What aggregates can be distinguished in college. subject of statistics. Statistical aggregate. Frequencies are numbers
Theory of Statistics
A guide for students enrolled in remote system
Introduction
Statistics, is one of the basic disciplines that forms professional level modern economist, occupies a special place in the system economic education, since the work of a competent and in-demand economist requires a unity of qualitative and quantitative analysis of socio-economic phenomena and processes. A specialist in the field of economics, whether it be a financier, manager, accountant, auditor, anti-crisis manager, marketer, must be proficient in the methods of processing and analysis statistical information to be able to make effective managerial decisions.
The purpose of teaching the discipline "Theory of Statistics"- to give future specialists an idea of the scientific foundations of statistical methods for studying mass socio-economic processes and phenomena, to help comprehend the categories of statistical science, to teach how to apply scientific methods statistical research in further practical and scientific work to solve socio-economic problems, as well as meaningfully interpret the results.
The main tasks of the discipline are to teach students how to use statistical reporting, apply scientific methods of statistical research and see their specific content behind statistical indicators, as well as use the acquired skills and knowledge in solving applied problems of analyzing socio-economic phenomena and processes.
According to the results of studying the course "Theory of Statistics", students should:
| o know | - basic concepts and categories of statistics; - types and organizational forms statistical observation; - ways of visual presentation of statistical data: tabular and graphical presentation of data; - statistical indicators and their types: absolute and relative, average, indicators of variation and interdependence of variables; - the concept of the sampling method, general and sampling populations, methods of selecting units population in the sample, types of statistical observation errors; - the essence of the theory of evaluation; - the concept of statistical hypotheses, their types, the algorithm for testing statistical hypotheses; - series of dynamics and their application, indicators of series of dynamics; - statistical indices, their types and application in the analysis of economic phenomena. |
| Ø be able | - determine the possibility of applying the theoretical provisions and methods of statistical analysis to solve specific practical problems; - to carry out the collection, processing and analysis of statistical information, including the organization of non-continuous observation; - develop, calculate and interpret various statistical indicators to assess the socio-economic situation, forecast and model economic and social processes on the various levels management, draw up the results in the form of distribution series, tables and graphs, formulate conclusions and analyze data. - to carry out point and interval estimation of unknown parameters of the general population according to sample data; - formulate the null and alternative hypotheses, determine the type of critical region, choose the test criterion statistical hypothesis; - distinguish between types of time series, calculate indicators of changes in the levels of time series, identify the main trend and the seasonal component of the time series; - make calculations of individual, summary and other types of indices, analyze the results obtained and draw scientifically based conclusions. |
| Ø have an idea | - about the history of development and modern directions in the theory of statistics; - about the importance of statistics and its place in the system of fundamental sciences and its role in solving practical problems. |
To acquire the necessary competencies, students are helped by the sequence of presentation of the material in the course for distance learning. After mastering the theoretical foundations, students can consolidate the material using practical examples and tasks. At the end of each topic, there are control questions, tests and assignments that allow students to conduct self-examination, contributing to a deeper understanding of the topics of the course, a stronger assimilation of the theory of statistics, and the acquisition of skills in calculating statistical indicators.
Test questions are formulated in such a way that not only the assimilation of theory is checked, but also the application of theoretical knowledge to practical problems.
Statistics develops methods for collecting, systematizing, analyzing, interpreting and displaying the results of observations of mass random phenomena and processes in order to identify the patterns existing in them.
If we consider statistics as a tool for studying socio-economic phenomena and processes, then the subject of research in statistics is the study of the size and quantitative ratios of mass social phenomena in specific conditions of place and time, as well as the numerical expression of patterns manifested in them.
Signs and their classification, statistical indicator
Units of the population have certain properties, qualities, which are usually called features.. For example, signs of a person: age, gender, education, weight, marital status, etc. Signs of an enterprise: form of ownership, industry, number of employees, size of the authorized capital, etc. Statistics studies phenomena through their features: the more homogeneous the set, the more common features its units have, the less its values vary. The peculiarity of a statistical feature is that it can be measured and described.
Statistical sign general property, feature or other feature of the population units that can be observed or measured.
statistic - generalizing quantitative characteristic socio-economic phenomena in specific conditions of place and time.
Statistical Features differ in the way they are measured and in other features that affect the techniques statistical study. This gives grounds for the classification of features (Scheme 1.1).
Descriptive (qualitative) features expressed verbally: nationality, type of stock (simple, privileged), type of fabric (silk, wool), etc. Descriptive features are divided into nominal and ordinal.
Rated - these are descriptive features on which data cannot be ranked, while ordinal- those by which you can rank, order the data. For example, evaluations of judges at sports competitions.
Scheme 1.1
Statistics method
The specifics of the subject of statistics determines specifics statistical method. It includes: data collection (statistical observation), generalization and presentation of data (summary and grouping), data analysis and interpretation.
At present, three branches of statistics have been completed: the general theory of statistics, economic statistics, and social statistics.
Control questions to the topic "Subject and method of statistics"
1. What is included in the range of subjects studied by statistics?
2. What is the meaning of the term statistics?
3. What is statistics as a science?
4. What is the subject of statistics?
5. What is a statistical pattern?
6. What is meant by a statistical population unit?
7. What is a statistic?
8. What is a statistic? What features play a predominant role in statistics?
9. What sciences are the theoretical basis of statistics?
10. What is the relationship between statistics and other sciences?
11. What is the specificity of the statistical method of studying socio-economic phenomena?
12. What are the organization and tasks of statistics at the present stage of Russia's development?
Control tasks to the topic "Subject and method of statistics"
1. What characteristics can characterize the population of university students?
2. The set of commercial banks of the city is investigated. What features can characterize it?
3. What are the essential varying features that characterize student group.
4. Indicate what populations can be identified at the university for statistical study?
5. What are the most significant features that can characterize such units of observation as:
a) an industrial enterprise;
b) a commercial bank;
c) a trading company;
d) university student;
e) university teacher.
