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science of collecting and classifying a group of facts according to their relative number and determining certain values that represent characteristics of the group. The most familiar statistical measure is the arithmetic meanmean,
in statistics, a type of average. The arithmetic mean of a group of numbers is found by dividing their sum by the number of members in the group; e.g., the sum of the seven numbers 4, 5, 6, 9, 13, 14, and 19 is 70 so their mean is 70 divided by 7, or 10.
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, which is an average value for a group of numerical observations. A second important statistic or statistical measure is the standard deviation, which is a measure of how much the individual observations are scattered about the mean. The chi-square test is a method of determining the odds for or against a given deviation from expected statistical distribution. Other statistics indicate other characteristics of the group of observations. In addition to the problem of computing certain statistics for a particular group of observations, there is the problem of sampling. This is an attempt to determine for what larger group (called the population) of individuals or characteristics the statistics for this particular group (called the sample) would be a representative figure and how representative a figure it would be for a given larger group. This second problem of sampling can be solved only by resorting to the theory of probabilityprobability,
in mathematics, assignment of a number as a measure of the "chance" that a given event will occur. There are certain important restrictions on such a probability measure.
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 and higher mathematics. In most applications of statistics to scientific and social research, insurance, and finance, the statistician is interested not only in the characteristics of the sample but also in those of some much larger population. Consequently, the theory of sampling is the most important part of statistical theory.


See J. F. Freund, Modern Elementary Statistics (1988); D. S. Moore and G. P. McCabe, Introduction to the Practice of Statistics (1989); D. H. Sanders, Statistics (1989).



(1) A social activity directed toward obtaining, processing, and analyzing information that describes the quantitative patterns in the multiform life of a society (its technical-economic, socioeconomic, and sociopolitical phenomena and culture), inseparably bound as they are to the qualitative content of social life. In this sense the concept of statistics coincides with the concept of statistical record-keeping, which is the leading type of socialist (national economic) record-keeping in a socialist society. Statistics is of determining importance since its ultimate function is to process and analyze all information of national economic significance, collected through bookkeeping accounts or operational records. The initial methodological principles for constructing the basic indexes are common to all types of record-keeping.

(2) A branch of the social sciences, together with its corresponding educational disciplines, which expounds the general questions of measuring and analyzing large-scale quantitative relationships and interrelationships.

In a narrower sense of the word, “statistics” denotes a set of data on some phenomenon or process—for example, election statistics. In the natural sciences the concept of statistics signifies the analysis of large-scale phenomena based on the methods of probability theory.

Statistics as we know it first appeared roughly at the time of the emergence of the state. There is evidence of elementary population and land censuses carried out several millennia ago. With the formation of centralized states, and especially in the age of capitalism, statistics gained a much broader application. Population censuses were conducted regularly. Elementary forms of statistical record-keeping emerged in other areas of society as well.

Statistics as a science appeared much later. Its sources lie in what was called political arithmetic, created in the late 17th century through the work of two Englishmen: W. Petty, who according to K. Marx was “to some extent the founder of statistics” (K. Marx and F. Engels, Soch., 2nd ed., vol. 23, p. 282), and J. Graunt, who first noticed the systematic patterns in population dynamics. At that time statistics had not yet separated itself from political economy and other socioeconomic disciplines. Another historical discipline that was a forerunner of modern statistics was the science of government: this took shape concurrently with political arithmetic in the works of the German scholar H. Conring and saw particular development in 18th century Germany and later in Russia. In the science of government, statistics was viewed as part of a whole that also included geography, ethnography, and jurisprudence. By the mid-19th century the Belgian statistician L. A. J. Quételet and his followers had proved the existence of regular patterns in statistical series. Credit goes to Quételet for the systematic application of mathematical methods in processing statistical data.

Statistics underwent intensive development in the second half of the 19th and early 20th centuries. This development was facilitated by various periodical censuses and surveys that gathered an abundance of material on each surveyed unit—such as an enterprise, a household, or an individual. State statistical agencies, and particularly those that carried out censuses, were being improved at the same time. A special scientific discipline took shape: mathematical statistics, a subdivision of mathematics.

