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. 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. It includes the most essential features that meet the goal. It is important to establish not only the signs, but also clearly and clearly give her wording and 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. 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. It is recommended to leave space for encryption on the form. Statistical forms—information carriers—are questionnaires that must be filled out by methodologists of these departments. 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 problem 5 of Chapter. 1. 7. In table. 1.2 provides a list of several statistical observations. Indicate in what form and type of statistical observation each of them belongs.

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.
The solution of 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) will be determined by the formula:

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

The growth rate (relative growth rate 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 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

(theory of statistics)

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 close connection, etc. are used as analytical indicators.

Currently, the main tasks 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 with 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, 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 an increase in the qualifications of drivers and the percentage of fulfillment of production standards, wages increase. Thus, the wages of Class I drivers who meet the production standard by 110% and above are 32.5% higher than the wages of Class II drivers who meet the standard 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 different parts of the population being studied, therefore, general averages for a homogeneous population must be supplemented by group averages that characterize 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. The frequencies are 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 the 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 K. Pearson's 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; thirty; 22; 23; 35; 33; 27; 24; thirty; 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 forms. 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 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 area of ​​the histogram and the area of ​​the polygon are equal in pairs, and, therefore, the area of ​​the histogram and the area of ​​the polygon 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 a probability of 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 monetary 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, the enterprise's 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.

Ministry of Education and Science of the Republic of Kazakhstan

Kostanay State University named after. A. Baytursynova

PRACTICUM IN STATISTICS

Tutorial

INTRODUCTION

Statistics is the art and science of collecting and analyzing data. Statistical methods should be viewed as an important part of the decision-making process, allowing the development of sound statistical decisions that combine specialist intuition with careful analysis of available information.

Modern specialists must master statistical methods, be able to apply them in assessing the conditions and results of the development of socio-economic relations, determine the influence of various factors, and know the system of indicators characterizing the economic and social life of the population and the country as a whole.

The purpose of this textbook is to provide methodological assistance to students and undergraduates in mastering the methodology for calculating statistical indicators and acquiring skills in analyzing the results obtained. The manual covers all topics of the general theory of statistics course. At the beginning of each section, a brief theoretical description of the topic is given, and formulas are given. The workshop provides examples of solving typical problems, their implementation in the MS Excel environment, and there are tasks for independent implementation.

For the most part, the tasks are based on actual data; in some cases, conditional indicators are given.

The textbook is intended for students of economic specialties.

TOPIC 1. SUBJECT AND OBJECTIVES OF STATISTICS

1.1 Guidelines

Historical information. The word “statistics” comes from the Latin word “status” - state, state of affairs. Initially it was used to mean “political state”. Hence the Italian word “stato” - state and “statista” - expert of the state. The word “statistics” came into scientific use in the 18th century. and was originally used in the meaning of “government”. Nowadays, statistics can be defined as the collection of mass data, their synthesis, presentation, analysis and interpretation. This is a special method that is used in various fields of activity, in solving various problems. Historically, the development of statistics was associated with the development of states, with the needs of public administration. Economic and military needs already in the ancient period of human history required the availability of data on the population, its composition, and property status. For tax purposes.

Kazakhstan's statistics have their roots in the distant past. There is historical evidence of statistical information about the first Kazakh state - the Kazakh Khanate: at the beginning of its formation (1459) in the valleys of the Shu and Talas rivers (in the territory of the present Zhambyl region), the population was 200 thousand people, and by the end of the 15th century it reached 1 million.

However, the emergence of more or less regular and centralized statistical activity on the territory of modern Kazakhstan dates back to the second half of the 18th century, i.e., to the period of Kazakhstan’s entry into the Russian Empire. The first general population census on its territory, as well as throughout tsarist Russia, was carried out on February 9 (January 28), 1897.

The first official state statistical body formed on the territory of Kazakhstan is the Turkestan Provincial Statistical Committee (founded on January 22, 1868) and its subordinate statistical bureaus in the Syr-Darya and Semirechensk regions. In the mid-70s of the 19th century, the Ural Regional Statistical Committee was organized, in 1877 - the Semipalatinsk and Akmola (in Omsk) and in 1895 - the Turgai regional statistical committees. However, until 1920, there was no single statistical body in Kazakhstan that united these and other local statistical services.

With the formation (August 26, 1920) of the Kazakh Autonomous Socialist Republic as part of the RSFSR, the Government of the Kazakh Autonomous Soviet Socialist Republic, by its resolution of November 8, 1920, approved the “Regulations on state statistics in the Kazakh Autonomous Soviet Socialist Republic” and formed the Statistical Department of the Autonomous Soviet Socialist Republic.

Thus, the date of formation of unified centralized statistical bodies of Kazakhstan is considered to be November 8, 1920 (see “Main historical milestones of Kazakhstan statistics” Appendix 2).

Stages of development of statistics in Kazakhstan. Over the past fifteen years, the Agency of the Republic of Kazakhstan on Statistics has conditionally gone through the following phases of development:

1. Formation of the Agency as a National Authority creating the main methodological know-how, implementation of the System of National Accounts standard (SNA 93) - 1992-1996.

