See what “Statistical field theory” is in other dictionaries. General theory of statistics: subject and method

GENERAL THEORY OF STATISTICS

1.1. Subject, method, objectives and organization

Statistics is a science that studies the quantitative side of mass phenomena in inextricable connection with their qualitative side, the quantitative expression of the laws of social development.

Statistics as a science has five features.

First feature statistics is the study not of individual facts, but of mass socio-economic phenomena and processes, acting as a set of individual facts that have both individual characteristics and general characteristics. The problem of statistical research consists in obtaining general indicators and identifying patterns of social life in specific conditions of place and time, which manifest themselves only in a large mass of phenomena through overcoming the randomness inherent in individual elements.

Second feature statistics is that it studies primarily the quantitative side of social phenomena and processes, but unlike mathematics, in specific conditions of place and time, i.e. The subject of statistics is the size and quantitative relationships of socio-economic phenomena, the patterns of their connection and development. At the same time, the qualitative certainty of individual phenomena is usually determined by related sciences.

Third feature statistics is that it characterizes the structure, i.e. internal structure of mass phenomena (statistical set) using statistical indicators.

Fourth feature statistics is the study of changes in social phenomena in space and time. Changes in space (i.e., in statics) are revealed by analyzing the structure of a social phenomenon, and changes in time (i.e., in dynamics) are revealed by studying the level and structure of the phenomenon.

Fifth feature statistics is to identify cause-and-effect relationships of individual phenomena of social life.

Under statistical methodology is understood as a system of techniques, methods and methods aimed at studying quantitative patterns manifested in the structure, dynamics and interrelations of socio-economic phenomena.

1.2. Statistical observation

The full cycle of statistical research includes the following stages:

1) collection of primary information (method of statistical observation);

2) preliminary data processing (grouping method, graphical method);

3) calculation and interpretation of individual and summary indicators (level, structure and variation, relationships and dynamics);

4) modeling and forecasting the relationship and dynamics of the processes and phenomena under study.

Statistical observation is a systematic, systematic, scientifically based collection of data on the phenomena and processes of social life by recording their most important features in accordance with the observation program.

The statistical observation plan includes programmatic, methodological and organizational parts. The program and methodological part indicates: the purpose, objectives and program of observation, the object and unit of observation, a set of characteristics of the unit of observation and observation tools (instructions for conducting observation and a statistical form containing the program and results of observation). The organizational part indicates: place and time of observation; a list of institutions and organizations responsible for organizing and performing observations, training and placement of personnel; selection of methods and registration of information, list of preparatory activities, etc.

Statistical observations are classified according to the form, type and method of observation.

The most common forms of statistical observation are: reporting (of enterprises, organizations, institutions, etc.) and specially organized observations in order to obtain information not included in reporting (censuses, surveys, one-time records).

Types of observation are distinguished: by the time of observation (continuous, periodic and one-time) and by the completeness of coverage of units of the statistical population (continuous and non-continuous).

According to the methods of statistical observation, they are distinguished: direct, documentary observation and survey. In statistics, the following types of surveys are used: oral (expeditionary), self-registration (when the forms are filled out by the respondents themselves), correspondent, questionnaire and personal surveys, using modern computer technology.

The indicators used in economic-statistical analysis characterize certain categories and concepts, and the calculation of such indicators should be carried out through a theoretical analysis of the phenomenon being studied. Therefore, in each specific area of application of statistics, its own system of statistical indicators is developed.

1.3. Methods of continuous and selective observation of socio-economic phenomena and processes

The task continuous observation is to obtain information about all units of the population under study. Therefore, when conducting continuous observation, an important task is to formulate a list of signs to be examined. The quality and reliability of the survey results ultimately depends on this.

Until recently, Russian statistics relied primarily on continuous observation. However, this type of observation has serious disadvantages: the high cost of obtaining and processing the entire amount of information; high labor costs; insufficient efficiency of information, since it takes a lot of time to collect and process it. And finally, not a single continuous observation, as a rule, provides complete coverage of all units of the population without exception. A larger or smaller number of units necessarily remain unobserved both when conducting one-time surveys and when obtaining information through such a form of observation as reporting.

For example, when conducting a comprehensive statistical survey of small enterprises based on the results of work in 2000, blank forms (questionnaires) were received from 61% of enterprises to which questionnaires were sent. The reasons for non-response are summarized in Table. 1.

Table 1

The number and proportion of units not covered depend on many factors: the type of survey (by mail, by oral interview); reporting unit type; registrar qualifications; the content of the questions provided for in the observation program; time of day or year of the survey, etc.

A partial survey initially assumes that only a portion of the units in the population being studied are subject to survey. When conducting it, it is necessary to determine in advance what part of the population should be subjected to observation and how to select those units that should be surveyed.

One of the advantages of non-continuous observations is the ability to obtain information in a shorter time and with less resources than with continuous observation. This is due to a smaller volume of collected information, and therefore lower costs for its acquisition, verification, processing and analysis.

There are many types of incomplete observation. One of them - selective observation, in which characteristics are recorded in individual units of the population under study, selected using special methods, and the results obtained during the survey with a certain level of probability are extended to the entire original population.

The advantage of selective observation is ensured through:

1) saving financial resources spent on data collection and processing,

2) saving material and technical resources (stationery, office equipment, consumables, transport services, etc.),

3) saving labor resources involved at all stages of sample observation,

4) reducing the time spent both on obtaining primary information and on its subsequent processing until the publication of the final materials.

The main problem when conducting a sample study is how confidently one can judge the actual properties of the general population based on the properties of the selected objects. Therefore, any such judgment inevitably has a probabilistic nature, and the task comes down to ensuring the greatest possible probability of a correct judgment.

The population from which selection is made is called general. The selected data is sample population or sample. In order for a sample to fully and adequately represent the properties of the population, it must be representative or representative. The representativeness of the sample is ensured only if the data selection is objective.

There are two types of selective observation: repeated and non-repetitive sampling.

At repeated selection, the probability of each individual unit being included in the sample remains constant, because after selection, the selected unit is returned to the population and can be selected again - the “return ball scheme”.

At repeatable During selection, the selected unit does not come back, the probability of the remaining units getting into the sample changes all the time - the “irreturnable ball scheme”.

The following are distinguished: ways selection of units from the general population:

A) individual selection, when individual units are selected for the sample,

b) group selection, when the sample includes qualitatively homogeneous groups or series of studied units,

V) combined selection, which is a combination of the first two methods.

The following are possible methods selection of units to form a sample population:

1) random(unintentional) selection, when the sample population is selected by drawing lots or using a table of random numbers,

2) mechanical selection, when the sample population is determined from the general population divided into equal intervals (groups),

3) typical selection (stratified, stratified) with preliminary division of the general population into qualitatively homogeneous typical groups (not necessarily equal),

4) serial or cluster selection, when not individual units, but series are selected from the general population, and within each series included in the sample, all units without exception are examined.

1.4. Statistical groupings

One of the main and most common methods of processing and analyzing primary statistical information is grouping. The concept of statistical grouping in the broad sense of the word covers a whole range of statistical operations. First of all, these include combining individual cases recorded during observation into groups that are similar in one way or another, since the holistic characteristics of the population must be combined with the characteristics of its main parts, classes, etc. The results of the summary and grouping of statistical observation data are presented in the form of statistical distribution series And tables.

The significance of groupings lies in the fact that this method, firstly, provides systematization and generalization of observation results, and secondly, the grouping method is the basis for the use of other methods of statistical analysis of the main aspects and characteristic features of the phenomena being studied.

The purpose of statistical grouping is to divide population units into a number of groups for the calculation and analysis of generalizing group indicators, which make it possible to obtain an idea of the composition, structure and relationships of the object or phenomenon being studied.

Generalizing statistical indicators characterizing each selected group can be presented in the form of absolute, relative and average values.

In table 2 summarizes various types of statistical groupings, differing depending on the grouping task:

table 2

The basis of grouping is the grouping characteristics by which units of the population under study are assigned to certain groups. If the grouping is performed according to one characteristic, then it is considered simple, if according to two or more characteristics – then combinational(or combined).

Primary called a grouping formed on the basis of primary data collected in the process of statistical observation.

Secondary grouping is performed based on primary data, if there is a need to obtain a smaller number, but larger groups, or to bring data grouped by interval size into a comparable form for the purpose of their possible comparison.

The classification and characteristics of the grouping characteristics are presented in Table. 3.

The tasks of typological grouping, which usually involves the division of a heterogeneous population into qualitatively homogeneous groups, are closely related to two other grouping tasks: the study of the structure and structural shifts in the homogeneous population under study and the identification of the relationship of individual features of the phenomenon under study in it.

Examples of typological groupings include the grouping of economic objects by type of ownership, the division of the economically active population into employed and unemployed, and workers into those engaged primarily in physical and mental labor.

The methodology of typological groupings is determined by how clearly the qualitative differences in the phenomena being studied are manifested. For example, when grouping industries by economic

Table 3

Principle of classification	Types of signs	Characteristics
By content (essence)	Essential	Express the main content of the phenomena being studied
Minor	Important for the characteristics of the phenomena being studied, but not classified as significant
If possible, quantitative measurement	Quantitative, including: a) discrete (discontinuous) b) continuous	Reflect a property of a phenomenon that can be measured Expressed only as a whole number Expressed as both a whole and a fraction
Attributive (qualitative), including alternative	The characteristic cannot be measured quantitatively and is written in text form. Found only in two mutually exclusive options (either - or)

According to the purpose of products, industries producing means of production and industries producing consumer goods are distinguished; in the macrostructure of retail trade turnover, production and non-production goods are distinguished. In most cases, qualitative differences between phenomena do not appear so clearly. For example, distinguishing large, medium and small enterprises in industries is a rather methodologically complex problem.

1.5. Methods for processing and analyzing statistical information

In the process of statistical observation, data is obtained on the values of certain characteristics that characterize each unit of the population under study. To characterize the population as a whole or its parts, data on individual units of the population are summarized and, as a result, generalized indicators are obtained, which reflect the results of knowledge of the quantitative side of the phenomena being studied.

Statistic indicator called a generalizing quantitative and qualitative value that characterizes socio-economic phenomena and processes.

Individual values of a population represent characteristics, and a quantitative-qualitative characteristic of any property of a population (group) is a statistical indicator. For example, the average performance of a particular student is a sign, the average performance of university students is an indicator.

Summary indicators can be presented absolute, relative And average quantities that are widely used in planning and analyzing the activities of enterprises and firms, industries and the economy as a whole.

Absolute indicators are obtained by summing the primary data. They can be individual and general (total). Individual absolute values express the size of quantitative characteristics in individual units of the population being studied. General and group absolute values are the final and group quantitative characteristics of characteristics. Using the absolute value, the absolute dimensions of the phenomena being studied are characterized: volume, mass, area, length, etc. Absolute indicators are always named numbers (have units of measurement), which can be natural, conditionally natural (for comparing homogeneous, but different-quality products of the unit physical quantities are converted into conventional units using special coefficients) and cost (monetary) ones.

For comparison, comparison of absolute values with each other in time, space and other relationships, relative values are used, i.e. generalizing indicators expressing the quantitative relationship of two absolute values to each other.