6. What signs according to the classification shown in Figure 1.1. are:
The population of the country;
Number of marriages and divorces;
Production in value terms;
The number of seats on the aircraft;
Gender and age of the person;
Floors of residential premises;
Retail turnover of trade associations;
The tariff category of the worker;
Academic score;
Type of ownership;
Nationality;
Married status.
Observation methods
In any survey source of primary data there may be direct observation, documents, survey.
Direct observation carried out by registering the units under study and their characteristics on the basis of direct inspection, counting, weighing, etc. and recording the results in a special observation form.
documentary way observation is based on the use of various primary accounting documents of enterprises, institutions and organizations as a source of statistical information, therefore this method of observation is often called reporting. For example, collecting information about the progress of university students based on test and examination sheets.
When polled the source of the data is the information provided by the interviewees. In this case, different methods of collecting data can be used: reporting, forwarding, self-registration, questionnaire and correspondent.
With forwarding method specially trained interviewers complete the census forms on the basis of a survey, while simultaneously using the correctness of the answers received. This method is mainly used in population censuses.
When self-registration or self-calculation employees of the organization conducting the survey distribute the questionnaires or questionnaires to the interviewees, instruct them, and then collect the completed forms. This method is used in budget surveys of the population, the study of pendulum migration - the movement of the population from the place of residence to the place of work and back.
The questionnaire method is the collection of statistical data using special questionnaires sent to a certain circle of people or published in periodicals. Widely used in sociological surveys.
Correspondent method consists in the fact that statistical or other organizations send specially designed forms and instructions for filling them out to individual organizations or persons who have agreed to periodically fill out the forms and send them to the statistical body within a specially established period.
Diary method(Budgets of the population)
Business Survey- a new way of observation for Russia. But widely used in more than 50 countries around the world. For its implementation, a special questionnaire has been developed, a list of indicators has been defined that reflect the entrepreneurial intentions of various enterprises. Business surveys are based on the collection and compilation of information on key indicators economic activity economic agents. Respondents, as a rule, managers are asked to assess the current economic condition of the company, as well as its change in the near future in the framework of "deterioration - improvement", "decrease - increase" and other qualitative questions.
2.4. Program and methodological issues of statistical observation
For statistical observation, a plan and program of statistical observation.
In terms of observation, program-methodological and organizational issues are formulated.
Programmatic and methodological issues include setting goals, formulating tasks, limiting the object, choosing the unit of observation, compiling an observation program and statistical tools.
The actual definition of the object of observation includes the definition of the unit of observation, the territory and time of observation.
Territory of observation covers all places of passage of observation units; its boundaries depend on the definition of the unit of observation.
Unit of observation- this is the phenomenon, the signs of which are subject to registration. The set of observation units is object of observation.
The unit of observation, as a rule, has many different features. It is impossible to take into account all of them, and many of them do not need to be taken into account. Therefore, when organizing statistical observation, the question arises of what signs should be recorded during the observation process.
The list of signs recorded for each unit of observation is called statistical observation program. Its content depends on the goals and objectives of the survey.
You can talk a lot about how to draw up an observation program, but these tips were best formulated by the famous Austrian statistician of the last century A. Quetelet:
1. Don't collect data just in case;
2. Don't ask questions that can't be answered;
3. Do not ask questions that cause any kind of suspicion.
The collected data must meet two requirements: reliability and comparability. Reliability is the correspondence of the data to what is actually there. In order for data on individual phenomena to be generalized, they must be comparable with each other: collected at the same time, according to a single methodology.
Statistical Toolkit represents instructions, forms of documents and should ensure uniformity of understanding and interpretation of the observation program.
to organizational Observation issues include such issues as determining the place and time of observation, establishing a critical moment in time. Appointment of responsible persons for monitoring, selection and briefing of personnel.
Examples of tasks on the topic "Statistical observation"
Exercise 1.
Registration of acts of civil status (births, marriages, divorces, deaths).
Solution.
2) Type of observation (by time, by completeness of coverage of the object, by source of information) - current, continuous, direct.
3) The method of collecting information (self-registration, questionnaire, private, correspondent, forwarding) - private.
Task 2.
What forms, types and methods of statistical observation should include:
Monthly reports on the output of industrial and trade enterprises.
Solution.
1) Organizational form (reporting or specially organized) - reporting.
2) Type of observation (by time, by completeness of coverage of the object, by source of information) - periodic, non-continuous, documentary.
3) The method of collecting information is reporting.
Task 3.
How can the definition of the object of observation be formulated:
1) the country's housing census
Solution.
Recall that the object of observation is understood as a certain statistical totality in which the studied socio-economic phenomena and processes occur. The object of observation can be a set of individuals (population of a region, country, persons employed at enterprises in the industry, etc.), physical units(cars, houses), legal entities (enterprises, farms, commercial banks, educational institutions).
To determine the object of observation, it is necessary to determine the boundaries of the studied population. To do this, you should specify the most important features that distinguish it from other similar objects. For example, for industrial enterprises to determine the form of ownership, organizational and legal forms of enterprises, industries and regions to be monitored.
1) Housing census
Observation boundaries - the territory of the country, the object of observation during the census of the housing stock is the totality of residential buildings and premises of all forms of ownership, in which at the time of the census people were registered and actually lived. Observation time - critical date, as of which the housing stock is taken into account.
The unit of observation is a residential building or premises.
