Main categories of statistics. Based on these data, make

Kamchatka State Technical University Department of Economics and Management R.A. Kildeeva PRACTICUM IN STATISTICS Methodological manual for students of economic specialties of full-time and part-time forms of study Petropavlovsk-Kamchatsky 2005 UDC 311 (075.8) BBK 60.6 K51 Reviewer Yu.S. Morozova, Candidate of Economic Sciences, Associate Professor of the Department of Management of Kamchat State Technical University Kildeeva R.A. K51 Workshop on statistics. Methodological manual for students of economic specialties in full-time and part-time forms of study. – Petropavlovsk-Kamchatsky: KamchatSTU, 2005. – 240 p. The statistics workshop was compiled in accordance with the requirements of the state educational standard for higher professional education and the standard curriculum for the discipline “Statistics”. Recommended for publication by decision of the educational and methodological council of KamchatSTU (protocol No. 6 of March 18, 2005). UDC 311 (075.8) BBK 60.6 © KamchatSTU, 2005 © Kildeeva R.A., 2005 2 CHAPTER 1. STATISTICAL OBSERVATION Any statistical study, any knowledge of social life begins with the collection of information (data, facts) about the phenomena and processes being studied. Scientifically organized work to collect statistical information about the phenomena and processes of social life is called statistical observation. Statistical observation has a program and organizational plan and is carried out with the observation of a number of requirements, the most important of which are the reliability and completeness of information. Practical classes on this topic are conducted in order to help students studying the general theory of statistics course to master the main topics and develop practical skills for conducting statistical observation. For this purpose, it is envisaged to solve the following typical problems: 1.1. Statistical observation program Methodological instructions and solution to a typical problem Statistical observation should be carried out according to a strictly defined plan, including both programmatic and organizational issues. In terms of statistical observation, the main issue is the observation program. When compiling it, they proceed from the purpose and objectives of the study. The statistical observation program includes: determination of the object of observation and units of the population; developing a program for describing population units, establishing a list of characteristics by which the phenomenon is characterized, or, in other words, a list of issues on which information is collected; formulating program questions and suggesting a number of possible answers; the sequence of asking questions in the program. Based on the goals and objectives of the statistical study, it is necessary to test and consolidate knowledge on these issues by designing an observation program. Task 1. The task was set to study the performance of first-year students at the All-Union Correspondence Institute of Finance and Economics (VZFEI) and the factors influencing it based on the results of the winter examination session. 3 It is required to determine the object of observation, the unit of the population and draw up an observation program. So, let's define the object of statistical observation. It would seem that the question is simple, since the objects of observation are first-year students of the VZFEI. But this is not entirely true. Clarification needed. Firstly, not all students are subject to examination, but only those taking part in the winter examination session. VZFEI correspondence students are conventionally divided into two categories: “urban”, living in cities or suburbs where there are territorial divisions of the institute (territorial faculties, branches or educational and consulting centers), and “peripheral”, attached to these divisions and those living in the rest of the territory they serve. From this contingent, some of the students could not take part in the winter examination session due to illness, business trips and other valid reasons. These students are not subject to examination. This means that only those students who took part in the winter examination session are subject to examination. Secondly, since the task is set not only to assess academic performance based on the results of the winter examination session, but also to characterize academic performance factors, it is necessary to separate the object of the survey from the part of students who were accepted as a result of transfer from other institutions or were were admitted to the institute not in this academic year (they had academic leaves and were left for repeated studies), but took part in the winter session. This part of students is also not subject to examination. Consequently, the object of the study is the totality of first-year students of the VZFEI admission of the current year who participated in the winter examination session. Next, we define the unit of the population. We established that the object of the study is a group of first-year students at VZFEI. This means that the unit of this population is the individual student. Next, we move on to developing a statistical observation program and a list of characteristics that must be used to characterize each student. A properly designed statistical observation program ensures the success of the study. It includes the most essential features that meet the goal. It is important to establish not only the signs, but also clearly, clearly give her wording, suggest the expected answers. Program questions 4 are recorded in a statistical form (form, questionnaire, reporting form, etc.). The central feature in our example is the results of the session. To get information about them, we will ask each student the following question: what grades did he receive in each subject at the winter session? We get the answer to the question posed in verbal form: excellent. Fine. Satisfactory or in the form of underlining the appropriate prompt. Next, we will identify the characteristics-factors of academic performance. First of all, we will establish the characteristics that characterize a first-year student before he enters a university: the type of educational institution he graduated from (high school, technical school), whether he graduated from school with a gold medal, technical school - with honors (yes, no), average score of the certificate, the duration of the break in study after graduation (how many years did not study), the length of practical work before entering the institute (number of years, if less than one year, then months), whether the student works in the specialty chosen at the university or not. The listed features characterize theoretical training and opportunities to study at a university. Important signs - factors of academic performance are signs that characterize students' studies in the 1st semester. In the conditions of a correspondence university, first-year classes are for students living in cities and suburbs where there are territorial divisions of the university, i.e. urban and peripheral students pass differently. The former are engaged in evening training, attending classes two to three times a week; the latter are called in for an orientation session in the fall, and in the intersession period (at their request) receive written consultations. Therefore, we are interested in the attendance of students at the orientation session and the attendance of face-to-face classes by city students, as well as the timeliness of completing practical written assignments (coursework, tests and classroom work). When answering the question about the timeliness of completing practical written work in each subject, you should indicate: completed on time, completed one week late, two weeks late, more than two weeks late. In sociological surveys, it is necessary to include general and demographic characteristics: last name, initials of the student (for control purposes), gender (male, female), age (number of years completed), marital status (married, not married) ), nationality, presence of children (no, yes, if so, how many). 5 There are many other factors that influence students' performance. But the observation program cannot be expanded without limits. There are factors that are difficult to measure statistically (for example, a student’s ability to master educational material, efficiency, his time budget). It should be remembered that in a statistical observation program it is necessary to pose only questions that do not allow for different interpretations and to which reliable answers can be obtained. The final part of the work on drawing up an observation program is determining the order of questions in the statistical form and developing its form. A mandatory element of the statistical form is the presence of a title and address part. The title part indicates the name of the statistical observation, the date and body that approved the form, the date of receipt of information, and the address part indicates the name or surname, first name, patronymic of the surveyed unit of the population and its address. In our example, in the address part, the name of the territorial division of the institute should be indicated (branch, faculty, educational and consulting center, for example Oryol UKP). When developing a form, we recommend taking the population census form given in Appendix 1 as a model. The order of questions in the form should be such that answers to previous questions logically control the correctness of answers to subsequent questions. Therefore, it is better to start with general and demographic data: last name, first name, patronymic. Gender, age, marital status, presence of children, nationality. This sequence of questions allows you to control the answers to them. Next, we should move on to questions characterizing a first-year student before entering college, the question of the type of educational institution he graduated from (high school, technical school), the time of graduation (year of graduation), the length of practical work (number of years, months ), about work in the specialty or not. Questions about the time of graduation from an educational institution, about work experience (if work and study were not combined) are checked using age data. Then it is necessary to ask questions about the results of admission tests (number of points on the certificate, diploma, number of points on entrance exams), studies in the 1st semester, results of the winter examination session. 6 Once the order has been established, carefully worded questions are arranged so that there is enough room for an answer, as well as for possible corrections. It is recommended to leave space for encryption on the form. Tasks 1.1. Determine the object of observation, the unit of the population and develop a statistical observation program to study the performance of students: 1) first year correspondence institute based on the results of the spring examination session; 2) second year at a correspondence institute due to the time spent on independent preparation. 1.2. Determine the object of observation, the unit of population, and develop a statistical observation program to study the relationship between the results of state exams and the current performance of full-time and part-time students. 2. Name the form of answering the questions on the population census questionnaire (Appendix D1). Present the classification results in table. 1.1. Table 1.1. Number Response form Number of the question on the census form, which is answered in the appropriate form 1 Verbal 2 Numerical 3 Alternative 3. To improve the organization of work and rest, draw up a draft program for the statistical study of the time budget, highlighting three groups of costs designated time – working, non-working time and free time of the following population groups: 1) full-time student; 2) student of the correspondence faculty; 3) a worker at an industrial enterprise; 4) trade worker. 4. Determine the list of the most important issues (features) that characterize as a unit of the population: 1) an industrial enterprise; 2) agricultural enterprise; 3) trading enterprise; 4) communications company; 5) family; 6) an individual. 7 5. Develop a draft statistical survey plan and determine the purpose of observation, the object of observation, the unit of the population, draw up an observation program, a form and instructions for it, design layouts of statistical tables intended to characterize the results of the survey: 1) industrial census enterprises; 2) agricultural census; 3) trade census; 4) school census. 1.2. Organization of statistical observation Methodological instructions and solution of a typical problem Organizational issues of statistical observation include: determining the unit of observation, establishing the time and timing of its implementation, determining the forms and types of observation, as well as methods of recording facts. Task 2. Using the data from standard task 1, we will solve organizational issues of statistical observation. The unit of observation from which statistical information will be obtained when examining the factors of academic performance of first-year students at VZFEI will be the territorial division of the institute (branch, faculty, educational and consulting center). Statistical forms—information carriers—are questionnaires that must be filled out by methodologists of these departments. The observation period is January-February, since the winter session is held at different times for urban and peripheral students. Completion of questionnaires should be limited to a short period of time (eg ten days) after the end of the session. When choosing the observation time, the issue of the critical moment is decided. It is very important for one-time observations, such as a population census. In our example, we do not record the critical moment due to the different end times of the winter examination session and will limit ourselves to indicating that the questionnaires must be completed within ten days after the end of the session. General and demographic information, as well as information about graduation from school, technical school, entrance exams, attendance at classes and timely completion of written work can be recorded before the start of the examination session. 8 Next, we will determine the form of organization of statistical observation and its types. There are two ways to organize the collection of statistical information – reporting and specially organized observation. Types of observation are classified according to the completeness of coverage of population units - continuous and non-continuous (sample, main array, questionnaire, monographic); for recording facts in time - current (constant), periodic and one-time. The study of student performance factors is organized through specially organized observation and is designed as a continuous and one-time observation. However, this study can also be organized as a non-continuous observation, but in this case it must be selective, so further issues must be resolved about determining the number of units in the sample population, about selection methods, etc. Then we move on to the question of methods of taking into account the facts of statistical observation. There are three methods of accounting for veils: direct accounting (by inspection, measurement, etc.), documentary accounting (based on documents mainly of an accounting nature) and interviewing persons surveyed (expedition method, self-registration, correspondent method) . For our research, we will use the documentary method of accounting. Methodists of territorial divisions fill out questionnaires on the basis of the following accounting documents: personal files of students (on general and demographic issues, type of educational institution and time of graduation, work experience, specialty), class attendance logs, books for recording the completion of assignments disciplines (on the timeliness of completing practical classes, tests and classroom work). Objectives 6. The study of indicators of the organization of work and rest is carried out in the order of partial observation. Determine the form, the best type of incomplete observation, the method of selection, time, place and critical moment according to the data in Chapter 5. 1. 7. In table. 1.2 provides a list of several statistical observations. Indicate the form and type of statistical observation in which each of them applies. 8. In the given list of statistical observations (task 7), highlight the non-continuous types of observations and indicate their types: sample, main array, questionnaire or monographic. 9 Table 1.2 Forms and types of observation By completeness Forms of organization By taking into account the coverage of single-statistical facts in nits-observation of time of aggregation Number p/p one-time Observation periodic not continuous statistical- special- continuous current reporting-organized 1 Report of an industrial enterprise on the implementation of the product sales plan 2 Census of industrial enterprises 3 Accounting for the use of working time 4 Accounting for cars on January 1 of each year 5 Population census 6 Civil registration (births) , deaths, marriages, divorces) 7 Livestock census as of January 1 annually 8 Checking the completeness of livestock records in 10% of households (10% control walks) 9 Quarterly accounting of goods balances in the trade and warehouse network 10