Relative values can be the result of comparison:

- statistical indicators of the same name (with the past period - relative values of dynamics and plan targets; with a plan - relative values of plan implementation; parts and the whole or parts among themselves - relative values of structure and coordination, respectively; in space - relative values of visibility);

– different statistical indicators (relative intensity values).

1.5.1. Method of averages

average value is a generalized indicator expressing a typical, i.e. level characteristic of most traits. The method of averages allows you to replace a large number of varying values of a characteristic with one averaged value.

There are averages: power and structural.

Formulas for calculating power averages are presented in table. 4.

In table 4 the following designations are used: the value of the characteristic of the th unit of the population or the th variant of the characteristic for the weighted average; volume of the population; weight of the attribute variant; number of variants of the characteristic being averaged.

The use of unweighted (simple) and weighted averages depends on the repeatability of the feature option:

Table 4

View of the middle	Formula for calculating the average
Unweighted	Weighted
Arithmetic mean
Harmonic mean
Geometric mean
Mean square
Average cubic

– in the absence of such repetitions or in case of repetition only individual option limited number of times apply unweighted average;

- when repeated everyone or almost everyone option many times apply weighted average.

Calculation of average values is used when:

– assessing the characteristics of a typical level for a given population;

– comparison of typical levels for two or more populations;

– calculating the norm when establishing plan targets and contractual obligations.

In practice, the arithmetic mean is most often used. The harmonic mean is used in cases where the numerator is known, but the denominator of the original mean ratio is unknown. Basically, the geometric mean is used to average individual indicators over time. Power averages of the second and higher orders are used when calculating indicators of variation, correlation, structural changes, asymmetry and kurtosis.

Structural averages include two main characteristics of the variation series of a distribution – mode and median.

Fashion– this is the value of the attribute that is most often found in a given population, i.e. reflects the value of the attribute that is the most typical, predominant, dominant. With a large number of observations, a population can be characterized by two or more modal options.

Median- this is a variant of the characteristic being studied, which divides the ranked series of data into two equal parts: 50% of the units of the population under study will have characteristic values less than the median, and 50% will have characteristic values greater than the median.

When determining the median from ungrouped (primary) data, you first need to arrange them in ascending order (rank). Then you need to determine the “position” of the median or determine the number of the unit whose attribute value will correspond to the median:

where is the number of units in the population under study.

1.5.2. Variational analysis

Variation– this is the difference in individual values (changes) of characteristics within the population being studied. Variation indicators allow us to evaluate:

Dispersion of attribute values among units of a statistical population;

Stability of development of the processes under study over time;

The influence of a factor characteristic on changes in the performance characteristic;

Various types of risks (insurance, systematic, etc.).

There are absolute and relative indicators of variation. Absolute measures of variation include: range of variation, average linear deviation, dispersion and standard deviation. The ratios for calculating these indicators are summarized in table. 5.

Table 5

Indicators	Calculation formulas
for ungrouped data	for grouped data
Range of variation (oscillations)
Average linear deviation
Dispersion
Standard deviation

where: attribute value; and, accordingly, the maximum and minimum value of the attribute in the aggregate; arithmetic mean; volume of the population; weight of the attribute variant.

Determining the scope of variation is a necessary stage in grouping primary statistical information. This variation indicator has two significant drawbacks: a) it strongly depends on the maximum anomalous values of the trait and b) it does not take into account the “internal” variation between the boundaries determined by the maximum and minimum values. Therefore, it does not provide an exhaustive description of variation.

The indicator of average linear deviation gives a generalized characteristic of the degree of dispersion of a characteristic in the aggregate, however, it is less often used compared to dispersion and standard deviation, since when calculating it one has to make actions that are incorrect from a mathematical point of view and violate the laws of algebra.

The dispersion is presented in squared units in which the registered characteristic is measured, so the interpretation of this indicator is quite difficult. In this regard, the standard deviation indicator has been introduced, which is measured in the same units of measurement as the individual value of the attribute.

Relative indicators of variation are calculated as percentages (relative to the arithmetic mean or median of the series). The following relative measures of variation are used in statistics:

1) oscillation coefficient

shows the relative spread of extreme values of characteristics around the arithmetic mean;

2) relative linear deviation

characterizes the share of the average value of absolute deviations from the arithmetic mean;

3) the coefficient of variation

most often used, as it characterizes the degree of homogeneity of the population. The population is considered homogeneous if the coefficient of variation does not exceed 33% (for distributions close to normal).

1.5.3. Correlation analysis

The most important task of the general theory of statistics is to study objectively existing connections between phenomena. In the process of statistical research, cause-and-effect relationships between phenomena are clarified, which makes it possible to identify factors (signs) that have a significant impact on the variation of the phenomena and processes being studied.

In statistics, a distinction is made between functional connection and stochastic dependence. Functional is a relationship in which a certain value of a factor characteristic corresponds to one and only one value of the resultant characteristic. This connection is manifested in all cases of observation and for each specific unit of the population under study.

If a causal relationship does not appear in each individual case, but in general, on average over a large number of observations, then such a relationship is called stochastic. A special case of stochastic is correlation a relationship in which a change in the average value of a resultant characteristic is due to a change in factor characteristics.

When studying specific dependencies, some characteristics act as factors that determine changes in other characteristics. The signs of the first group are called factorial, and the signs that are the result of the influence of these factors are effective.

Statistics do not always require quantitative assessments of the relationship; often it is important to determine only its direction and nature, to identify the form of influence of some factors on others. One of the main methods for identifying the presence of a connection is correlational a method that aims to quantify the closeness of the relationship between two characteristics (in a pairwise relationship) and between the resultant and multiple factor characteristics (in a multifactorial relationship).

Correlation is a statistical relationship between random variables that do not have a strictly functional nature, in which a change in one of the random variables leads to a change in the mathematical expectation of the other.

In statistics, the following dependency options are distinguished:

1) pair correlation – a connection between two characteristics (resultative and factor or two factor);

2) partial correlation - the dependence between the resultant and one factor characteristics with a fixed value of other factor characteristics;

3) multiple correlation - the dependence of the resultant and two or more factor characteristics included in the study.

The main method for identifying the presence of a correlation is the method of analytical grouping and determining group averages. It consists in the fact that all units of the population are divided into groups according to the value of the factor characteristic and for each group the average value of the resulting characteristic is determined.

The lecture notes meet the requirements of the State educational standard of higher professional education. Accessibility and brevity of presentation allow you to quickly and easily obtain basic knowledge on the subject, prepare and successfully pass tests and exams. General issues of the theory of statistics, methods of groupings, relative and average values, indicators of variations, correlation and dynamic analysis, economic indices in relation to solving management problems in commercial activities in the market of goods and services, economic and mathematical methods in statistical research. For students of economic universities and colleges, as well as those who independently study this subject.

* * *

The given introductory fragment of the book General theory of statistics: lecture notes (N.V. Konik) provided by our book partner - the company liters.

This textbook contains a complete course of lectures on the general theory of statistics, compiled by professional economists. Using this lecture notes in preparation for passing the exam, students will be able to systematize and concretize the knowledge acquired in the process of studying this discipline in an extremely short time; focus your attention on basic concepts, their characteristics and features; formulate an approximate structure (plan) of answers to possible exam questions.

The publication is intended for students studying in the specialty “Statistics” and other economic specialties.

LECTURE No. 1. Statistics as a science

1. Subject and method of statistics as a social science

Statistics- an independent social science, which has its own subject and methods of research, which arose from the needs of social life. Statistics is a science that studies the quantitative side of all socio-economic phenomena. The term "statistics" comes from the Latin word "status", which means "position, order". For the first time it was used by the German scientist G. Achenwal (1719-1772). The main task of statistics is to mathematically correctly describe the collected information. Statistics can be called a special branch of mathematics, which describes one or another aspect of human life. Statistics uses a variety of mathematical methods and techniques so that a person can analyze a particular problem.

Statistics can provide invaluable assistance to any manager at any enterprise if you know how to use it correctly.

Today, the term “statistics” is used in three meanings:

1) a special branch of practical activity of people, aimed at collecting, processing and analyzing data that characterize the socio-economic development of the country, its regions, individual sectors of the economy or enterprises;

2) science that deals with the development of theoretical principles and methods used in statistical practice;

3) statistics - statistical data presented in the reports of enterprises, sectors of the economy, as well as data published in collections, various reference books, bulletins, etc.

Statistics object– phenomena and processes of the socio-economic life of society, in which the socio-economic relations of people are reflected and expressed.

The general theory of statistics is the methodological basis, the core of all branch statistics. It develops general principles and methods of statistical research of social phenomena and is the most general category of statistics.

The objectives of economic statistics are the development and analysis of synthetic indicators that reflect the state of the national economy, the interrelationships of industries, features of the location of productive forces, and the availability of material, labor and financial resources.

Social statistics develops a system of indicators to characterize the lifestyle of the population and various aspects of social relations.

Statistics– a social science that deals with the collection of information of a various nature, its organization, comparison, analysis and interpretation (explanation). It has the following distinctive features:

1) studies the quantitative side of social phenomena. This side of the phenomenon represents its magnitude, size, volume and has a numerical dimension;

2) explores the qualitative side of mass phenomena. The provided side of a phenomenon expresses its specificity, an internal feature that distinguishes it from other phenomena. The qualitative and quantitative aspects of a phenomenon always exist together and form one single whole.

All social phenomena and events occur in time and space, and in relation to any of them it is always possible to determine at what time it arose and where it develops. Thus, statistics studies phenomena in specific conditions of place and time.

The phenomena and processes of social life comprehended by statistics are in constant change and development. Based on the collection, processing and analysis of mass data on changes in the phenomena and processes being studied, a statistical pattern is discovered. Statistical patterns reveal the effects of social laws that determine the existence and development of socio-economic relations in society.

The subject of statistics is the study of social phenomena, dynamics and directions of their development. With the help of statistical indicators, statistics establishes the quantitative side of a social phenomenon, observes the patterns of transition from quantity to quality using the example of a given social phenomenon. Based on the observations provided, statistics analyzes the data obtained in specific conditions of place and time.

Statistics deals with the study of socio-economic phenomena and processes that are widespread in nature, and also studies the many factors that determine them.

To derive and confirm their theoretical laws, most social sciences use statistics. Conclusions formed from statistical studies are used in economics, history, sociology, political science and many other humanities. Statistics is also necessary for social sciences to confirm their theoretical basis, and its practical role is very great. Neither large enterprises nor serious industries, when developing a strategy for the economic and social development of an object, can do without analyzing statistical data. For this purpose, special analytical departments and services are organized at enterprises and industries, attracting specialists who have completed professional training in this discipline.

Statistics, like any other science, has a certain set of methods for studying its subject. Statistical methods are selected depending on the phenomenon being studied and the specific subject of study (relationship, pattern, or development).

Methods in statistics are formed in the aggregate from the developed and applied specific methods and techniques for studying social phenomena. These include observation, summary and grouping of data, calculation of generalizing indicators based on special methods (method of averages, indices, etc.). In this regard, there are three stages of working with statistical data:

1) collection is a mass scientifically organized observation through which primary information is obtained about individual facts (units) of the phenomenon being studied. This statistical accounting of a large number or all of the units included in the phenomenon being studied is the information base for statistical generalizations, for formulating conclusions about the phenomenon or process being studied;

2) grouping and summary. This data is understood as the distribution of a set of facts (units) into homogeneous groups and subgroups, the final count for each group and subgroup, and the presentation of the results obtained in the form of a statistical table;

3) processing and analysis. Statistical analysis concludes the stage of statistical research. It contains the processing of statistical data that was obtained during the summary, the interpretation of the results obtained in order to obtain objective conclusions about the state of the phenomenon being studied and the patterns of its development. In the process of statistical analysis, the structure, dynamics and interrelation of social phenomena and processes are studied.