2) Census of scientific institutions of the republic
Observation boundaries - the territory of the country, the object of observation in the census of scientific institutions are organizations and institutions in the charter of which types of activity are recorded, classified as scientific. Observation time - critical date, as of which scientific institutions are taken into account.
Control questions to the topic "Statistical observation"
1. Name the stages of statistical observation.
2. What is the purpose of statistical observation?
3. What is the object and unit of statistical observation?
4. What is the purpose of a monitoring plan?
5. What is a Statistical Surveillance Program?
6. How does observation differ in terms of coverage of units of the observed population?
7. Name the types of non-continuous observation.
8. Name the methods of statistical observation.
9. What errors can occur during the observation process, what are the ways to prevent and control them?
10. What is the name of the set of elements that have mass character, qualitative homogeneity, a certain integrity, interdependence of the states of individual units and the presence of variation?
11. Which document of statistical observation defines the object and tasks of observation?
12. What is the name of the list of questions that in the process of statistical research should be answered about each unit of the population?
13. What is the unit of observation in a census?
14. What is the name of the survey, in which only a part of the population of interest to the researcher is subjected to registration on any basis and the results obtained serve as a characteristic of the entire population?
Control tasks to the topic "Statistical observation"
Exercise 1.
The supermarket manager decided to conduct a survey to identify reserves and areas for improvement in his departments.
Help: a) define and limit the object and unit of observation;
b) choose the type of observation and develop a program;
c) prepare a form and brief instructions.
Task 2.
Draft a statistical form for surveys:
a) current registration of immigrants in order to clarify their socio-demographic composition, the purpose of entry and the country of departure;
b) current accounting of clients of a commercial bank, which should find out their status (legal or natural person), type of activity, legal and actual address, level of solvency, guarantees and guarantees, intended use of loans.
Task 3. Make a list of the most essential features the following units of statistical observation:
Farming;
Dwelling house (for housing census);
Library;
Joint venture.
Task 4. What signs will you outline that should be recorded during the conduction:
Surveys of an industrial firm in order to study the turnover of the workforce;
Surveys of the work of urban transport in order to study the role of its various types in the transportation of passengers;
Surveys of university students in order to study the time budget.
Task 5. Formulate the object, unit and purpose of observation and develop a survey program:
kindergartens;
Companies producing baby food;
petrol stations; hotel complex in the region.
Task 6. Formulate questions to be included in the observation form according to the following features of the objects of observation:
The number of employees in the firm;
The size of the family;
Relationships of family members;
Gender and age of the person?
Task 7. Formulate the questions of the observation program and draw up a layout of the statistical form, as well as brief instructions for filling it out to study the dependence of academic performance on gender, age, marital status, housing conditions and social activity of a university student when conducting a special statistical survey as of September 1, 2007. Specify , to which type this observation belongs in terms of time, coverage and method of obtaining data.
Task 8. The trading company "Partiya" instructs you to develop a form of a questionnaire survey of buyers in order to study the contingent visiting the company, meet their demand and the time spent on purchasing the necessary audio and video equipment. Indicate what kind of observation this observation belongs to in terms of time, coverage and method of obtaining data.
Task 9. Determine the object and unit of observation of a one-time survey of public library readers. Develop a program and form for this survey.
Summary is a scientifically organized processing of observation materials, during which the collected data is controlled, their systematization and grouping, as well as the construction of tables and graphs, the calculation of results and derived indicators in the form of average and relative values.
The purpose of the reports and is to obtain generalizing statistical indicators that reflect the essence and statistical patterns of the analyzed socio-economic phenomenon.
The program of the statistical summary is developed before the collection of statistical data. Its development is carried out within the framework of drawing up a plan and a program of statistical observation. The summary program includes:
Definition of groups and subgroups, according to which the statistical population is classified;
Development of a system of indicators characterizing groups and the statistical population as a whole;
Development of layouts of statistical tables for presenting summary results.
According to the depth of material processing, a simple and complex summary is distinguished.
Distribution of the population of the Russian Federation
Absolute values
Absolute values- this is the number of units of the population as a whole or for its individual groups, which is obtained as a result of summing up the registered values of the characteristics of the primary statistical material. These indicators can be obtained by calculation on the basis of other indicators (for example, the increase in bank deposits of the population for a period is defined as the difference between deposits at the end and beginning of the period).
Absolute values as generalizing indicators characterize either the size of the population (the number of economically active population, the number of enterprises of various forms of ownership, etc.), or the volume of certain features of the population (the size of investments, labor costs, etc.).
Any absolute value always has its own unit of measure inherent in certain phenomena.
Are widely used natural units of measurement, both simple (ton, piece, square and cubic meter, kilometer, etc.), and complex, which are combinations of two quantities (tonne-kilometer, kilowatt-hour, etc.). A variety of natural indicators are conditionally natural indicators. They are used to obtain absolute generalizing indicators, when individual groups of terms included in the set cannot be directly summed up. Beforehand, all terms must be reduced to a comparable form. With the help of special conversion factors, the terms are expressed in a single standard unit of measurement, which makes it possible to obtain a generalizing indicator. For example, various types of fuel are measured by reference fuel with a calorific value of 7000 kcal / kg, chemical industry products, metal ores - by the content of useful substances.
As absolute generalizing indicators, we use cost indicators, they make it possible to commensurate in monetary terms quantities that cannot be commensurate in kind (for example, production costs and household expenditures).
In addition, as absolute generalizing indicators, and indicators measured in units of labor. Labor units of measurement - man-day, man-hour, etc. are used to measure labor costs for the production of any product, work, determine labor productivity.
There are three types of absolute values: individual, group and general. Group and general are sometimes called final or summary.