I.K. Abduljabarova

Workshop on Statistics

I.K. Abduljabarova 1

Statistics Workshop 1

Topic 1. subject and method of statistics 4

1.2. Statistical activities in the Russian Federation 11

1.3. Practice 13

Topic 2. Statistical observation 16

2.1. The concept of statistical observation 16

2.2. Basic organizational forms, types and methods of statistical observation 17

2.3. Program and methodological issues of statistical observation 22

2.4. Basic organizational issues and stages of statistical observation 26

2.5. Quality of statistical observation results and its control 28

2.6. Practice 30

Topic 3. Statistical summary and grouping 36

3.1. Summary objectives and contents 36

3.2. Types of statistical groupings 36

3.3. Principles of constructing statistical groupings and classifications 38

3.4. Comparability of statistical groupings. Secondary grouping 45

3.5. Practice 46

Topic 4. Graphical presentation of statistical information 51

4.1. The essence and significance of the graphical method in statistics 51

4.2. Basic requirements for a statistical graph and its elements 52

4.3. Main types of graphs and their classification 56

4.4. Comparison charts 57

4.5. Structure diagrams 61

4.6. Dynamics diagrams 64

4.7. Statistical maps 69

4.8. Practice 70

Topic 5. Absolute, relative and average statistical indicators 78

5.1. Absolute indicators 78

5.2. Relative indicators 79

5.3. Average 84

5.4. Practice 94

topic 6. Structural characteristics of distribution series and variation indicators 102

6.1. Structural characteristics of distribution series 102

6.2. Variation indices 111

6.3. Using variation indicators in relationship analysis 123

6.4. Practice 126

Topic 7. Statistical study of the relationship between socio-economic phenomena 135