The main stages of statistical analysis are:

1) approval of facts and establishment of their assessment;

2) identifying the characteristic features and causes of the phenomenon;

3) comparison of the phenomenon with normative, planned and other phenomena that are taken as the basis for comparison;

4) formulation of conclusions, forecasts, assumptions and hypotheses;

5) statistical testing of the put forward assumptions (hypotheses).

2. Theoretical foundations and basic concepts of statistics

For statistical methodology, the theoretical basis is a dialectical-materialistic understanding of the laws of the process of social development. As a result, statistics often uses categories such as quantity and quality, necessity and chance, regularity, causality, etc.

The main provisions of statistics are based on the laws of social and economic theory, since they are the ones who consider the patterns of development of social phenomena, determine their meaning, causes and consequences for the life of society. On the other hand, the laws of many social sciences are created on the basis of statistical indicators and patterns identified through statistical analysis, as a result of which we can say that the connection between statistics and other social sciences is endless and continuous. Statistics establishes the laws of social sciences, and they, in turn, correct the provisions of statistics.

The theoretical basis of statistics is also closely related to mathematics, since to measure, compare and analyze quantitative characteristics it is necessary to use mathematical indicators, laws and methods. A deep study of the dynamics of a phenomenon, its changes over time, as well as its relationship with other phenomena is impossible without the use of higher mathematics and mathematical analysis.

Very often, statistical research is based on a developed mathematical model of the phenomenon. Such a model theoretically reflects the quantitative relationships of the phenomenon being studied. Given its presence, the task of statistics is to numerically determine the parameters included in the models.

When assessing the financial condition of an enterprise, A. Altman’s scoring model is often used, where the bankruptcy level Z is calculated using the following formula:

Z = 1.2x 1 + 1.4x 2 + 3.3x 3 + 0.6x 4 + 10.0x 5,

where x 1 is the ratio of reverse capital to the total assets of the company;

x 2 – ratio of retained income to the amount of assets;

x 3 – ratio of operating income to total assets;

x 4 – the ratio of the market value of the company’s shares to the total amount of debt;

x 5 – the ratio of the amount of sales to the amount of assets.

According to A. Altman, at Z< 2,675 фирме угрожает банкротство, а при Z >2,675 The financial position of the company is beyond concern. To get this estimate, you need to substitute the unknowns x 1, x 2, x 3, x 4 and x 5 into the formula, which are certain indicators of the balance sheet lines.

Particularly widespread in statistical science are such areas of mathematics as probability theory and mathematical statistics. Statistics uses operations that are directly calculated using the rules of probability theory. This is a selective observation method. The main one of these rules is a series of theorems expressing the law of large numbers. The essence of this law is the disappearance in the summary indicator of the element of randomness with which individual characteristics are associated, as more and more of them are combined in it.

Mathematical statistics is also closely related to probability theory. The problems considered in it can be classified into three categories: distribution (structure of the population), connections (between characteristics), dynamics (change over time). Analysis of variation series is widely used; forecasting of the development of phenomena is carried out using extrapolations. Cause-and-effect relationships of phenomena and processes are introduced using correlation and regression analysis. Finally, statistical science owes its most important categories and concepts to mathematical statistics, such as aggregate, variation, characteristic, and pattern.

The statistical aggregate belongs to the main categories of statistics and is the object of statistical research, which means the systematic scientifically based collection of information about the socio-economic phenomena of public life and the analysis of the data obtained. In order to carry out statistical research, a scientifically reasoned information base is needed. Such an information base is a statistical aggregate - a set of socio-economic objects or phenomena of social life, united by a common connection, a qualitative basis, but differing from each other in certain characteristics (for example, a set of households, families, firms, etc.).

From the point of view of statistical methodology, a statistical population is a set of units that have such characteristics as homogeneity, mass, a certain integrity, the presence of variation, and the interdependence of the state of individual units.

Thus, a statistical population consists of individual units. An object, a person, a fact, a process can be a unit of a totality. The unit of the aggregate is the primary element and bearer of its basic characteristics. The element of the population from which the necessary data for statistical research is collected is called the unit of observation. The number of units in a population is called the volume of the population.

The statistical population can be the census population, enterprises, cities, and company employees. The choice of statistical aggregate and its units depends on the specific conditions and nature of the socio-economic phenomenon and process being studied.

The mass of the units of a collection is closely related to its completeness. Completeness is ensured by the coverage of units of the statistical population under study. For example, the researcher must make a conclusion about the development of banking. Therefore, he needs to collect information about all banks operating in a given region. Since any set has a rather complex nature, completeness should be understood as the coverage of many different features of the set that reliably and significantly describe the phenomenon being studied. If, in the process of monitoring banks, for example, financial results are not taken into account, then final conclusions about the development of the banking system cannot be made. In addition, completeness requires the study of the characteristics of population units over the longest possible periods. Quite complete data are, as a rule, massive and comprehensive.

The socio-economic phenomena studied in practice are very diverse, so it is difficult and sometimes impossible to cover all the phenomena. The researcher is forced to study only part of the statistical population, and draw conclusions based on the entire population. In such situations, the most important requirement is a reasonable selection of that part of the population for which the characteristics are studied. This part should reflect the main properties, phenomena and be typical. In reality, several populations can simultaneously interact in the phenomena and processes under study. In these situations, the object of study is found in such a way as to clearly identify the populations under study.

A sign of a unit of a population is its characteristic feature, a specific property, feature, quality that can be observed and measured. A population studied in time or space must be comparable. Consequently, the requirements of their comparability and uniformity are imposed on the characteristics of the units of the population. To do this, it is necessary to use, for example, uniform cost estimates. In order to qualitatively study a population, the most significant or interrelated features are studied. The number of features characterizing a unit of the population should not be excessive. This complicates data collection and processing of results. The characteristics of units of a statistical population must be combined so that they complement each other and are interdependent.

The requirement for homogeneity of a statistical population means choosing a criterion by which a particular unit belongs to the population being studied. For example, if the initiative of young voters is being studied, then it is necessary to set boundaries for the age of such voters in order to exclude people of the older generation. You can limit such a population to representatives of rural areas or, for example, students.

The presence of variation in units of a population means that their characteristics can receive various meanings or modifications in some units of a population. In this regard, such characteristics are called varying, and individual values or modifications are called variants

Signs are divided into attributive and quantitative. A characteristic is called attributive or qualitative if it is expressed by a semantic concept, for example, a person’s gender or his membership in a particular social group. Internally, they are divided into nominal and ordinal.

A characteristic is called quantitative if it is expressed as a number. Based on the nature of variation, quantitative characteristics are divided into discrete and continuous. An example of a discrete attribute is the number of people in a family. As a rule, variants of discrete characteristics are expressed in the form of integers. Continuous characteristics include, for example, age, salary, length of service, etc.

According to the method of measurement, characteristics are divided into primary (accounted) and secondary (calculated). Primary (accounted for) express the unit of the population as a whole, i.e. absolute values. Secondary (calculated) are not directly measured, but calculated (cost, productivity). Primary characteristics underlie the observation of a statistical population, and secondary ones are determined in the process of data processing and analysis and represent the ratio of primary characteristics.

In relation to the characterized object, signs are divided into direct and indirect. Direct attributes are properties directly inherent in the object that is being characterized (volume of production, age of a person). Indirect attributes are properties that are characteristic not of the object itself, but of other aggregates related to the object or included in it.

In relation to time, instantaneous and interval signs are distinguished. Instant signs characterize the object being studied at some point in time established by the statistical research plan. Interval characteristics characterize the results of processes. Their values can only occur over a time interval.

In addition to signs, the state of the object or statistical population under study is characterized by indicators. Indicators– one of the main concepts of statistics, which is a generalized quantitative assessment of socio-economic processes and phenomena. According to the target functions, statistical indicators are divided into accounting-evaluative and analytical. Accounting and evaluation indicators- this is a statistical characteristic of the magnitude of socio-economic phenomena in established conditions of place and time, i.e. they reflect the volume of distribution in space or the levels achieved at a certain time.

Analytical indicators are used to analyze data from the statistical population being studied and characterize the specific development of the phenomena under study. Relative, average values, indicators of variation and dynamics, and indicators of connection are used as analytical indicators in statistics. A set of statistical indicators reflecting the relationships that exist between phenomena forms a system of statistical indicators.

In general, indicators and signs fully characterize and comprehensively describe the statistical population, allowing the researcher to conduct a complete study of the phenomena and processes of life in human society, which is one of the goals of statistical science.

The central category of statistics is statistical regularity. By regularity we generally understand a detectable cause-and-effect relationship between phenomena, the sequence and repeatability of individual signs characterizing the phenomenon. In statistics, a pattern is understood as a quantitative pattern of changes in space and time of mass phenomena and processes of social life as a result of the action of objective laws. Consequently, a statistical pattern is characteristic not of individual units of the population, but of the entire population as a whole and is expressed only with a sufficiently large number of observations. Thus, a statistical pattern reveals itself as an average, social, mass pattern with the mutual cancellation of individual deviations of the values of characteristics in one direction or another.

So, the manifestation of a statistical pattern gives us the opportunity to present a general picture of the phenomenon, to study the trend of its development, excluding random, individual deviations.

3. Modern organization of statistics in the Russian Federation

Statistics plays an important role in managing the economic and social development of a country, since the accuracy of any management conclusion largely depends on the information on the basis of which it was made. Only accurate, reliable and correctly analyzed data should be taken into account at high levels of management.

The study of the economic and social development of the country, individual regions, industries, firms, and enterprises is carried out by bodies specially formed for this purpose that make up the statistical service. In the Russian Federation, the functions of the statistical service are performed by departmental statistics bodies and state statistics bodies.

The highest statistical management body is the State Committee on Statistics of the Russian Federation. It solves the main problems currently facing Russian statistics, provides a holistic methodological basis for accounting, consolidates and analyzes the information received, summarizes the data, and publishes the results of its activities.

The State Committee on Statistics of the Russian Federation (Goskomstat of Russia) was created in accordance with Decree of the President of the Russian Federation of December 6, 1999 No. 1600 “On the transformation of the Russian Statistical Agency into the State Committee of the Russian Federation on Statistics.” The State Committee of the Russian Federation on Statistics is a federal executive body that carries out intersectoral coordination and functional regulation in the field of state statistics.

The State Committee on Statistics of the Russian Federation performs the following functions:

1) collects, processes, protects and stores statistical information, maintains state and commercial secrets, and maintains the necessary confidentiality of data;

2) ensures the functioning of the unified state register of enterprises and organizations (USRPO) based on the registration of all economic entities on the territory of the Russian Federation with the assignment of identification codes to them, based on all-Russian classifiers of technical, economic and social information;

3) develops a scientifically based statistical methodology that meets the needs of society at the present stage, as well as international standards;

4) checks the compliance by all legal and other economic entities with the laws of the Russian Federation, decisions of the President of the Russian Federation, the Government of the Russian Federation on statistical issues;

5) issues resolutions and instructions on statistical issues that are binding on all legal and other business entities located on the territory of the Russian Federation.