Individual absolute values express the sizes of quantitative signs in individual units of the studied population.
For example, the number of deposits in a savings bank, the work experience of Ivanova I.I. - individual values of certain units of populations.
Group and general absolute statistical values express the value of a particular trait in all units of a given population, taken together, or in their individual groups, or the number of units in the entire population or its individual parts (groups). It is clear from the definition that the final absolute values (indicators) are obtained by summing up individual absolute values, or by counting the number of units included in separate groups.
Relative values
Relative statistic is an indicator obtained by comparing, comparing absolute or relative values in space (between objects), in time (for the same object) or comparing indicators of different properties of the object under study.
Relative statistics, obtained by comparing absolute indicators, can be called relative values of the first order, and those obtained by comparing relative indicators can be called values of higher (second, third, etc.) orders. Values higher than the fourth order are almost never used due to the complexity of interpretation. Relative statistical indicators express the relationship between absolute indicators: potato yield is the ratio of gross harvest to sown area; the share of the urban population in the country - the ratio of the population of cities to the total number of inhabitants of the country.
The main types of relative values are often expressed as abstract numbers, but can also be named relative indicators. Their construction is associated with the use of various statistical methods.
All relative statistical indicators used in practice can be divided into the following types:
dynamics;
implementation of the plan;
structures;
coordination;
intensity and level economic development;
Comparisons.
1. Relative indicator of dynamics(OPD) is the ratio of the level of the process or phenomenon under study for a given period of time (as of this moment time) to the level of the same process or phenomenon in the past:
The value calculated in this way shows how many times the current level exceeds the previous (basic) level or what proportion of the latter it is. This indicator can be expressed as a multiple ratio or converted into a percentage.
There are relative indicators of dynamics with a constant and variable base of comparison. If the comparison is carried out with the same base level, for example, the first year of the period under review, relative indicators of dynamics with a constant base (basic) are obtained. When calculating the relative indicators of dynamics with a variable base (chain), the comparison is carried out with the previous level, i.e. the base of the relative magnitude changes sequentially.
Let's use the data in Table 1 as an example.
Table 1
Topic 5. Averages
| After studying the topic, the student must | ||
| know | ||
| - methodological foundations for the use of averages, their economic essence; | ||
| - differences between typical and system averages; | ||
| - power averages and areas of their application; | ||
| - calculation formulas various kinds average values; | ||
| - structural averages and their economic meaning | ||
| be able to | ||
| - to choose correct form middle; | ||
| - calculate and interpret average values; | ||
| - apply structural averages | ||
| Plan | ||
| 5.1 | Average, its essence and definition | |
| 5.2 | Types and forms of averages | |
| 5.3 | Arithmetic mean | |
| 5.4 | Average harmonic | |
| 5.5 | Geometric mean | |
| 5.6 | Indicators of the structure of the variation series. Measures of the central tendency of a variation series. | |
Arithmetic mean
The most common type of average is arithmetic mean, which, like all averages, depending on the nature of the data available, can be simple or weighted. This form of average is used when the calculation is based on ungrouped data.
Suppose eight firms have the following monthly output:
In order to determine the average monthly output per enterprise, you can use the following initial ratio:
Using the conventions given in the previous paragraph, we write the formula for this average:
(5.1)
Given the available data, we get:
In this case, we used the simple arithmetic mean (unweighted) formula.
Arithmetic weighted average. When calculating the average values, individual values of the averaged feature can be repeated, occur several times. In such cases, the average is calculated using grouped data or variational series, which can be discrete or interval.
Consider the following conditional example:
Transactions on the shares of the issuer "X" for the trading session
Based on this discrete variational series, we determine the average selling price of 1 share, which can only be done using the following initial ratio:
To get the total amount of transactions, it is necessary to multiply the selling rate for each transaction by the number of shares sold and add the resulting products. In the end, we will have the following result:
The calculation of the average selling rate is made according to the weighted arithmetic average formula:
In some cases, the weights can be represented not by absolute values, but by relative ones (in percentages or fractions of a unit). So, in the above example, the number of shares sold during each transaction is respectively 37.8% (0.378); 10.8% (0.108) and 51.4% (0.514) of their total number. Then, taking into account a simple transformation of formula (5.4.), we obtain:
420 0.378 + 440 0.108 + 410 0.514 \u003d 417.03 rubles.
In practice, the most common error in calculating averages is ignoring weights when those weights are actually needed. Let's assume we have the following data:
Cost of production "Z"
| Company | Unit cost of production, rub. |
| 1 2 | 37 39 |
Is it possible to determine the average cost of a given product for the two enterprises taken together from the available data? It is possible, but only if the volumes of production of these products at the two enterprises are the same. Then the average cost will be 38.0 rubles. (The proof of this rule will be given below.). However, at the first enterprise for the period under review, for example, 50 units of products can be produced, and at the second - 700 units. Then, to calculate the average cost, you will need the arithmetic weighted average:
The general conclusion is as follows: the unweighted arithmetic mean can be used only when the absence of weights or their equality is precisely established.
When calculating the average interval variation series to perform the necessary calculations, one passes from the intervals to their midpoints. Consider the following example:
Average harmonic.
Example 1 Consider the use of the harmonic mean on a specific example. Suppose, observing the work of five workers for one hour, we received the following data on the cost of their working time for the manufacture of one part (x) in hours: 0.2; 0.3; 0.3; 0.5; 0.5.
Topic 1. Subject and method of statistical science
1.1 References
Statistics develops methods for collecting, systematizing, analyzing, interpreting and displaying the results of observations of mass random phenomena and processes in order to identify the patterns existing in them.