7.1. Causality, regression, correlation 135

7.2. Paired regression based on the least squares method and the grouping method 138

7.3. Multiple (multivariate) regression 140

7.4. Self-correlation parametric methods for studying communication 143

7.5. Decision Making Based on Regression Equations 147

7.6. Methods for studying the relationship of qualitative characteristics 150

7.7. Rank connection coefficients 153

7.8. Practical task 156

Topic 8. Statistical study of dynamics
socio-economic phenomena 165

8.1. The concept of dynamics series and their types 165

8.2. Comparability of levels and closure of dynamic series 166

8.3. Analytical indicators of the dynamics series 169

8.4. Average indicators in dynamics series and methods of their calculation 171

8.5. Methods for analyzing the main tendency (trend) in time series 173

8.6. Methods for identifying the seasonal component 178

8.7. Elements of forecasting and interpolation 180

8.8. Practical task 183

9.1. General concepts about indexes 198

9.2. Average forms of summary indices 201

9.3. Calculation of composite indices for successive periods 204

9.5. Practical task 207

Tasks for independent work of students 213

Appendix 1 219

Forms of census forms of the All-Union Population Census of 1979, 1989 and the All-Russian Population Census of 2002 219

Appendix 2 224

200 largest banks in Russia in terms of equity capital (as of 01/01/09, million rubles) 224

Appendix 3 234

Dynamics of sales of agricultural products in city markets for 2003 234

Topic 1. subject and method of statistics

The term statistics has several meanings. Firstly, statistics is understood as the branch of practical activity for collecting, processing, analyzing and publishing statistical information both for the country as a whole and for its individual regions. Such activities, with certain differences in the methodology used, are carried out in all countries. In Russia, this work is carried out by the State Committee of the Russian Federation on Statistics.

Statistics is also often called the result of statistical activity itself, i.e. an array of statistical data or general indicators characterizing the state of mass phenomena and processes for a particular aggregate for a certain period. Consumers of statistical information are government agencies, scientific organizations, news agencies, analytical services of companies and banks, and individuals. In recent years, the importance of statistical information in marketing research has rapidly increased.

Statistics as a science began to take shape in the 7th century in response to the state’s need to have reliable statistical data on available resources for effective management, organization of production, trade, taxation, etc. Currently, statistics is a science that includes an extensive system of scientific disciplines that study the quantitative side of mass phenomena and processes in inextricable connection with their qualitative side.

The phenomena and processes studied by statistics are diverse. First of all, statistics studies everything related to the economic activities of society - the production and sale of industrial and agricultural products, the construction of new facilities and the reconstruction of existing fixed assets, the work of transport and communications, the formation and movement of financial flows. Statistical methods are widely used in the analysis of social processes and phenomena - employment and unemployment, income, studying public opinion, etc. Statistics play an important role in technology and production activities, for example, in organizing product quality control. Statistical methods are used in economic analysis, management, marketing, business planning, logistics, real estate valuation, crisis management and in other areas of scientific and practical activity.

Let's consider the sectoral structure of statistics as a science.

The theory of statistics (general theory of statistics) is a branch of statistical science that considers its general concepts, categories, principles and methods of collecting, processing and analyzing data. The theory of statistics develops general indicators and methods for studying the structure, relationships and dynamics of the processes and phenomena being studied. The use of these indicators and methods in certain areas of scientific and practical activity fills them with qualitative content, and in some cases gives them a certain specificity.

Economic (macroeconomic) statistics studies the quantitative patterns of phenomena and processes occurring in the economy, identifying the main proportions and trends of economic development at the macro level, i.e. at the level of a large region or country as a whole. Economic statistics studies both the process of reproduction of material goods and services, as well as its results, as well as their impact on the standard of living of the population. The main indicators of economic statistics include gross domestic product, gross regional product, such elements of national wealth as fixed assets, material and working capital, household property.

In accordance with the classification of economic sectors, statistical science and practice also distinguishes the sectoral level. Industry statisticians include:

industrial statistics;

agricultural statistics;

capital construction statistics;

statistics of services, transport and communications;

trade statistics.

Population statistics studies the numerical and national composition, as well as the age-sex structure of the population, its distribution and reproduction both in the country as a whole and in the context of territorial units. One of the main tasks of population statistics is the construction of short-term and long-term demographic forecasts.

Social statistics studies the social structure of the population, its standard of living and, in particular, income, as well as the level of education and culture, health and medical care, use of free time, public opinion, crime rates and other social aspects of society.

In order to get a general understanding of statistical methodology, it is necessary to consider the process of statistical research itself, which includes four main stages:

The process of statistical research begins with the stage of collecting primary statistical material, checking its completeness and reliability. For this purpose, methods of continuous and non-continuous statistical observation are used. The final results of the entire statistical study largely depend on the quality of the obtained initial statistical data.

At the second stage, preliminary data processing, calculation of group and general results, and calculation of some relative indicators are carried out. The main method used at this stage is the grouping method. As a result of its implementation, a transition is made from large arrays of statistical data to compact and convenient statistical tables for analysis.

The third stage is the calculation and interpretation of general statistical indicators. At this stage, indicators of the average level and variation, structure, relationships and dynamics of the processes and phenomena being studied are calculated. The results obtained are analyzed.

In the process of implementing the fourth stage, the relationships between socio-economic processes and phenomena are modeled, regression equations are constructed, as well as trend models reflecting the main trends in the dynamics of the indicators being studied.

The statistical techniques and methods used in the process of implementing all stages generally constitute the statistical methodology of the study.

1.1. Main categories of statistics

The most important category of statistical science is the category of attribute. It is the values ​​of various characteristics that are observed and recorded at the first stage of statistical research - the stage of statistical observation. A characteristic is an objective characteristic of a unit of a statistical population, a characteristic feature or property that can be defined or measured. The characteristics that characterize an industrial enterprise are revenue from sales of products, profit, the cost of fixed assets, number of personnel, etc. The characteristics of a person are age, gender, place of residence, profession, average monthly income, etc. For any objects and phenomena around us, it is possible to distinguish enough a large number of characteristics that are observed or could potentially be observed during a statistical study.

The possible value that a feature can take is called a variant. For example, there are only four options for the values ​​of the attribute “examination grade”: “2”, “3”, “4”, “5”. If we take into account the grades entered in the bachelor's or master's grade-book, then there are three such options left, since an unsatisfactory grade is not entered in the grade-book. An individual student may have ten, twenty, or more values ​​for the “examination grade” attribute in his record book, but there will still be three options, and perhaps two or one if, for example, the student or listener studies without Cs or Bs .

Signs are divided into quantitative and qualitative, and the latter, in turn, into alternative, attributive and ordinal.

Quantitative is a sign, individual variants of which have a numerical expression and reflect the size and scale of the object or phenomenon being studied. Quantitative characteristics, for example, include household income, living space, price of goods, and length of service. Quantitative features in statistics predominate over other types of features; they are the most informative and analytical; most of the diverse statistical tools are aimed at working with these features.

An alternative is a characteristic that has only two possible meanings. For example, a company's products may meet specifications or be defective, a person's gender may be male or female, and the population of a country or region is usually divided into urban and rural. An alternative sign can also have a numerical expression. Suppose, when surveying consumers, the question about income in the questionnaire suggested only two options: “up to 5 thousand rubles per month” and “5 thousand rubles per month or more.” In this case, the quantitative characteristic was converted into an alternative one.