The set of methods of statistical indicators, methods and forms for collecting and processing statistical data, adopted by the State Statistics Committee of Russia, are the official statistical standards of the Russian Federation.

The Goskomstat of Russia in its main activities is guided by federal statistical programs, which are formed taking into account the proposals of the federal executive and legislative authorities, government bodies of the constituent entities of the Russian Federation, scientific and other organizations and are approved by the Goskomstat of Russia in agreement with the Government of the Russian Federation.

The main tasks of the country's statistical authorities are to ensure transparency and accessibility of general (not individual) information, as well as guarantee the reliability, truthfulness and accuracy of the recorded data. In addition, the tasks of the State Statistics Committee of Russia are:

1) presentation of official statistical information to the President of the Russian Federation, the Federal Assembly of the Russian Federation, the Government of the Russian Federation, federal executive authorities, the public, as well as international organizations;

2) development of scientifically proven statistical methodology that meets the needs of society at the present stage, as well as international standards;

3) coordination of the statistical activities of federal executive authorities and executive authorities of the constituent entities of the Russian Federation, providing conditions for the application by these authorities of official statistical standards when conducting sectoral (departmental) statistical observations;

4) development and analysis of economic and statistical information, preparation of the necessary balance sheet calculations and national accounts;

5) guaranteeing complete and scientifically based statistical information;

6) ensuring all users have equal access to open statistical information by disseminating official reports on the socio-economic situation of the Russian Federation, constituent entities of the Russian Federation, industries and sectors of the economy, publishing statistical collections and other statistical materials. Due to the reform of the economy of the Russian Federation, the structure of statistical bodies has also changed. Local regional statistical registries were abolished and inter-district statistics departments were formed, which are representative offices of territorial statistical bodies. The organization of statistical bodies in Russia is currently at the stage of reform.

As noted above, statistical science in Russia is currently undergoing some changes. The main areas in which reforms should be carried out can be noted:

1) it is necessary to comply with the basic law of statistical accounting - openness and accessibility of information while maintaining the confidentiality of individual indicators (trade secrets);

2) it is necessary to reform the methodological and organizational foundations of statistics: changes in the general tasks and principles of economic management lead to changes in the theoretical principles of science;

3) the transition to market statistics creates the need to improve the system for collecting and processing information by introducing such forms of observation as qualifications, registers (registers), censuses, etc.;

4) it is necessary to change (improve) the methodology for calculating some statistical indicators that characterize the state of the economy of the Russian Federation, while international standards and foreign experience in maintaining statistical records must be taken into account, it is necessary to systematize all indicators and put them in order, corresponding to the issues and requirements of the time, taking into account the system of national accounts (SNA);

5) it is necessary to ensure the interrelation of statistical indicators characterizing the level of development of the country’s social life;

6) computerization trends must be taken into account. In the course of reforming statistical science, a unified information base (system) must be created, which will include the information bases of all statistical bodies located at a lower level of the hierarchical ladder of the organization of state statistics.

Thus, structural changes are still taking place in Russia, which affect all spheres of the country’s public life. Since statistics is directly related to almost all these areas, it was not spared by the reform process. Currently, a lot of work has been done to organize the work of statistical bodies, but it has not yet been completed, and much attention remains to be paid to improving this information institution, which is very significant for the state.

Along with state statistical services, there are departmental statistics, which are maintained in ministries, departments, enterprises, associations and firms in various sectors of the economy. Departmental statistics deals with the collection, processing and analysis of statistical information. This information is necessary for management to make management decisions and to plan the activities of an organization or government body. In small enterprises, such work is usually carried out either by the chief accountant or directly by the manager himself. At large enterprises that have an extensive regional structure or a large number of employees, entire departments or departments are engaged in the processing and analysis of statistical information. This work involves specialists in the field of statistics, mathematics, accounting and economic analysis, managers and technologists. Such a team, armed with modern computer technology, relying on the methodology proposed by the theory of statistics, and applying modern analysis techniques, helps build effective business development strategies, as well as effectively shape the activities of government bodies. It is impossible to manage complex social and economic systems without having complete, reliable and timely statistical information.

Thus, state and departmental statistics bodies are faced with a very significant task of theoretically substantiating the volume and composition of statistical information, corresponding to modern conditions of economic development, promoting rationalization in the accounting and statistics system and minimizing the costs of performing this function.

Statistics is a social science that studies the quantitative side of qualitatively defined mass socio-economic phenomena and processes, their structure and distribution, location in space, movement in time, identifies existing quantitative dependencies, trends and patterns, and in specific conditions of place and time.

Statistics include:

General theory of statistics

Economic statistics and its branches

Socio-demographic statistics and its branches.

Statistics is related to history, sociology, mathematics, and economics.

The object of study is society.

Translated from Latin, the word “status” means a certain state of affairs. The term “statistics” was first used by the German scientist G. Achenwal in 1749, in his book on government.

In the 18th century, the Petty and Ground school of political arithmetic emerged.

19th century - statistical and mathematical school Kettle, Pearson, Galton.

Russian descriptive school of the 18th century Kirilov, Lomonosov, Chulkov. Radishchev and Herzen influenced the development of statistical thought. Chebyshev and Markov made great contributions

Statistics is a tool of knowledge.

There are 4 concepts of statistics:

A set of educational disciplines that have certain specifics and study the quantitative aspects of mass phenomena and processes.

The branch of practical activity, statistical accounting which is carried out by ROSSTAT.

A set of digital information - statistical data published in collections and directories of enterprise reporting.

Statistical methods used to study socio-economic phenomena and processes.

Statistics Features:

1) statistical data are reported in quantitative terms;

2) statistical science is interested in conclusions drawn from the analysis of collected and processed numerical data;

3) the state of the phenomenon being studied at a certain stage of its development in specific conditions of place and time is reflected by statistical data.

Subject of statistics.

Statistics- social science, which studies the quantitative side of qualitatively defined mass socio-economic phenomena and processes, their structure and distribution, location in space, movement in time, identifies existing quantitative dependencies, trends and patterns, and in specific conditions of place and time.

Subject of statistics– dimensions and quantitative relationships of qualitatively defined socio-economic phenomena, patterns of their connection and development in specific conditions of place and time.

Statistics object- society

The object of statistical research in statistics is called a statistical population.

Statistical population- this is a set of units that have mass, homogeneity, a certain integrity, interdependence of the state of individual units and the presence of variation.

The subject of statistics is the study of social phenomena, dynamics and directions of their development. With the help of statistical indicators, statistics establishes the quantitative side of a social phenomenon, observes the patterns of transition from quantity to quality using the example of a given social phenomenon. Based on the observations provided, statistics analyzes the data obtained in specific conditions of place and time.

Statistics deals with the study of socio-economic phenomena and processes that are widespread in nature, and also studies the many factors that determine them.

To derive and confirm their theoretical laws, most social sciences use statistics.

Basic concepts of statistical methodology

Currently, it is difficult to name a science that does not study mass processes in a particular area. In the knowledge of any mass phenomena of a specific type (i.e., any science), the general provisions of statistics as a science are used: data on a variety of objects (elements) of the phenomenon being studied are accumulated, these results are described (summarized) using a set of specific characteristics (indicators) in compliance with requirements (conditions, rules) developed by statistics. When applied to different areas of phenomena, the statistical method takes into account their characteristics. The specific techniques with which statistics studies mass phenomena form a statistical methodology (or method of statistics).

Statistical methodology– a system of techniques, methods and methods aimed at studying quantitative patterns manifested in the structure, dynamics and interrelations of socio-economic phenomena.

Statistical research

Statistical information

three stages:

statistical observation;

Statistical observation

summary and grouping of observation results;

Summary

Grouping

The results of the statistical summary and grouping are presented in the form of statistical tables.

Statistical table

analysis of the obtained general indicators.

Statistical analysis is the final stage of statistical research. In its process, the structure, dynamics and relationships of social phenomena and processes are explored. The following main stages of analysis are distinguished:

Statement of facts and their assessment;

Establishing the characteristic features and causes of the phenomenon;

Comparison of a phenomenon with other phenomena;

Formulation of hypotheses, conclusions and assumptions;

Statistical testing of proposed hypotheses using special statistical indicators.

The concept of a statistical indicator

Statistical indicator

Statistical indicators are classified according to:

degree of population coverage:

Individual, characterize one object or one unit of a population.

Summary, characterize a group of a population or the entire population as a whole.

Volumetric indicators are obtained by adding the value of the characteristic of individual units of the population.
Estimated indicators are determined using various formulas.

expression form:

Absolute indicators- these indicators reflect the physical dimensions of the processes and phenomena studied by statistics, namely their mass, area, volume, extent, time characteristics, and can also represent the volume of the population, i.e. the number of its constituent units.

Absolute statistics are always named numbers.

Depending on the socio-economic essence of the phenomena under study, their

physical properties are distinguished:

natural units of measurement: tons, kilograms, square, cubic and simple meters, kilometers, miles, liters, barrels, pieces.

Cost units of measurement, allowing to give a monetary assessment of socio-economic objects and phenomena.

labor units of measurement, which makes it possible to take into account both the total labor costs at the enterprise and the labor intensity of individual operations of the technological process, include man-days and man-hours.

Relative indicators - represent the result of dividing one absolute indicator by another and express the relationship between the quantitative characteristics of socio-economic processes and phenomena.

current, or compared, and the denominator is comparison base.

Averages

Purpose and application of statistical indicators

Statistical indicator- represents a quantitative characteristic of socio-economic phenomena and processes in conditions of qualitative certainty.

Each statistical indicator has qualitative socio-economic content and an associated measurement methodology. A statistical indicator also has one or another statistical form (structure). An indicator can express the total number of units in a population, the total sum of the values of a quantitative characteristic of these units, the average value of a characteristic, the value of a given characteristic in relation to the value of another, etc.

The main function of specific statistical indicators and their systems is the cognitive information function. Without statistical information, it is impossible to know the patterns of natural and social mass phenomena, their prediction, and therefore regulation or direct management, be it at the level of an individual enterprise, farmer, city or region, at the state or interstate level.. The condition for statistical indicators to fulfill their information , cognitive function is their scientific justification and sufficiently accurate and reliable, as well as timely quantitative determination.

Types of statistical indicators.

Statistical indicator- represents a quantitative characteristic of socio-economic phenomena and processes in conditions of qualitative certainty.

Indicators used to study statistical practice and science are divided into groups according to the following criteria:

1) according to the essence of the phenomena being studied, they are volumetric and qualitative;

2) according to the degree of aggregation of phenomena - these are individual and generalizing;

3) depending on the nature of the phenomena being studied - interval and momentary;

4) depending on spatial definition, indicators are distinguished: federal, regional and local;

5) depending on the properties of specific objects and the form of expressions, statistical indicators are divided into relative, absolute and average.

A system of statistical indicators is formed by a set of interrelated indicators that have a single-level or multi-level structure. The system of statistical indicators is aimed at solving a specific problem.