The subject of research in statistics is the study of the dimensions and quantitative ratios of mass social phenomena in the specific conditions of place and time, as well as the numerical expression of the patterns manifested in them.
A regularity that manifests itself only in a large mass of phenomena through overcoming the randomness inherent in its individual elements is called statistical regularity.
The object of statistical study is the statistical population- a set of units with a mass character, qualitative homogeneity, a certain integrity, the interdependence of the states of individual units and presence of variation. The statistical population consists of population units.
Population unit - this is the limit of fragmentation of the object of study, at which all the properties of the process under study are preserved.
Units of the population have certain properties, qualities, which are usually called features.
Statistical sign a common property, characteristic or other feature of units of a population that can be observed or measured.
statistic - a generalizing quantitative characteristic of socio-economic phenomena in specific conditions of place and time.
Statistical Features differ in the way they are measured and in other features that affect the methods of statistical study. This gives grounds for the classification of features (Scheme 1.1).
Descriptive (qualitative) features expressed verbally: nationality, type of stock (simple, privileged), type of fabric (silk, wool), etc. Descriptive features are divided into nominal and ordinal.
Rated - these are descriptive features on which data cannot be ranked, while ordinal - those by which you can rank, order the data. For example, evaluations of judges at sports competitions.
Scheme 1.1
Classification of features in statistics
Quantitative features expressed in numbers. For example, age, salary, share price, etc.
Primary signs characterize the unit of the population as a whole. These are absolute values that can be measured, counted, weighed. They exist on their own, independent of statistical study. For example, the population of the country, the price per share, etc.
Secondary, or calculated signs not measured directly, but calculated. For example, production cost, profitability, Dow Jones index, etc. Secondary signs are obtained by actions with primary ones. For example, dividing the volume of output by the number of employees, we get labor productivity.
Direct (immediate) signs - These are properties that are directly inherent in the object that is characterized by them. This, for example, the age of a person, the number of employees of the enterprise, the price per dollar.
Indirect signs are properties that are inherent not to the object itself, but to other collections related to the object, included in it. For example, the price per share, as an indirect sign of the company that issued this share. Although price is a characteristic of a stock, it also indirectly characterizes a company.
Alternative signs - these are signs that can take on only two possible values. For example, gender, place of residence (urban, rural), etc.
Discrete Features - this is quantitative signs, which can only take on individual values. For example, the number of family members, the number of issued shares, etc.
Continuous signs - these are signs that take on any values within certain limits.
Moment signs characterize the object under study at some point in time, established by a statistical study. For example, the value of the dollar as of February 1, 2005, the actual population as of January 1, 2005, etc.
Interval features - these are signs that characterize the results of the process. Therefore, their values can occur only for a time interval: year, month, day, and not at a point in time. For example, the number of births or deaths, daily trading volume on the MICEX, etc.
The specifics of the subject of statistics determines the specifics of the statistical method. It includes: data collection (statistical observation), generalization and presentation of data (summary and grouping), data analysis and interpretation.
At present, three branches of statistics have been completed: the general theory of statistics, economic statistics, and social statistics.
1.2. Security questions for topic 1
1. What is included in the range of subjects studied by statistics?
2. What is the meaning of the term statistics?
3. What is statistics as a science?
4. What is the subject of statistics?
5. What is a statistical pattern?
6. What is meant by a statistical population unit?
7. What is a statistic?
8. What is a statistic? What features play a predominant role in statistics?
9. What sciences are the theoretical basis of statistics?
10. What is the relationship between statistics and other sciences?
11. What is the specificity of the statistical method of studying socio-economic phenomena?
12. What are the organization and tasks of statistics at the present stage of Russia's development?
1.3. Control tasks for topic 1
1. What characteristics can characterize the population of university students?
2. The set of commercial banks of Rostov is investigated. What features can characterize it?
3. What are the essential varying features that characterize the student group.
4. Indicate what populations can be identified at the university for statistical study?
5. What are the most significant features that can characterize such units of observation as:
a) an industrial enterprise;
b) a commercial bank;
c) a trading company;
d) university student;
e) university teacher.
6. What signs according to the classification given in paragraph 1.1 are:
The population of the country;
Number of marriages and divorces;
Production in value terms;
The number of seats on the aircraft;
The number of employees in the firm;
Relationships of family members;
Gender and age of the person;
Floors of residential premises;
Retail turnover of trade associations;
The tariff category of the worker;
Academic score;
Type of ownership;
Nationality;
Married status.
Topic 1. Subject and method of statistical science.
1. What aggregates can be distinguished in higher educational institution for statistical study?
2. Specify, what aggregates can be allocated for statistical study in trade?
3. What are the most significant varying features that characterize the student group?
4. What indicators can characterize the totality of athletes?
5. What quantitative and qualitative features can characterize the population of Yaroslavl?
Topic 2. Statistical observation.
1. Forms of organization and types of statistical observation.
2. Preparation of statistical observation.
3. Errors of statistical observation.
Practical task.
1. Formulate the object, the purpose of observation and develop a program: a) a sample survey of cafe visitors; b) examination of the level of qualification of employees of a trade enterprise; c) surveys of graduates of an educational institution. d) census of trade enterprises.
2. Design a layout of a statistical table that characterizes the size of the turnover of several department stores known to you per one workplace and per square meter of sales area.
Essay topics
1. Tasks and main directions of development of methods of statistical observation.
2. The main directions of the use of statistical information in modern society.
3. Methods of collecting information in sociological research.
Topic 3. Summary and grouping of statistical data
Practical task.