Unlike an alternative attribute, an attribute has more than two options, which are expressed in the form of concepts or names. Attributive characteristics include area of ​​residence, type of product, specialty of the employee, color of the product. Such signs occur in various areas of research, but to a greater extent they are characteristic of the information that marketers, sociologists, and psychologists work with.

Ordinal characteristics differ from attributive ones in that they have several ranked ones, i.e. ordered in ascending or descending order, quality options. Examples of such characteristics are the level of education (primary, general secondary, etc.), level of qualifications, military rank, various types of ratings. Individual variants of an ordinal trait are difficult to compare quantitatively. For example, it is clear that higher education is better than specialized secondary education, but it cannot be said that it is 20% or 30% better. Driving category "E" is higher than driving category "B", but there are no quantitative proportions between them.

It should be noted that an ordinal attribute can have a numerical expression. Examples include such ordinal characteristics as the rank of a worker, the tariff rank of an employee, rating grades, and exam grades. A student who received a B did not necessarily demonstrate exactly twice as much knowledge as a student who received a D. A worker of the 6th category does not necessarily produce twice as much output and earn twice as much as a worker of the 3rd category. In the designation of variants of these features, numbers can be replaced by letters of the alphabet without any reduction in their information content.

The above examples show that the characteristics studied by statistics are usually subject to variation. Variation is fluctuation, a change in the value of a characteristic in a statistical population, i.e. acceptance by units of a population or their groups of different values ​​of a characteristic.

A statistical population is a set of objects or phenomena subject to statistical research, united by common characteristics, of which one or more characteristics do not vary. Statistics deals with the totality of industrial, agricultural, construction and trading enterprises, with the totality of commercial banks, with the total population of a country or its individual region. So, for example, all residents of Moscow can be considered as a statistical population, since one attribute - the city of residence - will not vary. According to other characteristics - gender, age, social status - the population will vary.

The individual component element of a statistical population, which is the carrier of the characteristics being studied, is called a unit of the population. For the industry, the unit of aggregate will be a separate enterprise, for the banking system - a separate bank. In some cases, different groups of units can be distinguished for the same population. For example, when studying the gender and age structure of the population, the unit is an individual, while when studying income, housing provision, and durable goods (TVs, refrigerators, etc.), the unit will be a household.

The total number of units that form a statistical population is called the volume of the population.

The volume of the population should be distinguished from the volume of the attribute, i.e. the total value of the attribute for all units of the population being studied. So, for example, the number of enterprises in an industry is the volume of the population, and the total output of all enterprises in the industry is the volume of the attribute. In some cases, the volume of the attribute has no real economic meaning, for example, it is difficult to interpret the total height of all students in one group. But to calculate individual statistical indicators, in particular averages, such summation is necessary.

One of the most important characteristics of a statistical population is its homogeneity. A homogeneous population is one whose units are close to each other in terms of the values ​​of characteristics that are essential for a given study, or they belong to the same type. Many methods and techniques of statistical research are applicable only to homogeneous populations.

An important role in statistical research is played by the law of large numbers - a general principle by virtue of which the quantitative patterns inherent in mass phenomena clearly manifest themselves only with a sufficiently large number of observations. Individual phenomena are more susceptible to the action of random and insignificant factors than the mass as a whole. With a large number of observations, random deviations in one direction or another from the general pattern of development cancel out each other. As a result of mutual cancellation of random deviations, generalizing indicators calculated for quantities of the same type become typical, reflecting the action of constant and significant factors in given conditions of place and time.

Statistical research, regardless of its scale and goals, always ends with the calculation and analysis of statistical indicators of various types and forms of expression.

A statistical indicator is a quantitative characteristic of socio-economic phenomena and processes in conditions of qualitative certainty. The qualitative certainty of the indicator lies in the fact that it is directly related to the internal content of the phenomenon or process being studied, its essence.

As a rule, the processes and phenomena studied by statistics are quite complex, and their essence cannot be reflected by one single indicator. In such cases, a system of statistical indicators is used.

A system of statistical indicators is a set of interrelated indicators that has a single-level or multi-level structure and is aimed at solving a specific statistical problem. For example, the essence of an industrial enterprise is the production of any product based on the effective interaction of means of production and labor resources. Consequently, for a complete economic characterization of the functioning of an enterprise, it is necessary to use a system that includes, first of all, indicators such as profit, profitability, number of industrial production personnel, labor productivity, capital-labor ratio, etc.

Unlike a characteristic, a statistical indicator is obtained by calculation. This can be a simple counting of population units, summing their characteristic values, comparing two or more values, as well as more complex calculations.

There is a distinction between a specific statistical indicator and a category indicator. A specific statistical indicator characterizes the size, magnitude of the phenomenon or process being studied in a given place and at a given time (by reference to place is meant the ratio of the indicator to any territory or object). So, if we name a specific value of the value of industrial production assets, then we must indicate which enterprise or industry it belongs to and at what point in time. However, in theoretical works and at the design stage of statistical observation (when constructing a system of statistical indicators, justifying the methodology for their calculation), they also operate with abstract indicators or category indicators.

The category indicator reflects the essence, general distinctive properties of specific statistical indicators of the same type without indicating the place, time and numerical value. For example, indicators of retail turnover of trade and public catering enterprises in Moscow and St. Petersburg in 2008 and 2010. differ in place, time and specific numerical values, but have the same essence (sale of goods through a retail trade network and a network of public catering establishments), which is reflected in the category indicator “Retail turnover of trade and public catering enterprises”.

All statistical indicators in terms of coverage of population units are divided into individual and summary, and according to the form of expression - into absolute, relative and average.

Individual indicators characterize a separate object or a separate unit of a population - an enterprise, a firm, a bank, a household, etc. An example of individual absolute indicators is the number of industrial production personnel of an enterprise, the turnover of a trading company, the total household income.

Based on the correlation of two individual absolute indicators characterizing the same object or unit, an individual relative indicator is obtained. In statistics, individual average indicators are also calculated, but only in a time dimension (the average annual number of industrial production personnel of an enterprise).

Aggregate indicators, in contrast to individual indicators, characterize a group of units representing part of a statistical aggregate or the entire aggregate as a whole. These indicators, in turn, are divided into volumetric and calculated.

Volumetric indicators are obtained by adding the characteristic values ​​of individual units of the population. The resulting value, called the volume of the attribute, can act as a volumetric absolute indicator (for example, the value of fixed assets of enterprises in the industry), or can be compared with another volumetric absolute value (for example, with the number of industrial production personnel of these enterprises) or the volume of the population (in a given example - with the number of enterprises). In the last two cases, volumetric relative and volumetric average indicators are obtained (in our examples - capital-labor ratio and average cost of fixed assets).

Estimated indicators, calculated using various formulas, are used to solve individual statistical problems of analysis - measuring variation, characterizing structural changes, assessing relationships, etc. They are also divided into absolute, relative or average. This group includes indices, coefficients of connection closeness, sampling errors and other indicators, discussed in detail in the relevant chapters.