Statistical indicators have interconnected quantitative and qualitative sides. The qualitative side of a statistical indicator is reflected in its content, regardless of the specific size of the attribute. The quantitative side of an indicator is its numerical value.

A number of functions that statistical indicators perform are primarily cognitive, managerial (control and organizational) and stimulating functions.

Statistical indicators in the cognitive function characterize the state and development of the phenomena under study, the direction and intensity of the development of processes occurring in society. Summary indicators– this is the basis for analyzing and forecasting the socio-economic development of individual areas, regions, regions and the country as a whole. The quantitative side of phenomena helps to analyze the qualitative side of an object and penetrates into its essence.

Three stages of statistical research.

Statistical research– the process of collecting, processing and analyzing statistical information.

Statistical information– primary statistical material about socio-economic phenomena, formed in the process of statistical observation, which is subject to systematization, analysis and generalization.

Statistical research consists of three stages:

1) statistical observation;

2) summary and grouping of observation results;

3) analysis of the obtained general indicators.

Statistical observation- mass, systematic, scientifically organized observation of the phenomena of social and economic life, which consists in recording selected characteristics of each unit of the population.

Statistical observation - primary statistical data is generated, or initial statistical information, which is the basis of statistical research. If an error is made during the collection of primary statistical data or the material turns out to be of poor quality, this will affect the correctness and reliability of both theoretical and practical conclusions;

Summary and grouping of data - at this stage, the population is divided according to differences and combined according to similarities; total indicators are calculated for groups and as a whole. Using the grouping method, the phenomena under study are divided into types, groups and subgroups, depending on their essential characteristics. The grouping method makes it possible to limit populations that are qualitatively homogeneous in significant respects, which serves as a prerequisite for the definition and application of generalizing indicators;

Summary- this is a complex of sequential operations to generalize specific individual facts that form a set in order to identify typical features and patterns inherent in the phenomenon being studied as a whole.

Grouping- division of units of the studied population into homogeneous groups according to certain characteristics that are essential for them.

Processing and analysis of received data, identifying patterns. At this stage, with the help of generalizing indicators, relative and average values are calculated, a summary assessment of the variation of characteristics is given, the dynamics of phenomena are characterized, indices and balance sheets are used, indicators are calculated that characterize the closeness of connections in changes in characteristics. For the purpose of the most rational and visual presentation of digital material, it is presented in the form of tables and graphs.

Structure of statistical science

The structure of statistical science includes:

general theory of statistics

General theory of statistics – is the science of the most general principles and methods of statistical research of mass socio-economic phenomena and processes. It defines the system of concepts and categories of statistical science, develops the scientific foundations of methods for collecting, summarizing and analyzing statistical data, and establishes the conditions for the application of these methods. Being the methodological basis of economic and socio-demographic statistics, as well as all industry statistics, the general theory of statistics creates a scientific foundation for the application of statistical methods of analysis to specific objects of research.

economic statistics

Economic statistics engages in a comprehensive study of economic phenomena and processes occurring at the macro level, i.e. in the country's economy as a whole and at the level of large regions. It reveals the essence, methods of calculation and analysis macroeconomic (synthetic) indicators characterizing the state of the national economy; scale, level, pace of its development; structure, proportions and relationships of industries; features of the location of productive forces; availability and composition of material, labor, financial resources, the achieved level of their use. Macroeconomic indicators include indicators such as gross national wealth(VNB), gross domestic product(GDP), gross profit of the economy(VPE) and gross national income(VND), gross national product(VNP), etc.

All macroeconomic indicators are determined based on systems of national accounts (SNA). This is a system of interconnected statistical indicators corresponding to the national market economy, built in the form of a certain set of accounts and balance sheets that characterize the results of economic activity, the structure of the economy and the most important relationships of its links. Being consistent with the standard methodology for constructing the SNA adopted by the UN and the European Union, the Russian SNA allows for in-depth analysis of the national economy in a variety of areas in accordance with international statistical standards.

socio-demographic statistics

Socio-demographic statistics forms and analyzes a system of indicators for a comprehensive description of the lifestyle of the population and various social aspects of society. It studies the size and composition of the population (by age, gender, nationality, etc.), the structure of families and households, income and expenses of the population, employment and unemployment, level and quality of life, consumption of material goods and services by the population, the state of healthcare, education, culture, crime rate, etc.

industry and special statistics. In sectoral statistics of large industries, sub-sectors are distinguished, for example, in industrial statistics - statistics of mechanical engineering, metallurgy, chemistry, etc., in population statistics - statistics of population size and composition, statistics of vital statistics and migration.

IN industry statisticians The essence and methods of calculating indicators characterizing the state and dynamics of development of the corresponding sector of the economy or social sphere are covered.

All industry statistics are formed on the basis of indicators of economic or socio-demographic statistics, using methods and techniques developed in the general theory of statistics. At the same time, the development of each sectoral statistics contributes to the improvement of statistical science as a whole.

Each of the components of statistical science has its own object of study, uses a specific system of indicators, develops rules and methods for their calculation and application in various areas of economic activity and the social sphere.

There is a close relationship and interdependence between statistical science and statistical practice. The theoretical principles of statistical science are applied in practice to solve specific statistical problems. In turn, science, using these practices, generalizes the experience of practical work, draws from it new ideas and provisions, and improves methods of conducting statistical research.

The concept of statistical observation, its goals .

The first stage of the study is statistical observation.

It represents mass, systematic, scientifically organized observation of the phenomena of social and economic life, consisting in the registration of selected characteristics in each unit of the population.

Statistical observation consists of recording selected characteristics of each unit of the population. It must be massive, systematic and carried out according to a developed program on a scientific basis.

There are stages of statistical observation:

Observation preparation;

conducting mass data collection;

Control and quality of information received

Observation object

Unit of observation

Reporting unit

Observation program

Organizational plan for observation- this is a document that records all the most important organizational activities, the implementation of which is necessary for the successful implementation of observation.

Observation Toolkit– a set of documents used during observation.

Forms of statistical observation

reporting,

special observation

registers.

Purpose of observation

Program and organization of statistical observation

Purpose of observation– obtaining reliable information to identify patterns of development of phenomena and processes.

Observation object– a set of social phenomena and processes that are subject to observation.

Unit of observation- an element of an object that is a carrier of characteristics subject to registration.

Reporting unit– this is the subject from which data about the observation unit comes.

Stages of statistical observation:

Observation preparation; the goals and objects of observation, signs to be registered are determined, documents for data collection are developed, methods and means of obtaining data are determined, personnel are selected and trained; drawing up a work schedule for the preparation and conduct of statistical observation; materials that will be used in statistical observation are processed

conducting mass data collection is the most important stage in conducting statistical observation, accumulating statistical information

Control and quality of information received. At this stage, the statistical observation data is monitored, conclusions and proposals are made regarding the statistical observation carried out.

Observation program- this is a list of indicators to be registered.

The statistical observation program must contain a list of characteristics that will characterize individual units of the population.

Program requirements: the signs must be significant; the program must include only those questions to which truthful, reliable answers can be given; questions must be precise and not ambiguous; availability of questions for verification; a certain sequence of questions; presence of open/closed questions.

There is an Organizational Observation Plan- this is a document that records all the most important organizational activities, the implementation of which is necessary for the successful implementation of observation.

Classification of statistical observation.12. Continuous and not continuous statistical observation. 13. Survey of the main body, selective and monographic observation. 14. Classification Art. observations by time. 15. Classification Art. observations based on sources of information.

Types of statistical observation are most often classified according to the following three criteria:

a) observation coverage of population units subject to statistical research;

Continuous (all units are examined completely)

Not continuous

Sample - based on collecting information on part of the population units and distributing the observation results to the entire population. The size of the sample depends on the nature of the phenomenon being studied. The sample population must represent all types of units that are present in the population.

Main array - data collection is carried out only for those units of the population that make the main contribution to the characteristics of the phenomenon under study.

Monographic is a description of individual units of a population for their in-depth study, which cannot be so effective with mass observation. Monographic observation is carried out in order to identify development trends, to study and disseminate the best practices of farms or enterprises.

b) systematic observation;

Continuous (register)

Intermittent

Periodic (as needed)

One-time (housing census)

c) the source of information on the basis of which the facts to be recorded during the observation process are established.

Direct (the registrars themselves establish the fact to be recorded by measuring, weighing, counting)

Documented (based on the use of accounting documents as a source of information)

Survey (information is obtained from the words of the respondent. Used to obtain information about phenomena and processes that are not directly observable)

Self-registration

Appearance method

Correspondent method

Questionnaire

D) by form:

Statistical reporting– this is a form of organizing statistical monitoring of the activities of enterprises and organizations, according to which state statistics bodies receive information in the form of reporting documents signed by persons responsible for the accuracy of the information.

Specially organized surveillance is the collection of information through censuses and one-time surveys.

Register is a form of continuous statistical observation of long-term processes that have a fixed beginning, a stage of development and a fixed end. This is a system that constantly monitors the state of observation units and evaluates the influence of various factors on the indicators being studied. Each unit in the register is characterized by a set of indicators. Some remain unchanged throughout the observation period, others, the frequency of which is unknown, are updated as they change.

Every observation is subject to error.

Observation errors– errors that appear during the observation process:

Registration errors– all errors that arise during continuous observation.

Random errors– these are errors made when filling out forms, a reservation in the answers, vagueness in the question and, accordingly, in the answer, etc.

Systematic errors:

Intentional errors (conscious) are obtained as a result of the fact that, when knowing the actual state (value) of the attribute, incorrect data are deliberately reported.

Unintentional are called errors caused by random reasons: for example, incorrect measuring instruments, inattention of recorders, etc.

Errors of representativeness - arise as a result of the fact that the composition of the part of the mass phenomenon selected for the survey does not fully reflect the features and essence of the entire population being studied.

Material quality control:

Logical – checking the consistency of the obtained data with each other or comparison with previous periods.

Arithmetic – arithmetic verification of final and calculated indicators.

Completeness control- this is a check of how completely the object is covered by observation, in other words, whether information has been collected about all observation units.

Reporting as the most important type of Art. observations. Classification of statistical reporting.

Statistical observation is carried out in 2 forms:

1) by providing reports;

2) by conducting specially organized statistics. observations.

Reporting is an organized form of statistical observation in which information is received in the form of mandatory reports within certain deadlines and in approved forms. Reporting as a form of statistical observation is based on primary accounting and is its generalization.

Primary accounting is a registration of various facts (events, processes, etc.) produced as they occur and, as a rule, on a primary document.

The management of statistical reporting and its organization are entrusted to the state statistics bodies. All forms of statistical reporting are approved by state statistics bodies. Submitting reports on unapproved forms is considered a violation of reporting discipline, for which heads of enterprises and departments are held accountable.

The list of reporting is a list of reporting forms indicating their most important details.

Reporting program- system of performance indicators of a trading enterprise.

General reporting- this is reporting containing the same data for a certain sector of the national economy and for enterprises (institutions, etc.) of the entire national economy.

IN specialized reporting contains specific indicators of individual industries, agriculture, etc.

Based on the period of time for which reporting is presented, and its duration, a distinction is made between current and annual reporting. If information is presented for the year, then such reporting is called annual. Reporting for all other periods within less than a year, respectively quarterly, monthly, weekly, etc., is called current.