Russian statistics made a major contribution to statistical theory and practice. The concept of comprehensive statistical description of a country was elaborated first by M. V. Lomonosov and V. N. Tatishchev and later by K. I. Arsen’ev. In The Sources and Use of Statistical Information, D. P. Zhuravskii demonstrated the role of grouping in statistics and proposed a broad system of indexes for the statistical study of society. P. L. Che-byshev and his students prepared a mathematical base for the application of scientifically sound sample surveys. In the second half of the 19th century, zemstvo (elected district administration) statistics played an important role in refining statistical methods. Zemstvo statistics was also responsible for the development of several types of branch statistics, and above all of agricultural statistics. Russian statisticians, and in particular A. A. Chuprov, devoted a great deal of attention to statistical theory and mathematical statistics.

Under state-monopoly capitalism the technical means and potential of statistics, especially in the economic sphere, continue to improve. This is fostered by the monopolies’ need for careful analysis of the current economic situation and by the state’s need to regulate certain economic ratios. At the same time, the contradictions of bourgeois statistics are becoming more acute— between the abundance and rich content of the statistical material collected, on the one hand, and the methods used to process it, on the other. A characteristic feature of bourgeois statistics is apologia, or the effort to conceal the social contradictions of capitalism and to paint the workingman’s life in glowing colors.

The emergence and development of Marxist-Leninist statistics marked a new stage in the history of this science. The classical works of Marxism-Leninism, and especially the writings of V. I. Lenin, reviewed the fundamental problems of statistical theory and methodology, set forth models for the use of statistical methods in economic analysis, and defined the basic objectives of statistics in a socialist society. The ideas of Marxist-Leninist statistics, which were first implemented in the USSR and later in other socialist countries, have had a continued and ever-growing influence on the progress of statistical science. Soviet statistics is organically bound up with national economic planning; it is nationwide in character and strictly centralized in principle. In a socialist society, statistics, as the main element in a single, uniform system of national economic record-keeping, is a crucial means of state control and planned management of the national economy.

The collection, processing, and analysis of statistical information for the entire country is carried out according to uniform principles and a common program and methodology by the state statistical agencies. These agencies are headed by the Central Statistical Board of the Council of Ministers of the USSR, which was established on the initiative of V. I. Lenin. Statistical data are printed in special statistical publications.

The primary objective of Soviet statistics is the collection and timely presentation to state agencies of valid, scientifically substantiated data showing the progress being made in state plans, the growth of the socialist economy and culture, the availability of material resources in the economy and their utilization, and the relative development of different sectors of the national economy. The Communist Party has posed the task of further refining statistics and of actively applying it to the analysis of large-scale economic problems, such as all-out intensification of social production, higher productive efficiency, stepped-up scientific and technological progress, and the advanced well-being of the Soviet people.

The technical base of modern statistics is a network of state statistical computer centers and information-processing and mechanical computer stations. The rapid development of cybernetics and the application of computer technology are increasingly affecting the organization of statistics and the methods of statistical analysis. The automated system of state statistics (ASGS) will not only enlarge the volume of statistical information and make its preparation and submission to state agencies more timely, but will also significantly bolster the cognitive functions of statistics, multiplying and deepening its analytical potentialities. The first phase of the ASGS went into operation during the ninth five-year plan (1971–75).

The theoretical and practical importance of statistics and its broad use in different areas of life and in many scientific disciplines follow from its special character as a science and as a method. According to Lenin, “Socioeconomic statistics [is] one of the most powerful means of acquiring social knowledge” (Poln. sobr. soch., 5th ed., vol. 19, p. 334). It is impossible to apprehend the qualitative laws of development of a phenomenon without analyzing it quantitatively. The specific character and strength of statistics lie in the very fact that it considers the quantitative relationships of objective reality as inseparably bound to the qualitative properties of phenomena and processes. Through statistics, analysis is more clearly seen as a unity of qualitative and quantitative aspects.