The coverage of population units and the form of expression are the main, but not the only classification characteristics of statistical indicators. An important classification feature is also the time factor. Socio-economic processes and phenomena are reflected in statistical indicators either at a certain point in time, usually at a certain date, the beginning or end of a month, year (population, value of fixed assets, accounts receivable), or for a certain period - day, week, month, quarter, year (product production, number of marriages, amount of insurance payments). In the first case, the indicators are momentary, in the second - interval.

Depending on belonging to one or two objects of study, single-object and inter-object indicators are distinguished. If the former characterize only one object, then the latter are obtained as a result of comparing two values ​​​​related to different objects (the ratio of the population of the cities of Tula and Ryazan, the ratio of the number of preschool children and the number of places in preschool institutions, etc.). Interobjective indicators are expressed in the form of relative or average values.

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Problem 4
Natural gas consumption by the population of the region is characterized by the following data:
Table 10
Years 1992 1993 1994 1995 1996
Gas consumption, million m3 287.9 ​​396.3 475.6 502.2 506.3
To analyze the dynamics of gas consumption by the population, determine: a) absolute growth, growth and growth rates by year and by 1992, the absolute value of one percent of growth. Present the obtained indicators in the form of a table: b) average annual gas consumption; c) the average annual absolute increase in gas consumption and the average annual growth rate and increase in consumption. Describe the dynamics of gas consumption graphically and draw conclusions.
Solution to the problem:
a) Absolute growth (absolute rate of change in series levels over a certain period of time, expressed in million m3) by 1992 (basic absolute growth) will be determined by the formula:

The absolute increase compared to the previous year (chain absolute increase) is determined by the formula:

The growth rate (the intensity of change in the level of the series, expressed in %) by 1992 (basic growth rate) is determined by the formula:

The growth rate compared to the previous year (chain growth rate) is determined by the formula:

The growth rate (the relative growth rate of change in the level of the series, expressed in %) by 1992 (the basic growth rate) is determined by the formula:

The growth rate compared to the previous year (chain growth rate) is determined by the formula:

The absolute value of 1% growth is determined by the formula:

Let us determine the value of these values ​​for 1994:
AP (to 1993) = 475.6-396.3 = 79.3
AP (to 1992) = 475.6-287.9 ​​= 187.7
TR (to 1993) =475.6/396.3x100%=120%
TR (to 1992) = 475.6/287.9 ​​x 100% = 165%
TP (to 1993) = 79.3/396.3x100%=20%
TP (to 1992) = 187.7/287.9x100%=65%
A=79.3/20=3.965
Let us calculate the values ​​of the quantities and present them in the form of the following table 10:
Table 11.
Years Gas consumption, million m³ Absolute growth, million m³ per year Growth rate, % compared to Growth rate, % compared to Absolute value of 1% increase, million m³
by 1992 to the previous year to 1992 to the previous year to 1992 to previous year
1992 287,9
1993 396,3 108,4 108,4 138 138 38 38 2,853
1994 475,6 187,7 79,3 165 120 65 20 3,965
1995 502,2 214,3 26,6 174 106 74 6 4,433
1996 506.3 218.4 4.1 176 101 76 1 4.1b) Based on the data obtained, we determine the average annual gas consumption for the 5-year period from 1992 to 1996:

c) determine the average annual absolute increase in gas consumption:

Let's determine the average annual growth rate of gas consumption:

Let's determine the average annual growth rate:

Let us depict the dynamics of gas consumption graphically in Fig. 3:

Rice.
3. Dynamics of gas consumption for the period from 1992 to 1996.
Based on the results obtained, the following conclusions can be drawn: during the period from 1992 to 1996, gas consumption increased by 218.4 million m³ or by 76%. Gas consumption increased annually. The highest growth rate was in 1993, when the volume of gas consumed increased by 38%. The absolute value of one percent increase over the period from 1992 to 1996 increased from 2.853 to 4.433 million m³. In 1993, each percent increase resulted in an increase in gas consumption by 2.853 million m³.

Geniatulin V. N.

STATISTICS

(statistics theory)

Educational and methodological manual for students

economic specialties

Tolyatti 2016

SUBJECT OF STATISTICAL SCIENCE
AND ITS METHODOLOGY

Each science has significant specific features that distinguish it from other sciences and give it the right to independent existence as a special branch of knowledge. The main feature of any science lies in the subject of knowledge, in the principles and methods of its study, which together form its methodology.

The subject of statistical research is the mass phenomena of socio-economic life; it studies the quantitative side of these phenomena in inextricable connection with their qualitative content in specific conditions of place and time.

Phenomena and processes in the life of society are characterized by statistics using statistical indicators. Statistical indicators is a quantitative assessment of the properties of the phenomenon being studied. Statistics, using statistical indications, characterizes the dimensions of the phenomena being studied, their features, patterns of development and their interrelations. In this case, statistical indicators are divided into accounting-evaluative and analytical. Accounting and evaluation indicators reflect the volume or level of the phenomenon being studied; analytical indicators are used to characterize the development features of a phenomenon, its prevalence in space, the relationship of its parts, and the relationship with other phenomena. Average values, indicators of structure, variation, dynamics, degree of connection closeness, etc. are used as analytical indicators.

Currently, the main objectives of Russian statistics are:

Development of scientifically based statistical methodology that meets the needs of society at the present stage, as well as international standards;

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

Providing all users with equal access to open statistical information through the dissemination of official reports on the socio-economic situation of the Russian Federation, constituent entities of the Russian Federation, industries and sectors of the economy, publication of statistical collections and other materials.

The formation of an information system of statistical indicators for a comprehensive analysis of economic and social processes occurring in the country as a whole and in its regions is carried out on the basis of indicators contained in statistical state reporting (about 700 forms) and on the basis of sample statistical surveys.

At the regional level, additional statistical observations are carried out, reflecting the specifics of each region.

The statistical information system operating in Russia has a set of tools to provide the necessary diverse information to both government bodies, scientific institutions, and the media.

In order to promptly inform government bodies about certain important trends in economic development, express information is systematically released. Equipped with a brief analysis, it reaches the consumer a few hours after the completion of machine data processing.

The Government of the Russian Federation has approved a target program for reforming statistics. The goal of the program is to most fully meet the needs of the federal executive authorities of the constituent entities of the Russian Federation and all interested users of objective and up-to-date information on the socio-economic development of the Russian Federation, constituent entities of the Russian Federation, economic sectors, business entities, and the population.

Based on a theoretical basis, statistics applies specific methods of digital illumination of a phenomenon, which are expressed in three stages (stages) of statistical research:

1. Mass scientifically organized observation, with the help of which primary information is obtained about individual units (facts) 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 formatting the results obtained in the form of a statistical table. Groupings make it possible to identify units of different quality from all cases and to show the features of phenomena developing in different conditions. After grouping, they begin to generalize the observation data. This stage is called summary.

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. Conclusions are usually presented in text form and accompanied by graphs and tables.

Thus, a specific statistical method is based on a combination of analysis and synthesis. First, the parts (groups and subgroups) within the phenomenon under study are identified and studied separately, the significance or insignificance of the observed differences in the value of the attribute is assessed, and the causes are identified as a whole, in the totality of its aspects, trends and forms of development. All stages of statistical work are closely related to each other.