According to the method of presentation, reporting is distinguished urgent, when all information is submitted by teletype, telegraph, and postal

In commercial practice reporting is subdivided on the:

1) nationwide - provided both to a higher organization and to the relevant state bodies. statistics;

2) intradepartmental - which is submitted only to higher trade authorities;

3) current - presented during the year;

4) annual - the most complete in terms of the composition of displayed indicators.

Grouping. Concept and application.

The most common method of processing and analyzing primary statistical information is grouping.

Grouping- division of units of the studied population into homogeneous groups according to certain characteristics that are essential for them.

Grouping functions:

identification of socio-economic types of phenomena;

study of the structure and structural changes occurring in socio-economic phenomena;

analysis of relationships between phenomena.

Types of grouping:

Typological grouping- this is the division of a qualitatively heterogeneous population into separate qualitatively homogeneous groups and the identification on this basis of economic types of phenomena.

Structural grouping- this is the identification of patterns of distribution of units of a homogeneous population according to varying values of the studied

sign.

Analytical grouping is a study of the relationships between varying characteristics within a homogeneous population. In this case, one characteristic will be effective, and the other (others) will be factorial. Factorial signs that influence the change in results are called. Effective characteristics that change under the influence of factors are called.

A type of structural grouping is distribution series.

Stages of building a group:

The choice of a grouping characteristic, i.e. the characteristic by which

Units of the population under study are combined into groups.

Determining the number of groups and the size of the interval

(n-number of groups, R-range of variation, a-size of the interval, N-number of units of the population)

R=x max -x min

n = 1 + 3.322 –log N

Establishing a list of indicators that should characterize

Creating a table layout based on grouping results

Calculation of absolute, average, relative indicators, filling out tables and drawing graphs.

By number of signsgroupings:

Simple (one attribute)

Combinative

Multidimensional

Secondary grouping- an operation to form new groups based on a previously carried out grouping.

Secondary grouping methods:

Changing Initial Intervals

Business regrouping

Classification –

Types of classification:

Types of groups.

Statistical groupings have the following purposes:

Identification of qualitatively homogeneous populations;

Study of population structure

Research existing dependencies

Each of these goals corresponds to a special type of grouping:

Typological is the division of a population into groups that are homogeneous in quality and conditions of development (solves the problem of identifying and characterizing socio-economic types). There are two ways to form typological groupings:

A method of sequential partitioning, which consists in the formation of groups, all objects of which have the same values of classification characteristics (first dividing the entire population according to one characteristic, then obtaining parts using another, etc.)

A method of multidimensional classification, when objects forming groups can have different values of classification characteristics (groups are formed based on the proximity of objects simultaneously according to a large number of characteristics, it has become widely used with the development of pattern recognition methods and the advent of computers)

Structural – used to study the structure of a population, characteristics of its structure and structural shifts. Structural groupings are built either on the basis of a previously conducted typological grouping, or on the basis of primary data

Analytical (factorial) - designed to establish the close relationship between interacting characteristics - factorial and resultant. It allows you to identify the presence and direction of a connection, as well as measure its closeness and strength. Therefore, a factor characteristic identified on the basis of an analysis of the phenomenon being studied is most often used as a grouping characteristic.

In cases where a qualitative characteristic has a large number of varieties, a classification is developed.

Classification – a special type of grouping; this is a stable nomenclature of classes and groups formed on the basis of the similarities and differences of the units of the object being studied. Classification is the distribution of phenomena and objects into certain groups, classes, categories.

Types of classification:

Product nomenclatures as a systematic list of objects and groups.

Classifiers are a classification where each attribute value is assigned a code, i.e. conventional digital designation.

Depending on the number of characteristics underlying the grouping, the following groups are distinguished:

simple - made according to one characteristic. Among the simple ones, distribution series stand out. A distribution series is a grouping in which one indicator is used to characterize groups (ordering those arranged by characteristic value) - the number of the group. Series constructed according to an attribute are called attribute distribution series. Distribution series constructed on a quantitative basis are called variation series.

Complex ones, which are divided into:

a combinational grouping based on two or more characteristics taken in interrelation, in combination. In this case, classification is carried out by sequential logical division of the population according to individual characteristics;
multidimensional groupings are carried out simultaneously according to several characteristics.

According to the relationships between the characteristics, the following are distinguished:

hierarchical groupings performed according to two or more characteristics, with the values of the second characteristic determined by the range of values of the first (for example, classification of industries by sub-sectors);

non-hierarchical groupings that are constructed when there is no strict dependence of the values of the second characteristic on the first.

According to the order in which information is processed, the groups are:

primary (compiled on the basis of primary data);

secondary, resulting from the regrouping of previously grouped material.

In accordance with the time criterion, they distinguish:

static groupings that characterize the population at a certain point in time or for a certain period;

dynamic - groupings showing the transitions of units from one group to another (as well as entry and exit from the aggregate).

Statistical tables

Statistical table– a table that contains a summary numerical characteristic of the population under study according to one or more essential characteristics, interconnected by the logic of economic analysis.

Types of headers:

Ostaf– a table without numbers and headings.

Layout– table with headings.

Subjects of statistical table- an object that is characterized by numbers. (A set, individual units of a set in the order of their list or territorial units grouped according to one or several characteristics, time periods, etc.)

INDepending on the structure of the subject, they are distinguishedstatistical tables

simple, in the subject of which a simple list of units of the population is given ( list) or only one of them, a unit identified according to a specific characteristic ( monographic);

complex, the subject of which contains groups of units of the aggregate one at a time ( group) or several ( combinational) quantitative or attributive characteristics.

Predicate of a statistical table– a system of indicators that characterize the object of study, i.e., the subject of the table. The predicate forms the headings of the graph and makes up their content.

According to the structural structure of the predicate, statistical tables are distinguished with:

simple predicate development- the indicator that determines it is obtained by simply summing the values for each characteristic separately, independently of each other.

complex predicate development involves dividing the characteristic that forms it into groups.

Matrix - a rectangular table of numerical information consisting of m-rows and n-columns.

Application of multidimensional grouping and data classification methods. Cluster analysis.

Grouping- division of units of the studied population into homogeneous groups according to certain characteristics that are essential for them.

By number of signsgroupings:

Simple (one attribute)

Complex (according to two or more characteristics)

Combinative

Multidimensional

Let's consider the use of multidimensional groupings. Since it is difficult to choose any one characteristic as the basis for a grouping. It is even more difficult to group according to several characteristics. The combination of two characteristics allows us to maintain the visibility of the table, but the combination of three or four characteristics gives a completely unsatisfactory result: even if we identify three categories for each of the grouping characteristics, we will get 9 or 12 subgroups. A uniform distribution of units among groups is impossible in principle. So we get groups that include 1-2 observations. Methods of multidimensional groupings make it possible to preserve the complexity of describing groups and at the same time overcome the disadvantages of combinational grouping. They are often called multidimensional classification methods.

These methods have become widespread through the use of (computers and application software packages). The purpose of these methods is data classification, in other words, grouping based on many characteristics. Such problems are widespread in the sciences of nature and society, in practical activities to control mass processes. For example, the identification of types of enterprises according to financial status and economic efficiency of activities is carried out on the basis of many characteristics: identification and study of types of people according to the degree of their suitability for a certain profession (professional suitability); diagnosis of diseases based on many objective signs (symptoms), etc.

The simplest version of multivariate classification is grouping based on multivariate averages.

A multidimensional average is the average value of several characteristics for one unit of the population.

A more reasonable method of multidimensional classification is cluster analysis. The name of the method itself comes from the same root as the word “class”, “classification”. The English word the cluster has the meaning: group, bunch, bush, i.e. associations of some homogeneous phenomena. In this context, it is close to the mathematical concept of “set”, and, like a set, a cluster can contain only one phenomenon, but, unlike a set, cannot be empty.

Each population unit in cluster analysis is considered as a point in a given feature space.

The concept of statistical graphs, the rules for their construction

Graphical method –

Schedule

When constructing a graphic image, a number of requirements must be observed. First of all, the graph must be quite visual, since the whole point of a graphic image is to clearly depict statistical indicators. In addition, the schedule must be expressive, intelligible and understandable. To fulfill the above requirements, each the schedule should include a number of basic elements:

Graphic image

Graph field

Spatial orientation

Scale guidelines

Explication of the graph (explanation)

Graphic image- these are geometric signs, i.e. a set of points, lines, figures with the help of which statistical indicators are depicted.

Graph field- this is the part of the plane where graphic images are located. The graph field has certain dimensions, which depend on its purpose. The most optimal ratio is 2 in width and 3 in height.

Spatial landmarks graphics are specified in the form of a system of coordinate grids. A coordinate system is necessary to place geometric signs in the graph field. Two coordinate systems are used: a rectangular coordinate system and a polar coordinate system.

Scale guidelines statistical graphics are determined by the scale and system of scales. The scale of a statistical graph is a measure of the conversion of a numerical value into a graphic one. A scale is a line whose individual points can be read as specific numbers. The scale is of great importance in graphics and includes three elements: a line (or scale carrier), a certain number of points marked with dashes, which are located on the scale carrier in a certain order, and a digital designation of numbers corresponding to individual marked points.

Explication of the graph– names of axes, graphics, symbols.

The most important part of charting is choosing the right composition., i.e.:

What data should be depicted from the many available,

What type of chart to use.

Charts are intended for:

Monitoring the reliability of information,

Studying the patterns of development of phenomena,

Identification of possible relationships between phenomena.

Classification of statistical graphs.

Modern science cannot be imagined without graphic methods. The use of graphs to present statistical indicators makes it possible to provide clarity and expressiveness, facilitate their perception, and in many cases helps to understand the essence of the phenomenon being studied, its patterns and features, to see the trends in its development, the relationship of indicators characterizing it.

Graphical method – This is a method of conventionally depicting statistical data using geometric shapes, lines, points and other images.

Schedule– a means of summarizing statistical data and identifying connections between phenomena.

Classification of graphs:

-according to the method of constructing a graphic image:

1) charts – depiction of statistical data using lines, shapes, etc.

2) statistical maps – image of a feature on a map

Cartogram - image of a feature by coloring or shading

Cardiogram – combination and diagrams

-according to geometric characteristics

1) linear

2) planar

3) volumetric

-by type of problems solved using graphs

1) comparison charts

2) structure diagrams

3) dynamic charts

Diagrams

linear - this is an image of data using lines in a rectangular coordinate system

columnar - image of data in the form of columns of the same width, but different in height in relation to the scale

tape (strip) - these are columns placed horizontally. They can be bilateral and directional.

square - the value of the attribute is proportional to the area of the square. Therefore, to construct them, the square root of the attribute value is extracted.

circular

sectoral - used to characterize the structure of a phenomenon. The circle is divided into sectors, the areas of which are proportional to the parts of the phenomenon. Absolute values are converted to percentages.

The Varzar sign is a rectangle whose length and width are two interrelated features. Then the area of the figure corresponds to the product of these features.

A Lorenz curve is a graph that shows the distribution of one characteristic among certain groups. The Lorenz curve is constructed using relative indicators (their accumulated values). The larger the area of the figure, the more uneven the distribution.

radial diagrams - used to visually depict a phenomenon over time. The circle is divided into 12 equal parts. Each ray corresponds to a specific month. On the radii, starting from the center, segments are laid out, depicting the value of the characteristic by month on a scale. The resulting figure characterizes the seasonal fluctuations of the phenomenon.