1. The following data are available on the sale of goods and distribution costs for trade enterprises, million rubles:
| No. p / p | Retail turnover | The amount of distribution costs |
| 30,0 34,0 46,0 30,9 15,9 25,2 42,0 26,0 16,4 34,8 37,0 28,6 18,7 39,0 36,0 36,0 25,0 38,5 44,0 37,0 27,0 35,0 40,0 25,0 24,0 |
To identify the relationship between the volume of retail turnover and distribution costs, group the enterprises according to the volume of retail turnover, forming four groups at equal intervals.
For each group and set of enterprises as a whole, calculate:
1) number of enterprises;
2) the volume of trade - total and on average per enterprise;
3) the amount of distribution costs - in total and on average per enterprise;
4) the relative level of distribution costs (percentage of the sum of distribution costs to the volume of retail turnover).
Present the calculation results in the form of a group table. Write short conclusions.
2. Using the method of analytical grouping, establish the presence and nature of the relationship between the number of industrial and production personnel and output per enterprise according to the following data (Create five groups at equal intervals, arrange the results in the form of a working and analytical table):
Topic 4. Statistical quantities.
1. Essence, meaning and classification of statistical indicators.
2. The concept of systems of statistical indicators.
3. Statistical tables.
4. Main types of charts.
Practical task.
1. Indicate what types of relative values can be calculated from the following data:
2. Based on the following data, determine the degree of fulfillment of the plan for the production of products by the workshop, using the method of conditionally natural measurement.
According to the previous task, construct a statistical series of distribution of enterprises by output, forming five groups of enterprises with equal intervals. Plot Distribution Series Plots
Essay topics
1. Systems of indicators of the standard of living.
2. The system of statistical indicators of the service sector
3. Development of a system of indicators of regional statistics.
4. System of indicators of gender statistics.
5. A system of indicators characterizing the situation of children in Russian Federation.
Topic 5. Mean values and indicators of variation.
Practical task.
1. Calculate the characteristics of the distribution series obtained in task No. 1 of topic 3: arithmetic mean, standard deviation, variance, coefficient of variation.
Topic 6. Statistical study of dynamics
1. Concept and classification of series of dynamics.
2. Rules for constructing time series.
3. Indicators of the analysis of series of dynamics.
4. The structure of the series of dynamics. Checking the series for a trend.
5. Analysis of seasonal fluctuations.
Essay topics
1. Problems of reconstruction of Russian statistics for a long period.
2. Statistics in the works of Western Sovietologists: the rate of economic growth of the USSR.
3. Alternative estimates of the dynamics of the Russian economy.
4. System of indicators of market conditions.
Topic 8. Statistical study of relationships.
1. The role of statistics in the study of relationships. Statistical methods for studying relationships.
2. Problems of statistical modeling.
3. Correlation and regression methods of communication analysis.
4. Non-parametric methods for estimating the connection.
Essay topics
1. Relationship between socio-economic indicators and voting results.
2. Non-traditional applications of statistical methods (catastrophe theory).
3. Application of mathematical and statistical methods for analyzing relationships.
CHAPTERI
INTRODUCTION TO THE THEORY OF STATISTICS
CHAPTER 1. STATISTICS AS A SCIENCE
1.1. Guidelines
This theme has great importance not only for the course of the theory of statistics, but for all statistical disciplines in general. It sets out critical issues statistical science: about the subject of statistical science, its method, theoretical foundations, tasks, etc. As a result of studying the topic, the student should get a clear idea of what statistics studies, its place in the system of sciences, theoretical basis, the most important principles, categories and concepts, the main tasks of statistics at the present stage.
The study of the topic should equip the student with an understanding of the fundamentals of statistical theory and statistical methodology.
When considering the material of the topic, it is important to understand the need to attract mass data for an objective knowledge of reality; the leading role of socio-economic categories in statistical research.
It is necessary to master well such important concepts of statistical science as a statistical population, a unit of a population, features and their classification, variation of features, and a statistical indicator. It is impossible to do without them in the further study of other statistical disciplines, in which concepts, terms, indicators, formulas of the theory of statistics are used, but their essence, meaning and significance are not explained, since this is the task of the theory of statistics.
The concept of statistics. Statistics, or rather its research methods, is widely used in various areas human knowledge. However, like any science, it requires the definition of the subject of its study. In this regard, a distinction is made between statistics dealing with the study of socio-economic phenomena, which belongs to the cycle of social sciences, and statistics dealing with the laws of natural phenomena, which belongs to the natural sciences.
This course is devoted to the theory of statistics of socio-economic phenomena.
The authors of most modern domestic university textbooks on the theory of statistics (general theory of statistics) understand statistics as a subject social science, i.e. a science that has its own special subject and method of knowledge. Therefore, in the process of studying the topic, it is necessary to understand that 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, revealing the existing quantitative dependencies, trends and patterns, and in specific conditions of place and time.
subject of statistics. When studying the topic, it is necessary first of all to pay special attention to the definition of the subject, method and tasks of statistics, to understanding the essence and content of statistical science, which distinguish it from other socio-economic sciences, as well as from mathematics. Questions of the subject and method of statistics are the initial ones, the first acquaintance with the foundations of statistical science begins with them.
In the process of studying this topic, it is important to understand that statistics as a science studies not individual facts, but mass socio-economic phenomena and processes, acting as a set of individual factors that have both individual and common features.
The object of statistical research (in each specific case) in statistics is called a statistical population. A statistical aggregate is a set of units that have mass character, homogeneity, a certain integrity, interdependence of the state of individual units and the presence of variation. For example, as special objects of statistical research, i.e. statistical aggregates, there can be many commercial banks registered in the territory of the Russian Federation, many joint-stock companies, many citizens of any country, etc. It is important to remember that the statistical population consists of really existing material objects.