The structure of statistical science is presented in Fig. 1.

Fig.1. Structure of statistical science

Thus, the following parts are distinguished in statistical science: general theory of statistics, economic statistics and its branches, social statistics and its branches.

General theory of statistics develops general principles and methods of statistical research of social phenomena, the most general categories (indicators) of statistics.

The task 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.

Statistics of large industries can be divided into smaller industry statistics: for example, industrial statistics - into statistics of mechanical engineering, metallurgy, chemistry, etc.; agricultural statistics - into statistics of agriculture and livestock farming, etc.

Social statistics forms a system of indicators to characterize the lifestyle of the population and various aspects of social relations; its branches are statistics of population, politics, culture, health care, science, education, law, etc.

Branches of economic statistics- statistics of industry, agriculture, construction, transport, communications, labor, natural resources, environmental protection, etc.; their task is to develop and analyze statistical indicators of the development of relevant industries. Industry statistics are formed on the basis of indicators of economic or social statistics, and they are based, in turn, on categories (indicators) and methods of analysis developed by the general theory of statistics.

The general theory of statistics is the academic discipline from which the formation of the necessary knowledge begins for economists, managers, and enterprise leaders.

Solving typical problems

1. The following data is available on drivers’ wages for September:

To identify the dependence of drivers' wages on the level of qualifications and the percentage of fulfillment of production standards, carry out an analytical grouping. Develop intervals for grouping drivers by percentage of fulfillment of production standards yourself. Based on the completed grouping, build a combination table. Formulate a conclusion.

Solution

To solve the problem, it is necessary to group drivers according to two characteristics-factors: first - into groups according to qualifications, then within each group - into subgroups according to the percentage of fulfillment of production standards.

Based on the percentage of fulfillment of production standards, two subgroups are accepted:
1) drivers fulfilling the norm from 100 to 110%; 2) drivers who fulfill the norm by 110% and above.

The grouping results are presented in the supporting table. 1.1.

Based on the auxiliary table for each subgroup, the number and total of the attribute (total amount of wages) are determined; the results are presented in the form of a combination table (Table 1.2).

Table 1.1

Auxiliary table

Table 1.2

Dependence of drivers’ wages on classification and percentage of fulfillment of production standards

From the data in table. 1.2 it follows that with increasing qualifications of drivers and the percentage of fulfillment of production standards, wages increase. Thus, the wages of Class I drivers, who meet the production norm by 110% and above, are 32.5% higher than the wages of Class II drivers, who fulfill the norm from 100 to 110%.

Average values

The average value is a general indicator that characterizes the typical level of a varying quantitative characteristic per unit of a population under certain conditions of place and time.

The average value is always named; it has the same dimension as the characteristic of individual units of the population.

When using averages in practical work and scientific research, it is necessary to keep in mind that the average indicator hides the characteristics of various parts of the population being studied, therefore, general averages for a homogeneous population must be supplemented by group averages characterizing parts of the population.

In economic research and planning calculations, two categories of averages are used:

Power averages;

Structural averages.

The category of power means includes: arithmetic mean, harmonic mean, quadratic mean, geometric mean. The quantities for which the average is calculated are denoted by the letter x i. The average is denoted by . This method of designation indicates the origin of the average of specific quantities. The line at the top symbolizes the process of averaging individual values. Frequency - the repeatability of individual values ​​of a characteristic - is denoted by the letter f.

Formulas for averages can be obtained based on the power average, for which the defining function is the equation

,

.

In the future, when writing formulas for averages, the subscripts i, n will not be used, but it is understood that all products x i are summed . f i,.

Depending on the degree of 1c, various types of average values ​​are obtained; their formulas are presented in table. 2.1.

As can be seen from the data in table. 2.1, weighted averages take into account that individual variants of attribute values ​​have different numbers, therefore each variant is “weighted” by its frequency, i.e. multiply by it. Frequencies are then called statistical weights or simply average weights.

However, it must be taken into account that statistical weight is a broader concept than frequency. Any other values ​​may be used as weight. For example, when calculating the average working day for an enterprise, the only correct way is to weigh it by the number of person-days worked. The frequencies of individual options can be expressed not only in absolute values, but also in relative values ​​- frequencies.

The values ​​of power averages calculated on the basis of the same individual values ​​of a characteristic at different values ​​of power (k) are not the same. The higher the degree of k average, the greater the value of the average itself.

Table 2.1

Formulas for various types of power averages

Value, k	Name of the average	Average formula
simple	weighted
-1	Harmonic
	Geometric
	Arithmetic
	Quadratic

The arithmetic mean and the harmonic mean are the most common types of mean, which are widely used in planned calculations, in calculating the overall average of group means, as well as in identifying the relationship between characteristics using groupings. The choice of arithmetic mean and harmonic mean is determined by the nature of the information available to the researcher.

The mean square is used to calculate the standard deviation (a), which is an indicator of the variation of characteristics, as well as in technology (for example, in the construction of pipelines).

The geometric mean (simple) is used when calculating the average growth coefficient (rate) in the dynamics series.

Structural averages - mode and median - in contrast to power averages, which are largely an abstract characteristic of a population, act as specific values ​​that coincide with well-defined variants of the population. This makes them indispensable for solving a number of practical problems.

Mode is the value of a characteristic that occurs most frequently in the aggregate (in a statistical series).

The median is the value of the attribute that lies in the middle of the ranked series and divides this series into two equal parts.

Ranked series - a series arranged in ascending or descending order of attribute values.

To determine the median, first determine its place in the series using the formula

If a series consists of an even number of terms, then the arithmetic mean of their two median values ​​is conventionally taken as the median.

Fashion is used in expert assessments, in determining the most popular sizes of shoes and clothing, which is taken into account when planning their production. The median is used in statistical control of product quality and technological process in industrial enterprises; when studying the distribution of families by income, etc. Mode and median have an advantage over the arithmetic mean for a series of distributions with open intervals.

Distribution curves

The most reliable way to identify distribution patterns is to increase the number of observations. As the number of observations increases (within the same homogeneous population) with a simultaneous decrease in the size of the interval, the pattern characteristic of a given distribution will appear more and more clearly, and the broken line representing the frequency polygon will approach some smooth line and in the limit should turn in a crooked line.

A curved line that reflects the pattern of changes in frequencies in a pure form, excluding the influence of random factors, is called a distribution curve.

Currently, a significant number of different distribution forms have been studied. In the practice of statistical research, the Poisson and Maxwell distributions, especially the normal distribution, are often used. Distributions close to the normal distribution have been discovered in the study of a wide variety of phenomena both in nature and in the development of society.

In statistical practice, it is of great interest to solve the question of the extent to which the distribution of a characteristic obtained as a result of statistical observation in the population under study can be considered to correspond to a normal distribution.

To solve this issue, one should calculate the theoretical frequencies of the normal distribution, i.e. those frequencies that would exist if the given distribution exactly followed the law of normal distribution. To calculate theoretical frequencies, the following formula is used:

where i is the normalized deviation;

Consequently, depending on the value of t, theoretical frequencies are determined for each interval of the empirical series.