Graphs that characterize distribution series

polygon - broken line. Constructed for discrete distribution series

histogram - used for interval series. The columns should fit tightly to each other

cumulate - used for distribution series, for accumulated series

ogive - constructed in a similar way that the abscissa and ordinate axis are swapped

Classification and assignment of relative quantities.

Statistical indicator- represents a quantitative characteristic of socio-economic phenomena and processes in conditions of qualitative certainty.

Statistical indicators are distinguished by form:

Absolute

Relative

Relative values represent various coefficients or percentages.

Relative statistics- these are indicators that provide a numerical measure of the relationship between two comparable quantities.

When calculating a relative indicator, the absolute indicator found in the numerator of the resulting ratio is called current, or compared, and the denominator is comparison base.

The main condition for the correct calculation of relative values is the comparability of the compared values and the presence of real connections between the phenomena being studied.

Relative value = compared value / basis

According to the method of obtaining, relative quantities are always derivative (secondary) quantities.

They can be expressed: in coefficients, in percentages, in ppm, in prodecimille.

The following types of relative statistical quantities are distinguished:

Relative dynamics indicator (RDI) represents the ratio of the level of the process or phenomenon under study for a given period of time (as of a given point in time) and the level of the same process or phenomenon in the past:

OPD = Current level / Previous or baseline level

OPD = OPP * OPRP

OPD can be with a permanent base - basic, and variable – chain.

Relative Plan Performance (RPP) characterizes tension, i.e. how many times the planned production volume (or any financial result of the enterprise’s activity) will exceed the achieved level or what percentage of this level it will be.

OPP = level planned for (i+1)th period / level reached ini-th period

Relative plan implementation indicator (RPI) reflects the actual production volume as a percentage or coefficient compared to the planned level.

OPRP = level reached in (i+1)th period/level planned for (i+1)th period

Relative structure index (RSI) represents the relationship between the structural parts of the object being studied and their whole:

OPS = indicator characterizing part of the population / indicator for the entire population as a whole (*100%)

Relative Coordination Index (RCI) represents the ratio of one part of a population to another part of the same population:

OPC = indicator characterizingi-th part of the population / indicator characterizing the part of the population selected as a comparison base

Relative intensity index (RII) characterizes the degree of distribution of the process or phenomenon being studied and represents the ratio of the indicator under study to the size of its inherent environment:

OPI = indicator characterizing phenomenon A / indicator characterizing the environment of distribution of the phenomenonA

Type of OPI - Relative indicator of the level of economic development, characterizing production per capita and playing an important role in assessing the development of the state’s economy.

Relative comparison index (RCr) represents the ratio of the same absolute indicator characterizing different objects (enterprises, firms, districts, regions, countries, etc.)

OPSR = indicator characterizing object A / indicator characterizing object B

Rice. 1a The process of decay of sound energy

Basic provisions. In statistical theory, acoustic processes in a room are considered as a gradual decrease in the energy of waves repeatedly reflected by barriers in the room. This decay occurs after the sound source ceases. By idealizing, this process is considered to be continuous to a first approximation. Then it can be depicted on a linear scale as an exponential (Fig. 1, a), and on a semi-logarithmic scale as a straight line (Fig. 1, b). A prerequisite for such consideration is the fulfillment of two conditions: all directions of wave motion are equally probable, and the sound energy density e = E/V at each point in the space of the room is the same.

Rice. 1b. The process of decay of sound energy on a semi-logarithmic scale

Before analyzing the process of decay of sound energy in a room, it is necessary to explain why in architectural acoustics more attention is paid not to the stationary process (the process of steady-state oscillations), but to the transitional (non-stationary) one. The latter begins after the cessation of the sound source, consists of a gradual decline in sound due to loss of sound energy and is called echo, or reverberation.

Reverberation significantly affects the quality of both speech and musical sound. Excessive duration of reverberation leads to the fact that new syllables of speech sound against the background of previous fading syllables. Speech intelligibility deteriorates. With a short echo, the intelligibility of speech is quite satisfactory, but the peculiar “lifelessness”, “sterility” of such a sound is perceived as a deficiency, especially in artistic reading. The echo process when listening to music is even more important. Each musical phrase is a sequence of sound pulses. A prolonged echo disrupts the aesthetics of the perception of music, the more strongly the faster the tempo of performance, since the sounds “run into” each other. On the contrary, with a very short response or no response (when performed outdoors), the music sounds dry. The coherence of the sound is lost. Only with a certain time of response, quite specific for each style of performance, is the necessary coherence of sound formed, creating the best aesthetic result.

Let's consider the processes occurring in the room when the source I is sounding (Fig. 2). The first to arrive at the receiving point Pr, where the listener's ears or microphone are located, is direct sound along path 1, then along path 2 are sounds reflected from the surfaces closest to the source, then sounds along path 3 reflected from distant surfaces. Later, sounds arrive that have undergone double reflections on path 4, etc. The number of reflections per unit time increases in proportion to the second power of time. The room is gradually filled with sound energy. After the source stops sounding, the echo process begins. In the same sequence as at the beginning of sound, relatively rare initial reflections arrive at the receiving point first. Further, the density of delayed pulses increases, and their energy gradually decreases (Fig. 3).

Statistical theory deals with precisely this, the second part of the echo, with an increasing density of impulses over time and a decreasing energy. Direct sound and initial relatively rare reflections are not taken into account by statistical theory.

Rice. 3. Structure of early reflections of the reverberation response

The method proposed by W. Sabin is based on a model of an ideal room in which the sound field after the cessation of the sound signal can be calculated based on a statistical consideration of the sound attenuation process. It is assumed that the amplitudes and phases of reflected sound waves are distributed chaotically, that is, in the wave motion there are no prevailing directions of flows and symmetry in the distribution of amplitudes. The accepted assumption allows us to assume that the average values of sound energy in different directions are the same, that is, the sound field is isotropic, and the time-average sound energy density at any point in the room is also the same. This sound field is called diffuse. Its consideration made it possible to neglect interference phenomena and apply energy summation in calculations. This approach is similar to that used in the kinetic theory of gases and is based on the mathematical theory of probability. L. Brekhovskikh showed that for rooms whose linear dimensions are large compared to the wavelength, fairly satisfactory results are obtained.

Using the methods of mathematical statistics in a diffuse field, the average path length of a sound beam between two reflections is determined. For a room in the shape of a rectangular parallelepiped with linear dimensions close to the "golden ratio" (length relates to width and height as 2: 20.5: 1, according to another definition 5: 3: 2), the statistically determined mean free path is sound beam

where V is the volume of the room, S is the total area of all bounding surfaces (floor, ceiling, walls).

Subsequently, it was found that the obtained dependence is approximately preserved both for rooms whose linear dimensions deviate from the “golden section” and for rooms of more complex shape.

With each reflection, part of the incident energy is absorbed by obstacles and converted into heat. W. Sabin called the process of gradual decrease in the density of sound energy reverberation (reverberation in translation means “reflection”, “echo”). In Germany, the word Nachhall is used to denote this process, translated into Russian as “echo”, “echo”, “response”. The term “echo” was previously found in Russian technical literature.

The duration of the reverberation process - reverberation time - was considered to be the period during which the sound energy density decreases by 106 times, the sound pressure by 103, and the sound pressure level by 60 dB.

There are no direct explanations for the reasons for choosing a level decline of 60 dB. Let's try to find reasonable reasons. Fortissimo orchestra corresponds to sound pressure levels of 90-100 dB, and pianissimo - 35-40 dB. Then the average levels will be 63-70 dB and the reverberation time accepted by definition (decline by 60 dB) will approximately correspond to the duration of the decrease in the average levels to the threshold of audibility. Perhaps this circumstance was the reason for choosing this definition of reverberation time.

Of course, all this is true in the absence of acoustic interference. With noise levels of, for example, 30-40 dB, which is typical for both a living room and a concert hall, a significant part of the echo will be masked by noise, and the audible echo will last less than half the reverberation time.

Calculation ratios. To experimentally determine the reverberation time, Sabin used the simplest devices: organ pipes as a sound source and a stopwatch. He found that the reverberation time T is directly proportional to the volume of the room V and inversely proportional to the product of the average absorption coefficient aср and the area of all barriers S:

Average absorption coefficient:

where a1, a2,... are absorption coefficients of various materials;

S = S1 + S2 + ... - total area of obstacles; n is the number of different obstacles.

From this expression we can conclude that the average absorption coefficient corresponds to a single material that could cover all surfaces of the room’s barriers while maintaining the overall sound absorption A = aсрS. A unit of absorption is considered to be 1 m2 of an open opening that completely absorbs all the energy incident on it (without taking into account diffraction). This unit was called sabin (Sb).

Based on measurements of the reverberation time in five different rooms in the shape of a rectangular parallelepiped and volumes from 96 to 1960 m3, W. Sabin took the value = 0.164 (this number is approximately equal to the well-remembered fraction 1/6). When theoretically deducing the formula for calculating the reverberation time, the value k = 0.161 was obtained, which is indicated in most textbooks. In order to harmonize the physical dimensions on the left and right sides of the formula, it was decided to give the k coefficient the dimension s/m.

It was later discovered that k is different for rooms of different shapes. The measured values of k are given in the table.

Room shape k

Cross-shaped in plan, with a domed ceiling 0.177

Close to the "golden ratio" 0.164

Trapezoidal in plan, theater type 0.160

Cubic 0.157

Very wide in plan, with a low ceiling 0.152

From the above examples it is clear that reverberation, although this does not follow from the structure of W. Sabin’s formula itself. The fact is that the average path length between two reflections lcr depends on the ratio of linear dimensions, therefore, the reverberation time T also depends.

The theoretical derivation of Sabin's formula is based on the assumption of a diffuse, uniform distribution of sound energy throughout the space of the room and the continuous absorption of energy by obstacles during the reverberation process.

This assumption gives a relatively small deviation of the calculated value of T from the measured one if the average absorption coefficient is small, and therefore the number of reflections is large enough to neglect the discreteness of this process.

In fact, sound energy is absorbed by barriers not continuously, but in jumps as the wave reaches a particular surface. Therefore, there will not be a completely uniform filling of the entire volume of the room with energy.

More precise studies of reverberation were carried out in 1929 by Schuster and Wetzmann, and in 1930 by Karl Eyring. Eyring's formula looks like:

Expanding the expression ln(1-a) into a series and leaving only the first term in it due to the smallness of a, we find that for small values of a, the Eyring formula turns into the Sabin formula. Really,

Let us explain the meaning of the minus sign in the denominator of the formula. The logarithm of numbers less than one has a negative value. The minus sign is introduced to eliminate the physical inconsistency - the negative value of T. The expression in the denominator is the equivalent of the total absorption A = acрS contained in Sabin's formula.

Comparing the Sabin and Eyring formulas, we come to the conclusion that the Sabin approximation gives an overestimated value of T. The discrepancy increases with increasing acр: acр 0.2 0.5 0.8

Overestimation of T, % 11 37 100

With the value acр = 1, a physically unrealistic result is obtained: T = V/6S, although in this case it should be T = 0.

The Sabin and Eyring formulas can be applied if the sound-absorbing materials are distributed over the surfaces enclosing the room evenly enough so that the concept of an average absorption coefficient can be used.