Each individual element of this set is called population unit.Units of the statistical population are characterized common properties, referred to in statistics signs, those. Qualitative homogeneity of an aggregate is understood as the similarity of units (objects, phenomena, processes) according to some essential features, but differing in some other features. For example, out of the aforementioned aggregates, many commercial banks, along with qualitative certainty (belonging to the category of credit institutions), have differences in the size of the declared authorized funds, the number of employees, the amount of assets, etc.
The qualitative certainty of the population, although it has an objective basis, is established in each specific statistical study in accordance with its goals and cognitive tasks.
Units of the population, along with features common to all units, which determine the qualitative certainty of the population, also have individual characteristics and differences that distinguish them from each other, i.e. exists symptom variation. It is due to a different combination of conditions that determine the development of the elements of the set. For example, the level of labor productivity of bank employees is determined by their age, qualifications, attitude to work, etc. It is the presence of variation that predetermines the need for statistics. It must be remembered that the variation of a trait can be reflected statistical distribution aggregate units.
It is also important to remember that statistics, as a science, primarily studies the quantitative side of social phenomena and processes in specific conditions of place and time, i.e. the subject of statistics is the size and quantitative correlations of socio-economic phenomena, the patterns of their connection and development.
Statistics expresses a quantitative characteristic through a certain kind of number, which are called statistical indicators. A statistical indicator reflects the result of measurement for the units of the population and the population as a whole.
However, then the question arises, how is statistics different from mathematics?
The main difference is that statistics studies the quantitative side of qualitatively defined mass social phenomena in given conditions of place and time. Wherein the qualitative certainty of individual phenomena is usually determined by the associated sciences.
When studying this topic, it is important to find out the theoretical foundations of statistics and the problem of applying the law big numbers.
Theoretical foundations of statistics as a science. The theoretical basis of any science, including statistics, is made up of concepts and categories, in the aggregate of which the basic principles of this science are expressed. In statistics, the most important categories and concepts include: totality, variation, sign, regularity.
When studying this issue, it is important to understand that statistical aggregates have certain properties, the carriers of which are aggregate units (phenomena), with certain characteristics. According to the form of external expression, signs are divided into attributive (descriptive, qualitative) and quantitative. attributive(qualitative) signs are not amenable to quantitative (numerical) expression.
difference quantitative characteristics from qualitative ones is that the former can be expressed in total values, for example, the total volume of cargo transportation by transport enterprises, etc., the latter - only in the number of aggregate units, for example, the number of theaters by type of activity.
Quantitative features can be divided into discontinuous (discrete) and continuous.
statistical regularity is a form of expression causation, expressed in the sequence, regularity, recurrence of events with a sufficiently high degree of probability, if the causes (conditions) that give rise to the events do not change or change slightly. Statistical
the regularity is established on the basis of the analysis of mass data. It arises as a result of the action of objective laws, expressing causal relations.
Since a statistical pattern is found as a result of mass statistical observation, this determines its relationship with the law of large numbers.
The essence of the law of large numbers lies in the fact that in the numbers summing up the result of mass observations, certain regularities appear that cannot be detected on a small number of factors. The law of large numbers is generated by the properties of mass phenomena. It is important to remember that the tendencies and regularities revealed with the help of the law of large numbers are valid only as mass tendencies, but not as laws for each separate, individual case.
The subject and method are the essence of any science, including statistics.
statistics method. Statistics as a science has developed techniques and methods for studying mass social phenomena, depending on the characteristics of its subject and the tasks that are posed in its study. The techniques and methods by which statistics studies its subject form the statistical methodology.
Statistical methodology is understood as a system of techniques, methods and methods aimed at studying quantitative patterns that manifest themselves in the structure, dynamics and relationships of socio-economic phenomena. The task of statistical research is to obtain generalizing characteristics and identify patterns in 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 its individual elements. It is important to understand that statistical study consists of three stages:
- statistical observation;
- summary and grouping of observation results;
- analysis of the obtained generalizing indicators.
All three stages are interconnected, and each of them uses special methods, explained by the content of the work performed.
Cognitive tasks of statistics. Based on the nature and main features of the subject of statistics as a science, the following tasks can be formulated. This study:
The level and structure of mass socio-economic phenomena and processes;
Interrelations of mass socio-economic phenomena and processes;
Dynamics of mass socio-economic phenomena and processes.
It is also important to understand that statistics consists of a number of branches that have emerged in the process of development, and general theory of statistics is the methodological basis, the core of all sectoral statistics, as it develops the most general concepts, categories, principles that have a general statistical meaning, and methods for the quantitative study of socio-economic phenomena.
1.2. Tasks and exercises
1.1. Name as an example the spheres of public life studied by statistics.
1.2. Formulate a definition of statistics as a science and give it an appropriate justification.
1.3. Describe the main features of the definition of the subject of statistics:
a) Why is statistics a social science?
b) why does statistics study the quantitative side of social phenomena in connection with their qualitative content?
c) why does statistics study mass phenomena?
d) why should every statistical study be based on the study of all relevant facts?
1.4. What types (quantitative or attributive) do the following features belong to:
a) the number of employees in the firm;
b) family ties of family members;
c) gender and age of the person;
d) the social status of a depositor in Sberbank;
e) number of storeys of residential premises;
f) the number of children in the family;
g) retail turnover of trade associations.
1.5. Indicate what aggregates can be distinguished in a higher educational institution for statistical study?
1.6. Indicate which statistical aggregates of credit institutions can be distinguished; spheres of the consumer market; peasant farms.
1.7. What quantitative and attributive features can characterize the totality of university students?
1.8. The totality of commercial banks in Moscow is investigated. What quantitative and qualitative features can characterize it?