To check the closeness of the theoretical and empirical distributions, special indicators called goodness-of-fit criteria are used. The most common is the K. Pearson goodness-of-fit test 2 (“chi-square”), calculated by the formula

where f are the empirical frequencies (frequencies) in the interval;

f"" - theoretical frequencies (frequencies) in the interval.

The resulting criterion value (calculation 2) is compared with the table value (table 2). The latter is determined using a special table depending on the accepted probability (P ) and the number of degrees of freedom k (for a normal distribution, k is equal to the number of groups in the distribution series minus 3).

If 2 calculation<= 2 табл, то гипотеза о близости эмпирического распределения к нормальному не отвергается.

When calculating the Pearson criterion, the following conditions must be met: the number of observations must be large enough (n > 50); if the theoretical frequencies in some intervals are less than 5, then the intervals are combined so that the frequencies are greater than 5.

Solving typical problems

The following data are available on the age composition of the workshop workers (years): 18; 38; 28; 29; 26; 38; 34; 22; 28; 30; 22; 23; 35; 33; 27; 24; 30; 32; 28; 25; 29; 26; 31; 24; 29; 27; 32; 25; 29; 29.

To analyze the distribution of workshop workers by age, it is necessary to: 1) construct an interval distribution series; 2) give a graphical representation of the series; 3) calculate the indicators of the distribution center, indicators of variation and distribution shapes. Formulate a conclusion.

Solution. The size of the grouping interval is determined by the formula

Interval distribution series

2. Graphically, an interval variation series can be presented in the form of a histogram, polygon, cumulate.

The histogram is plotted in a rectangular coordinate system. The x-axis shows the intervals of the values ​​of the variational characteristic, and it is advisable to increase the number of intervals by two - one at the beginning and at the end of the existing series) for the convenience of converting the histogram into a frequency polygon. Rectangles are constructed on segments (intervals), the height of which corresponds to the frequency.

To convert a histogram into a frequency polygon, the midpoints of the upper sides of the rectangles are connected by straight segments, and the two extreme points of the rectangles are closed along the abscissa axis in the middle of the intervals in which the frequencies are equal to zero.

In Fig. Figure 2 shows a graphical representation of the constructed interval variation series in the form of a histogram and a frequency polygon.

As can be seen from the graph, the triangles related to the histogram area and the polygon area are equal in pairs, and, therefore, the histogram area and the polygon area of ​​a given variation series also coincide.

Based on the constructed histogram, the mode value can be determined graphically. To do this, the right vertex of the modal rectangle is connected by a straight line to the upper right corner of the previous rectangle, and the left vertex of the modal rectangle is connected to the upper left corner of the subsequent rectangle. The abscissa of the intersection point of these lines will be the distribution mode. Mo = 28.3 years. In Fig. 2, these straight lines connecting the vertices of the rectangles and the perpendicular from the point of their intersection are shown with a dotted line.

Rice. 2. Histogram and polygon of distribution of workshop workers by age

In Fig. Figure 3 shows the cumulative curve (cumulate).

The cumulate can be used to determine the median graphically. To do this, the last ordinate of the cumulate is divided in half. A straight line is drawn through the resulting point until it intersects with the cumulate. From the intersection point, a perpendicular is lowered to the abscissa axis. The abscissa of the intersection point is the median. The lines defining the median in Fig. 3 are shown with dotted lines. Me = 28.6 years.

Rice. 3. Cumulative curve (cumulate)

Selective observation

Simple random sampling

In simple random sampling, the selection of units in the sample population is made directly from the entire mass of units in the general population in the form of random selection, in which each unit in the general population is provided with the same probability (opportunity) of being selected. The sampling unit is the same as the observation unit. Random selection is carried out by using lots (lottery) or using tables of random numbers.

Random sampling can be carried out in two forms: in the form of a return (repeated) sample and in the form of a non-return (non-repeat) sample. With repeated selection, the probability of each unit in the population remaining constant, since after selecting a unit it can be selected again. With non-repetitive sampling, the selected unit is not returned to the general population and the probability of individual units getting into the sample changes all the time (for the remaining units it increases).

The use of simple random resampling is very limited in practice; Non-repetitive sampling is usually used.

In table 5.1 shows the formulas for calculating the errors of a simple random sample.

Maximum error formulas allow you to solve problems of three types:

1. Determination of the limits of general characteristics with a given degree of reliability (confidence probability) based on indicators obtained from sample data. Confidence intervals for the general mean:

Confidence intervals for the general share:

2. Determination of the confidence probability that the general characteristic may differ from the sample characteristic by no more than a certain specified value.

The confidence probability is a function of t, determined by the formula

The value of t determines the confidence probability.

3. Determination of the required sample size, which with practical probability ensures the specified sampling accuracy.

Table 5.1

Simple random sampling error formulas

In table 5.2 shows formulas for calculating the size of a simple random sample.

Table 5.2

Formulas for determining the size of a simple random sample

Solving typical problems

1. A 20% random non-repetitive sample was taken from a batch of electric lamps to determine the average weight of the spiral. The sample results are as follows:

Determine with probability 0.997 the limits within which the percentage of defects will be for all products

Solution

The share of defective products in the sample is determined:

With probability P = 0.997 t = 3.0.

Marginal error size

Confidence intervals for the general share with probability P = 0.997

Index- a relative value characterizing changes in the levels of complex socio-economic indicators in time, space or in comparison with the plan. A complex indicator consists of directly incommensurable (non-summable) elements. For example, an enterprise produces several types of products, but it is impossible to obtain an overall total of product volume by summing the number of its different types in physical terms.

Index indicators are calculated at the highest level of statistical generalization and are based on the results of the summary and processing of statistical observation data. With their help, the following main tasks are solved:

Characteristics of the general change in a complex economic indicator and its individual elements;

Measuring the influence of factors on the overall dynamics of a complex indicator, including characterizing the influence of changes in the structure of the phenomenon.

The index is the result of comparing two indicators of the same name, therefore, when calculating them, the compared level (numerator of the index ratio) is distinguished, called current or reporting, and the level with which the comparison is made (the denominator of the index ratio), called basic. The choice of base is determined by the purpose of the study.

When making territorial comparisons, data from another territory is taken as the base.

When using indexes as indicators of plan implementation, planned indicators are taken as the basis for comparison.

Depending on the content and nature of the socio-economic indicators being studied, a distinction is made between indices of quantitative (volume) indicators and indices of qualitative indicators.

To indices of quantitative (volume) indicators include indices of the physical volume of production, physical volume of product consumption (industrial and personal) and indices of other indicators, the sizes of which are characterized by absolute values.

To the indexes of quality indicators include price indices, cost indices, average wage indices, and labor productivity indices. A qualitative indicator characterizes the level of the studied effective indicator per quantitative unit and is determined by dividing the effective indicator by the quantitative indicator per unit of which it is determined. For example, the average wage is determined by dividing the wage fund by the number of employees; Labor productivity is determined by dividing the total volume of output by the number of employees.