To optimize acoustic conditions in concert halls, acр = 0.19 is recommended. Therefore, it is quite acceptable to calculate the reverberation time in this case using Sabin’s formula.

When deriving the Sabin and Eyring formula, some assumptions were made that are rarely stated in the literature on acoustics. Sabin's formula was obtained under the assumption that waves fall on obstacles at any angle, and when deriving Eyring's formula, it was assumed that waves fall on obstacles at angles close to the normal. Therefore, strictly speaking, the values of the absorption coefficient determined in a diffuse field in a reverberation chamber should be substituted into the Sabin formula, and into the Eyring formula - the values of the absorption coefficient measured in a flat field at normal incidence, i.e. in the pipe.

If the distribution of total absorption is very uneven, the result calculated using the Eyring formula may turn out to be far from the measured one. Millington explained the reason for this discrepancy. Eyring believed that the number of reflections from different surfaces with areas S1, S2,... is the same. In fact, the larger the surface itself, the greater the probability of the number of reflections from a given surface. Based on these considerations, Millington derived another formula for calculating reverberation time:

where Si is the area of materials with absorption coefficients ai.

The disadvantage of Millington's formula is the following: the calculated value of the reverberation time is equal to zero if at least one element of the obstacle, no matter how small, has acр = 1. Apparently, some dubious assumption was made when deriving the formula. However, the paradoxical result can be easily avoided by accepting that no absorption coefficient is equal to unity.

Practice has shown that for rooms with small ASR (theater and concert halls, classrooms, etc.) all three formulas give equally satisfactory results. For rooms with average attenuation coefficients (for example, studios), the reverberation time values calculated using the Eyring formula are closer to the measured ones. If the materials have very different ai, and the materials themselves are distributed unevenly over the surfaces, the T values calculated using the Millington formula are closer to the measured ones. Using the above formulas, it is necessary to accept those a that were calculated using the same formulas when processing the experimental material obtained in the sound-measuring chamber.

Determination of absorption coefficient. The absorption coefficients of materials are determined by measurements in a “booming” (reverberation) chamber. Let us denote the volume of the chamber by V, and its reverberation time by T0. After introducing the material under study with an area SM into the chamber, the reverberation time decreases to TM. Then:

If the area of the object under study (for example, a table, chair, etc.) cannot be expressed in a certain number, find the absorption of the object

So, using the above formulas of Sabin and Eyring, they solve the inverse problem: determine a or A from the measured reverberation time.

General theory of statistics

Statistics . This word comes from the Latin words stato and status, meaning state, position and state of phenomena in the state, which is why statistics was translated as state science several hundred years ago. In the Middle Ages, the word statista (statistician) was applied to a person who had knowledge in the field of politics, an expert on different states and peoples. As a scientific discipline, the term “statistics” was introduced by the German scientist G. Achenwal in 1743 to denote the body of knowledge about the state. It was he who began teaching statistics at the University of Göttingen, where the so-called discrete (descriptive) school of statistics was founded.

In Renaissance Italy, knowledge of politics became widespread, forming a special discipline called ragione di stato. The word stato or statu corresponded to the concept of "state". A person skilled in politics, an expert in different states, was called a statista. Achenval introduced the word statistica, which denoted the amount of knowledge needed by politicians and merchants. This is how the formation of statistics began as a science of economic and administrative accounting.

At the same time, there was another scientific school of “political arithmetic” in England, founded by V. Petty and named after his famous book (1690). Political arithmetic seemed to him as a tool of social cognition not on the basis of ideas, but on the basis of collected real facts and the use of quantitative characteristics. All this was consistent with the ideas of natural science, which is based on observation, which is what we see in modern statistics.

As is known, V. Petit and the English school were the first to calculate national wealth and national income and apply the sampling method.

In fact, the statistics were based on these two schools. From discretive (descriptive) statistics she received a methodology for quantitative description, and from political arithmeticians - a statistical methodology for studying the quantitative characteristics of mass phenomena.

In one form or another, statistics is taught to students of all forms of education and almost all specialties. At the present stage, a third element has been added, which has made statistics a universal method. It is based on probability theory and mathematical statistics, which makes it quite different from nineteenth-century statistics.

In the history of Russian statistics, all known schools and directions existed. Tatishchev V.N. (1686 - 1750) and Lomonosov M.V. (1711 - 1765) representatives of the Russian descriptive school. Bernoulli D. (1700 - 1782) and Kraft L. (1743 - 1814) are typical political arithmetics. Russian mathematicians Chebyshev P.P. (1821 – 1894), Markov N.A. (1856 – 1922), Lyapunov A.M.

(1857 – 1919) contributed to world mathematical statistics. Comparing the years of life and work of Russian statisticians, we can conclude that it developed in Russia in parallel with global trends.

Currently, the term “statistics” is used in three meanings.

Firstly, substatistics is understood as a special branch of practical activity of people aimed at collecting, processing and analyzing data characterizing the socio-economic development of the country, its regions, sectors of the economy, and individual enterprises.

Secondly, statistics is the science that deals with the development of theoretical principles and methods used in statistical practice. There is a close relationship between statistical science and statistical practice.

Thirdly, statistics are considered statistical data presented in the reports of enterprises, organizations, sectors of the economy, as well as published in collections, reference books, periodicals, which represent the result of statistical work.

In the course of the historical development of statistical science, a number of independent statistical disciplines emerged within its composition; this is explained by the presence of a specific subject of research and a special system of statistical indicators to characterize it. The structure of statistical science can be represented as follows (Fig. 1)

Thus, in statistical science it is traditional to distinguish the following parts: general theory of statistics, economic statistics and its branches, social statistics and its branches, such as for example 1 - financial statistics, 2 - industrial statistics, 3 - agricultural statistics, 4 - statistics forestry, 4 - state budget statistics, 5 - price statistics, etc., can be detailed indefinitely, for example, industry can be divided into light and heavy, mining and manufacturing, and the like. In addition, all statistical sciences, and not only economic, but also natural sciences, have a common basis - mathematical statistics.

General theory of statistics develops general principles and methods of statistical research of processes and phenomena, the most general categories, signs, meters, statistical indicators, as well as the organization of collection, processing, analysis and presentation of information.

The task of economic statistics is the development and analysis of synthetic indicators that reflect the state of the national economy, the interrelationships of industries, features of the location of production forces, the availability of material, labor and financial resources, and the achieved level of their use.

Branches of economic statistics – At the same time, there is a tradition in Russian statistics, passed down from the Soviet school of statistics, which presupposes the presence of separate disciplines with their own subject - statistics of industry, agriculture, construction, transport, communications, labor, natural resources, environmental protection, etc. d.; their task – development and analysis of statistical indicators of development of relevant industries.

Social statistics forms a system of indicators to characterize the lifestyle of the population and various aspects of social relations. Her industry – statistics of population, politics, health care, science, education, law.

Industry statistics are formed on the basis of indicators of economic or social statistics, and both are based in turn on categories (indicators) and methods of analysis developed by the general theory of statistics.

In "General Theory of Statistics" the main categories and methods of statistical science, the nature of statistical aggregates, the cognitive properties of statistical indicators, the conditions for their application using modern computer technology are considered. With its help, a foundation is created for the assimilation and qualified application of statistical methodology for understanding the patterns of development of socio-economic phenomena in the conditions of the modern economy.

Abroad, as a rule, all statistical disciplines are combined into one course, which differ in different levels of complexity: “statistics 1” includes descriptive (discretionary) statistics and basic laws of distribution, as well as the fundamentals of the sampling method, “statistics 2” includes statistical inference (test statistical hypotheses and statistical evaluation, correlation - regression and variance analysis, time series analysis, “statistics 3” - multivariate statistical analysis.

Statistics are necessary for an economist, first of all, to justify decision-making, as well as, based on analysis, to refute erroneous decisions.

Statistical methodology is a set of general rules (principles) and special techniques and methods of statistical research. The general rules of statistical research are based on the provisions of socio-economic theory and the principle of the dialectical method of cognition. They form the theoretical basis of statistics . Based on a theoretical basis, statistics applies specific methods of numerical or quantitative illumination of a phenomenon , which find their expression in the four stages (stages) of statistical research :

1. Mass scientifically organized observation, with the help of which primary information is obtained about individual units (factors) of the phenomenon being studied.

2. Grouping and summary of material, which represents the division of the entire mass of cases (units) into homogeneous groups and subgroups, calculating the results for each group and subgroup and recording the results in the form of a statistical table.

3. Processing of statistical indicators obtained during the summary and analysis of the results to obtain substantiated conclusions about the state of the phenomenon being studied and the patterns of its development.

Presentation of the obtained analysis results in a user-friendly form based on various information media. E

The subject of statistics, as a science, is the study of the quantitative side of mass social phenomena in inextricable connection with their qualitative characteristics. From this definition, three main features of statistics can be identified:

1. the quantitative side of phenomena is explored;

2. mass processes and phenomena are studied;

3. a quantitative description of mass processes and phenomena is given based on the study of qualitative parameters.

Thus, we can say that statistics deals with the collection, processing, analysis and presentation of information, and the object of statistics is the statistical population.

Statistical population- this is a mass of units united by a single qualitative basis, but differing from each other in a number of varying (changing) characteristics . The concept of “variation” is widely known in various fields of knowledge, in living and scientific languages, and everywhere it means change or variability within certain limits or around a certain standard, for example, a variation on a theme in music, cooking food in soup, Varangians - people of different origins employed river and sea trade and (or) piracy, and finally the Old Slavonic word - varum, which means a wavering (changeable) sea. Variation (change) of characteristics (usually quantitative) can occur in time, in space, in the mutual change of one characteristic from another. For example, the size of a worker’s wages depends on the amount of products he produces.

In the state standard, in the programs of most economic universities, statistics consists of two parts - the general theory of statistics and socio-economic statistics. Only after studying both parts, you will be able to:

1. gain theoretical knowledge and practical skills in the field of statistical methodology and, above all, in the organization of statistical observation.

2. use this knowledge in a wide variety of production and economic situations for the purpose of decision-making;

3. conduct a comprehensive economic and statistical analysis of indicators and thereby objectively evaluate the results of the activities of your enterprise, state or business.

4. interpret statistical data and organize planning and forecasting indicators.

The entire course consists of sections and is divided into topics and contains tasks and tests that will help you develop statistical thinking and ensure active assimilation of the material covered. Consolidation of the acquired theoretical knowledge on topics is carried out with the help of test tasks that you perform independently (to check the correctness of the solutions, answers are provided at the end of both parts of the textbook).

Statistics as a universal methodology for working with quantitative characteristics of objects of study is the basis of almost all specific economic disciplines and, first of all, econometrics.

In the process of writing a textbook, the author sometimes deliberately departs from the traditional manner of presenting the material, trying to give more lively examples and sometimes stating what can be expressed in words by a formula. Considering the current level of students’ training, when on the one hand, with alarming frequency, young people began to come across who in their second year have no idea how to get a percentage, and on the other hand, there are students who are almost professionally related to scientific creativity and who, for example, own a computer at the system level administrators, I would like to make at least part of the textbook accessible to the general reader without losing it, but the content is quite difficult to understand.

In addition, the textbook also has a practical orientation.