An important, though not the only, function of statistics is the precise description and measurement of social patterns. Statistical methodology makes it possible to examine an aggregate of factors, depict a process as a whole, and take account of developmental trends and the diversity of forms of phenomena—which Lenin valued especially. It also helps discover and analyze the causal relationships and laws of phenomena. Statistics deals with regularities which are characteristic of a mass of phenomena (objects) that differ among themselves in many individual traits. The law of large numbers, according to which random deviations from the basic line of development in a mass of phenomena cancel each other out, is very important in statistics.

To perform its functions, statistics has at its disposal such means of mass statistical observation as reporting and comprehensive or sample surveys; a system of indexes that comprehensively characterize a phenomenon, an object, or an aggregate as a whole (including a system of national economic indexes); summary, grouping, and combining tables that present the results of statistical groupings; generalizing indexes (averages and the like); and generalizing methods of analyzing national economic processes as a whole.

With its unique position among the sciences, statistics is organically bound to the scientific disciplines that study the basic patterns and qualitative characteristics within a particular range of phenomena. Soviet statistics on the one hand relies on the propositions of historical materialism and Marxist-Leninist political economy in analyzing statistical patterns; on the other hand, it deals with the quantitative aspect of phenomena and is closely related to mathematics.

Statistics today is not a single scientific discipline; it is a series of sectoral statistical fields and composite branches. The science classification system commonly used in the USSR distinguishes the following areas of statistics: a general theory of statistics, which sets forth general principles and methods; economic statistics, which studies the system of national economic indexes, the economy’s structure and proportions, and interrelations among the sectors and elements of social reproduction; and the various branch statistics—for example, industrial, agricultural, construction, transportation, communications, demographic, and labor statistics—which study the set of indexes and analyze the socioeconomic processes of the corresponding branches of the national economy or areas of society. A social statistics, in the narrow sense of the word, is taking shape: it studies a class of indexes that describe a way of life and various aspects of social relations.

Some major contributors to the development of the theory and practice of Soviet statistics have been V. S. Nemchinov, P. I. Popov, V. N. Starovskii, S. G. Strumilin, and B. S. Iastremskii.


Londonskaia konferentsiia Pervogo Internatsionala 17–23 sentiabria 1871 g. ǀProtokoly]. [Moscow] 1936.
Lenin, V. I. Razvitie kapitalizma v Rossii. Poln. sobr. soch., 5th ed., vol. 3.
Lenin, V. I. “K voprosu o nashei fabrichno-zavodskoi statistike.” Ibid., vol.4.
Lenin, V. I. “Kapitalisticheskii stroi sovremennogo zemledeliia.” Ibid., vol. 19.
Lenin, V. I. “Iazyk tsifr.” Ibid., vol. 23.
Lenin, V. I. “K voprosu o zadachakh zemskoi statistiki.” Ibid., vol. 24.
Lenin, V. I. “Novye dannye o zakonakh razvitiia kapitalizma v zemledelii.” Ibid.,vol. 27, fasc. 1.
Lenin, V. I. “Statistika i sotsiologiia.” Ibid., vol. 30.
Lenin, V. I. Ocherednye zadachi Sovetskoi vlasti. Ibid., vol. 36.
V. I. Lenin i sovremennaia statistika, vol. 1–3. Moscow, 1970–73.
Statisticheskiislovar’. Moscow, 1965.
Ptukha, M. Ocherkipo istorii statistiki XVII-XVIII vekov. [Moscow] 1945.
Ptukha, M. Ocherkipo istorii statistiki v SSSR, vol. 1. Moscow, 1955.
Chuprov, A. A. Ocherkipo teoriistatistiki. Moscow, 1959.
Iastremskii, B. Trudy po statistike. Moscow, 1937.
Boiarskii, A. Teoreticheskie issledovaniia po statistike. Moscow, 1974.
Riabushkin, T. V. Problemy ekonomicheskoi statistiki. Moscow, 1959.
Mills, F. Statisticheskie metody. Moscow, 1958. (Translated from English.)



A discipline dealing with methods of obtaining data, analyzing and summarizing it, and drawing inferences from data samples by the use of probability theory.


(statistics, mathematics)
The practice, study or result of the application of mathematical functions to collections of data in order to summarise or extrapolate that data.

The subject of statistics can be divided into descriptive statistics - describing data, and analytical statistics - drawing conclusions from data.
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