According to the degree of coverage of the elements of the population, individual and summary (general) indices are distinguished. Individual indices characterize changes in one element of the population. Summary indices characterize changes in a complex phenomenon as a whole. Depending on the method of calculating general (aggregate) indices, aggregate indices and average weighted indices are distinguished.

For the convenience of using the index method, compiling index formulas and their use in statistical and economic analysis, certain symbolism has been developed in the theory of statistics and the corresponding conventions are used.

Each indexed value has its own symbolic designation:

q is the quantity of products of one type in physical terms;

p - price per unit of production;

z is the cost per unit of production;

t - labor costs (working time) per unit of production.

Indices for individual elements of the complex economic phenomenon being studied (i.e. individual indices) are designated by the symbol i, which is marked with the symbol of the corresponding indexed value. For example:

i q - individual index of volume (quantity) of a particular type of product;

i p - individual price index for a specific type of product (good);

i z - individual cost index per unit of a particular type of product;

i qp - cost index for a particular type of product;

i qz - index of cash costs for the production of one type of product;

i qt - index of labor costs for the release (production) of one type of product.

The general (composite) index of the complex economic phenomenon being studied is denoted by the symbol I, which reflects the symbol of the indexed value. For example:

I q - general index of physical volume of production;

I p - general price index;

I z - general cost index;

I qp - general index of the cost of all types of products;

I qz - general index of costs for production of all types of products;

I qt is the general index of labor costs for the production of all types of products.

To reflect the basic time periods, special notations are used, which are written at the bottom of the symbol used when writing the index of quantities. The base period, with the data of which the comparison is made, is indicated by a zero value, the first reporting period - by one, etc. In addition, the designations of the compared and base periods can be placed at the bottom of the index symbol (for example, I q 1/0).

Solving typical problems

Task 1. The output of the soil tillage machinery plant for two quarters is as follows:

Define:

1) change (in %) in the output of each type of product, as well as a change in output for the enterprise as a whole;

2) price change (in%) for each type of product and the average price change for the entire product range;

3) absolute change in the total cost of production, separating from the total amount the change due to changes in the quantity of products and due to changes in prices.

Solution

To characterize changes in product output for the enterprise as a whole, an aggregate index of the physical volume of production is calculated:

or 101.3%, i.e. in general, for the enterprise, product output increased by 1.3%, as a result, the cost of production increased by 673,000 rubles. (51,973 - 51,300).

The average price change for the entire product range is determined using the aggregate price index formula.

Note:

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Responsible for the release: Kurasheva Tatyana Aleksandrovna

Compiled by: Borisova Elena Grigorievna (I – 3, 4); Galkin Sergey Alekseevich (I – 5, II – 1); Grigoruk Natalia Evgenievna (I – 6); Kulikova Natalia Ivanovna (I – 2); Kurasheva Tatyana Aleksandrovna (II – 3); Kournikova Elena Leonidovna (I – 1, II – 9); Maltseva Galina Aleksandrovna (II – 5, 6); Onuchak Viktor Aleksandrovich (II – 7); Simonova Marina Demyanovna (II – 8); Tarletskaya Lidiya Vladimirovna (II – 2, 3)

Part I. General theory of statistics

Topic 1. Summary and grouping. Statistical tables and graphs Problems and solutions

Problem 1

In a company with 50 employees. During the statistical observation, the following data were obtained on the length of service of workers and employees:

Make a ranked (in ascending order) distribution series;

Construct a discrete distribution series;

Group by forming 7 groups at equal intervals;

Present the grouping results in a table and analyze them.

Solution

Problem 2

The following data is available on annual turnover for 20 stores in the city:

Based on this data, create:

Store distribution rows:

1. By the size of turnover and number of stores;

   By the number of jobs and number of stores;

A combination table, dividing all stores into 5 groups according to the size of turnover, and in the predicate of the table, highlight 4 subgroups according to the number of jobs.

Solution

Problem 3

Based on the results of a study of the time spent by company employees on the road to their place of work, the following data are available (in millions):

Group the data into four groups

Present the grouping results in a table

Solution

Problem 4

The total sales of 50 branches of a large concern for the week amounted to the following values ​​in thousands of dollars:

Make a ranked series in ascending order

Group your data:

1. Using an interval of $2 thousand.

   Using an interval of 4 thousand dollars.

In which group will the loss of information be greater?

Solution

Problem 5

Having data on the dynamics of world trade, build a statistical table.

World imports amounted to (in billion dollars):

2000 – 6230, 2001 – 5995, 2002 – 6147, 2003 – 7158, 2004 – 8741, 2005 – 9880, 2006 – 11302

World exports were characterized for the corresponding years by the following data (billion dollars):

6026, 5824, 7003, 8517, 9676, 11191.

Source: Monthly Bulletin of Statistics, New York, UN, 2005. No. 6. P. 114

Solution

Problem 6

The following data are available on the geographical distribution of world trade for 2006 (in billion dollars): world exports - 11191; exports from EU countries – 4503; RF – 301; China – 969; USA - 1038; Germany – 1126; Japan - 650.

Calculate the share of these countries in world trade and arrange this data in the form of a table, as well as display it graphically.

Source: Monthly Bulletin of Statistics, New York, YN, 2007. No. 6. P.114, 118, 129, 139, 136.

Solution

Problem 7

As an expert at a credit institution, you need to create a table layout that gives an idea of ​​the number of loans provided to your organization over 5 years. At the same time, you must reflect the terms of the loans (long-term, medium-term, short-term) and the amount of loans, both in absolute terms and as a percentage of the total.

Solution

Problem 8

The following data is available on the number and length of service of the organization’s employees at the beginning of the current year:

Heads of departments and their deputies with experience

up to 3 years – 6,

up to 6 years – 8,

up to 10 years – 11,

years and above – 5.

Accounting employees with experience

up to 3 years – 3,

up to 6 years – 7,

up to 10 years – 12,

10 years and above – 12.

Department employees with experience

up to 3 years – 40,

up to 6 years – 26,

up to 10 years – 21,

10 years and above – 53.

Based on these data, build a statistical table, in the subject of which provide a typological grouping; Divide each group of workers into subgroups based on length of service.

Solution

Problem 9

Based on the data on the size of living space per person in two districts of the city in 2006, regroup, taking as a basis groups of families in 2 ohm area.

Solution

Problem 10

The following data is available for 2 branches of the company:

Perform a secondary grouping of data in order to bring it into a comparable form, and conduct a comparative analysis of the results.

Solution

Problem 11

The following data is available on the distribution of Omega food stores by turnover for the quarter (conditional data):

Based on these data, make a secondary grouping, dividing the specified set of stores into new groups:

Up to 100 thousand USD: 100 – 250; 250 – 400; 400 – 700; 700 – 1000; 1000 thousand.u. and higher.

Solution

Problem 12

Using data on fertility and mortality in some countries of the world, construct linear graphs (in ppm):

Source: Monthly Bulletin of Statistics, New York, UN, 2007. No. 6. P. 8, 9, 10, 11; China Statistical Yearbook, 2005, China Statistical Press, 2005. P. 93.

Solution

Problem 13

The commodity structure of Russian exports in 2005 was characterized by the following data (%):