, of units from the list. A purely random selection is applied less frequently—that is, a selection in which units are chosen by lot, from a table of random numbers, or by some other analogous method. If preliminary information about the totality under study is available, then the totality is broken into more or less uniform and typical groups and a selection is made separately from each group, thereby obtaining a typical or stratified sample. Separate elements (for instance, persons) may be selected, as well as groups of such elements (for instance, families). In the latter case, it is called a cluster, or serial, selection. In large-scale studies the sample is usu-ally made in several steps—that is, the larger entities are selected first (for instance, populated areas) and then the smaller entities within them (for instance, families). In practice, various selection techniques are usually combined.

Sample surveying was widely practiced in prerevolutionary Russian zemstvo (local elected administration) statistics. Several methods, particularly the multiphase selection that V. I. Lenin esteemed very highly, have retained their significance to the present time. The Central Statistical Administration of the USSR regularly studies the budgets of about 62,000 families of workers, office workers, and collective farmers and also carries out one-time field studies in different areas of socioeconomic statistics. Part of the information in the 1970 All-Union Population Census was obtained by sampling. Scholarly institutions use sampling research widely, particularly in sociological research. An independent sphere of sample survey is under development—the quality control of industrial products.