2. Mastering the methodology for compiling integrated accounts and SNA tables; launching the systematic use of internationally agreed statistical classifiers; the beginning of the creation of statistical registers; introduction of statistical methods for producing information on small enterprises; introduction of new information and communication technologies - 1996-1998.

3. The actual implementation of international classifications in all areas of statistical production; successful implementation of the first Kazakhstan population census in 1999 and the development of demographic social statistics; introduction of advanced methods of mass data processing, obtaining technical assistance within the framework of international cooperation 1995-2005.

4. Implementation of the Program for Improving State Statistics, including the revision of methodologies and classifications, adaptation of developing international standards, the beginning of the implementation of a metadata system and integrated classifications - 2006-2008;

Workshop on the theory of statistics. Shmoilova R.A., Minashkin V.G. and etc.

3rd ed. - M.: 2014 - 4 16 p.

Compiled in accordance with the standard curriculum for the course “Theory of Statistics”. Contains a brief overview of the basic concepts of the general theory of statistics, grouping of statistical data, absolute, relative and average values, statistical distributions, sample observation, time series, indices and their use in economic and statistical research, etc. Typical examples with solutions and problems (with answers) on the material being studied are presented, as well as recommendations for teachers. The appendices contain the mathematical and statistical tables necessary to solve the problems. For teachers, graduate students, students of economic universities, managers, students of special faculties of second higher education.

Format: pdf ( 2014 , 3rd ed., 416 pp.)

Size: 90 MB

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Format: djvu (2009 , 3rd ed., 416 pp.)

Size: 6.4 MB

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TABLE OF CONTENTS
Preface 5
Section I. DESCRIPTIVE STATISTICS
Chapter 1. Statistics as a science 7
1.1. Guidelines 7
1.2. Problems and exercises 12
1.3. Recommendations for teachers 15
Chapter 2. Collection of statistical information (theory of statistical observation) 16
2.1. Guidelines 16
2.2. Problems and exercises 22
2.3. Recommendations for teachers 28
Chapter 3. Statistical summary and grouping 29
3.1. Guidelines and solutions to typical problems 29
3.2. Problems and exercises 47
3.3. Recommendations for teachers 53
Chapter 4. Statistical tables 53
4.1. Guidelines and solutions to typical problems 53
4.2. Problems and exercises 62
4.3. Recommendations for teachers 72
Chapter 5. Graphical representation of statistical data 73
5.1. Guidelines and solutions to typical problems 73
5.2. Problems and exercises 90
5.3. Recommendations for teachers 99
Chapter 6. Forms of expression of statistical indicators 100
6.1. Guidelines and solutions to typical problems 100
6.2. Problems and exercises 112
6.3. Recommendations for teachers 123
Section II. ANALYTICAL STATISTICS
Chapter 7. Variation indicators and analysis of frequency distributions 124
7.1. Guidelines and solutions to typical problems 124
7.2. Problems and exercises 156
7.3. Recommendations for teachers 167
Chapter 8. Selective observation 169
8.1. Guidelines and solutions to typical problems 169
8.2. Problems and exercises 178
8.3. Recommendations for teachers 186
Chapter 9. Statistical study of the relationship between socio-economic phenomena 187
9.1. Guidelines and solutions to typical problems 187
9.2. Problems and exercises 222
9.3. Recommendations for teachers 233
Chapter 10. Statistical study of the dynamics of socio-economic phenomena 234
10.1. Guidelines and solutions to typical problems 234
10.2. Problems and exercises 260
10.3. Recommendations for teachers 279
Chapter 11. Statistical analysis of structure 280
11.1. Guidelines and solutions to typical problems 280
11.2. Problems and exercises 292
11.3. Recommendations for teachers 299
Chapter 12. Economic indices 300
12.1. Guidelines and solutions to typical problems 300
12.2. Problems and exercises 317
12.3. Recommendations for teachers 325
Chapter 13. General issues of analysis and synthesis of statistical data 325
13.1. Guidelines and solution of complex problems 325
13.2. Problems and exercises 349
13.3. Recommendations for teachers 352
Tasks for independent work of students 353
Applications 359
Answers to problems 412

The purpose of the workshop is to help students better understand the categories of statistical science, teach them to apply scientific methods of statistical research and see the specific content behind statistical indicators, as well as develop practical skills in solving specific problems of various types in different areas of economics. In terms of content, terminology and symbolism used, the workshop is focused on the textbook edited by Professor R.A. Shmoilova “Theory of Statistics”, which has successfully gone through four editions: the first edition was published in 1996, and the fourth in 2003.
The workshop consists of two sections and thirteen chapters. Each chapter contains three subsections: Methodological instructions and solutions to typical problems, Tasks and exercises, and Recommendations for teachers.
The first subsection provides methodological instructions for students, which reveals the main categories of statistical science and shows the methodology for calculating indicators that are used in analytical work, as well as solutions to typical problems (except for chapters 1 and 2).
The second subsection presents a set of tasks and exercises for conducting practical classes and independent assignments for students, based on factual data taken from statistical collections and periodicals, or on conditional data. At the end of the workshop, answers to complex problems are given.