1.9. What are the most significant varying features that characterize the student group.
1.10. What are the main factor signs, which determine the variation in student performance.
1.11. What indicators can characterize the population of the city?
1.12. Give a list of indicators that could fully characterize the following phenomena in a statistical survey:
a) population;
b) consumer market;
c) industry;
d) transport and communications.
For this purpose, use the monthly journal of the Goskomstat of Russia "Statistical Review" or the statistical yearbooks of the Goskomstat of Russia.
1.13. Name the variable and non-variable signs in people, farms.
1.14. Find relevant data and compare the sex composition of the Russian population according to the 1970, 1979 and 1989 censuses. Based on this comparison, what conclusions can be drawn about the sex structure of the Russian population and the trends in its change?
1.15. What signs - discontinuous or continuous - are:
a) the population of the country;
b) the number of marriages and divorces;
c) production of light industry products in value terms;
d) capital investments in value terms;
e) the percentage of implementation of the plan for sold products;
f) the number of seats in the aircraft;
g) the yield of grain crops in centners per 1 ha.
1.16. What types (qualitative or quantitative) are the following characteristics:
a) the wage category of the worker;
b) academic score;
c) form of ownership;
d) type of school (primary, incomplete secondary, etc.);
e) nationality;
e) being married.
1.17. Find in the statistical collection of the State Statistics Committee of Russia and write down the statistical indicators for several qualitative and quantitative characteristics.
1.18. From the same collection (see task 1.17), write out the data on several discontinuous and continuous quantitative characteristics.
1.19. Using statistical collections, write down the data characterizing the structure:
b) use of monetary income of the population;
c) production investments by sectors of the economy.
1.20. According to the statistical collections of the State Statistics Committee of Russia, write down the data characterizing the dynamics for four to five years:
a) population;
b) production certain types food products;
c) export and import;
d) the US dollar exchange rate and the consumer price index for goods and paid services.
1.21. Name what concepts, categories and methods are presented in the branch of statistical science - the general theory of statistics.
1.22. What is the study of economic statistics. Which industries economic statistics you know?
1.23. Specify what explains the division of statistical science into separate branches and why the study of statistical science begins with the general theory of statistics?
1.24. List the specific methods inherent in statistical research.
1.25. What statistical collections do you know that are published in Russia?
1. Practical exercises. On this topic, it is advisable to hold a seminar "Statistical science, its subject and method." Sample workshop plan:
a) the subject of statistics;
b) statistical method;
c) branches of statistical science and tasks of statistics in a market economy.
In the process of discussing points a) and b) of the seminar plan, the following should be disclosed: the object of statistical study, the specific features of statistical science, its differences from other social sciences and the role qualitative analysis in statistics. Here, questions about the significance of the theory of knowledge as the methodological basis of statistical science and about the specific features of the statistical method should be considered. In the last paragraph of the seminar plan, it is necessary to consider the role of the general theory of statistics as a branch of statistical science.
Since the seminars are the first classroom studies in statistics, it is advisable to conduct them according to the reporting system. Practice shows that students usually experience significant difficulties in speaking at the first lessons without special and thorough preparation on any issue. The presentation of reports mobilizes the attention of the entire audience, arouses a desire to speak out on the issues under discussion.
At the same time, we do not consider the reporting system of seminars obligatory for everyone. Depending on the specific features of the group, its composition, a “free” form of the seminar can also be used, without preliminary distribution of reports among students.
2. Tasks for independent extracurricular work of students. You can offer to write short essays on the topic, as well as essays on outstanding scientists, such as A. Quetelet, V. Petty, Yu.Ya. Yanson, A.I. Chuprov, A.A. Kaufman, A.A. Chuprov and others.
3. Auditor's examination. On the topic, it is advisable to spend a half-hour test in the form of students' short answers to one or two questions (for example, "What is a statistical pattern?", "What does statistics study?", etc.). You can also recommend control questions based on and interpretation of specific statistical material. In particular, students are encouraged to offer a system of indicators characterizing the population, for example, countries, regions, districts, and ask them to draw the appropriate conclusions, as well as control questions in the form of tests.
Tasks
1. Indicate which statistical aggregates can be distinguished in material production.
Answer
2. Make a list of the most significant features of the following units of statistical observation: a) farms, b) theater.
Answer
3. The number of convicts in the region is distributed by age as follows (persons):
Determine in which year and in which age group the number of convicts per 1000 people was greater if the distribution of the region by age groups the following (thousand people):
4. The annual plan of the enterprise for 2004 provided for the release of marketable products in the amount of 36 million rubles. Actually released marketable products for this year in the amount of 31.5 million rubles. Determine relative value implementation of the plan for the release of marketable products.
Solution
5. There is the following distribution of 60 workers by age:
Define average age workers.
Solution
6. For one of the branches of the savings bank, the following data are available on the balance of deposits for 2003 and as of January 1, 2004 (million rubles):
Determine the chain and basic individual price indices, the physical volume of sales and turnover.
Solution
8. How did the prices for dairy products change on average if it is known that the volume of sales of these products increased by 18%, and the turnover - by 20%?
Solution
List of used literature:
1. Workshop on social statistics: textbook. allowance / ed. R.E. Efimova. - M.: Finance and statistics, 2005.
2. Salin, V.N. Socio-economic statistics: textbook / V.N. Salin, E.P. Shpakovskaya. - M.: Jurist, 2001.
3. Socio-economic statistics: workshop / ed. V.N. Salina, E.P. Shpakovskaya. - M.: Finance and statistics, 2003.
4. Salyeva, L.S. Workshop on socio-economic statistics: studies.-pract. allowance / L.S. Saliev; UrSEI ATiSO. - Chelyabinsk: UrSEI, 2005.
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