1

The analysis of disproportions in employment in the municipalities of the region as a whole, and in the context of large and medium-sized, small and micro enterprises, was carried out using the Ryabtsev Index, the main advantage of which over other methods for measuring shifts in the number of employed population in the regions of the republic is that that its value does not depend on the number of gradations of structures, that is, on the number of municipalities, therefore there is no overestimation of structural changes, and also that there is a scale for assessing the significance of differences in structures according to the index. A comparison of the structural indicators of the average number of employees in large and medium-sized enterprises showed that the processes of gradual reduction of workers in large and medium-sized enterprises had similar dynamics in each territorial entity of the Republic of Mari El, while the small business system not only does not cease to exist, but is also constantly expanding, although Of course, the level of small business development in the Republic of Mari El is still extremely low. Its formation is hampered by the current concentration of production, unstable economic situation, imperfections of the current tax legislation, and weak government support, which makes it necessary to increase the economic efficiency of municipalities.

regional employment structure

employment of the population of municipalities

Ryabtsev index

level of structure difference

1. Bredneva L.B. Study of the structure and structural differences in the economy of the Khabarovsk Territory // Bulletin of the KhSAEP. - 2011. - No. 1 (52). - P. 4-10.

2. Podzorov N.G. Analysis of the influence of factors on the volume and structure of the gross regional product of the Republic of Mordovia [Electronic resource]. - URL: http://sisupr.mrsu.ru/2010-1/pdf/podzorov3.pdf.

3. Republic of Mari El: statistical yearbook “Republic of Mari El” / Territorial body of the Federal State Statistics Service for the Republic of Mari El. - Yoshkar-Ola, 2011. - 464 p.

4. Statva A.L. Geographical analysis of employment of the population of the Omsk region: abstract. dis. ...cand. geogr. Sci. - Barnaul, 2005. - 24 p.

5. Utinova S.S. Employment and the labor market in the conditions of transformation of the Russian economy: abstract. dis. ... doc. econ. Sci. - M., 2003. - 48 p.

One of the main and most difficult tasks of market transformations is the formation of an effectively functioning, dynamic and civilized labor market. The state has ceased to be the only guarantor of employment, and in the current conditions, each person decides for himself whether to work or not. The idea of ​​the role of employment has changed radically. The results and consequences of the transformation of social and labor relations are reflected in changes in the employed population and its structure, which, under the influence of macroeconomic factors, are subject to further distortions that reduce economic activity and quality of life. First of all, this is due to the restructuring of employment due to changes in structure.

To study employment and the processes of its regulation in the region, it is advisable to carry out a typology of the regions included in it, since the Republic of Mari El does not act as a single monolith, but as a set of regions with specific characteristics of employment, priorities and development prospects.

To analyze employment in 17 administrative units of the republic (3 city districts and 14 municipal districts) we used data for two time periods - 2000 and 2010. - values ​​are the following indicators:

• number of employed population (total), people, calculated according to the ILO methodology based on sample surveys on employment problems at the end of the year;
• average annual number of employees at large and medium-sized enterprises, people, calculated according to data from organizations and enterprises for the year;
• average annual number of employees in small and micro enterprises, people, calculated according to data from organizations and enterprises for the year.

An analysis of the total number of employed showed that the majority of the total employed population in both 2000 and 2010. accounted for urban districts: 63.4 and 60.5%, respectively. In 2000, the share of the employed population in the total number of workers was 53.7% - Yoshkar-Ola; 6.6% - Volzhsk, 3.0% - Kozmodemyansk. A fairly large share of the total employed population at that time belonged to the Gornomarisky (4.5%) and Zvenigovsky districts (3.5%).

In 2010, Yoshkar-Ola continued to account for the largest share of workers - 46.2%. But if during the period under study the number of employees in the capital of the Republic of Mari El decreased by more than 18 thousand people, then the cities of Volzhsk and Kozmodemyansk during the time period under study not only expanded their shares in the distribution of workers to 8.2 and 3.8 %, respectively, but also increased the absolute values ​​of the total number of employees in their territory by 28.2 and 32.0%, respectively. Among the municipal districts in terms of the number of people employed in 2010, the leaders were the Medvedevsky district, which provided jobs for 9.3% of the employed population of the republic, and the Zvenigovsky district, where 5.9% of the employed worked. Such disproportions in employment are primarily associated with the geographical distribution of enterprises on the territory of the republic, which are predominantly located in the cities of the region, which, of course, serves as an additional factor in increasing the role of cities in the development of society - urbanization.

An analysis of the average number of employees at large and medium-sized enterprises showed that the reduction of workers in this group occurred everywhere during the study period. The Paranginsky, Mari-Tureksky, Kuzhenersky and Novotoryalsky districts stand out especially, where the growth rates of the analyzed indicator were 34.8, 39.0, 40.2 and 40.7%, respectively. The Medvedevsky district stands out significantly against the general background, in which the reduction in the average number of employees at enterprises of this group amounted to only 9.0%. In 2000, 54.9% of the average number of employees at large and medium-sized enterprises were in cities (Yoshkar-Ola - 42.4%, Volzhsk - 8.3%, Kozmodemyansk - 4.2%). Among the districts, Zvenigovsky (6.2%) and Medvedevsky (9.6%) stood out in terms of the number of employees in large and medium-sized enterprises. A similar situation was observed in 2010.

As for small businesses, the picture here is somewhat different. If in 2000 in the urban districts of the republic 16,013 people were employed in small enterprises and this accounted for 86.3% of the total number of employees in this group (76.4% worked in the city of Yoshkar-Ola), then by the end of 2010 , despite the impressive growth in the number of workers in this group, only 68.8% of the employed remained in cities (58.6% in Yoshkar-Ola). The Medvedevsky and Morkinsky districts have achieved especially significant success in the development of small businesses. If in 2000 their total contribution to the average number of employees of small and micro enterprises was slightly more than one percent, then by 2010 the Medvedevsky district already provided 6.0% of jobs, and the Morkinsky district - 2.2%.

Figure 1 shows the growth rates of the studied indicators for 2010/2000. The Medvedevsky district had the highest growth rates for all employment indicators. Here, the growth of the total number of employees reached 275.6%, which is primarily caused by the formation and development of small businesses, the average number of employees in which increased by 16.4 times. Yurinsky district, on the contrary, against the backdrop of a reduction in total employment by 51.9%, achieved the most insignificant success in the development of small businesses. The growth rate of the average headcount at enterprises of this group was the smallest in comparison with other administrative units of the republic - only 262.4%.

Rice. 1. Growth rate of the average annual number of employeesin the context of municipalities.

The growth rate of the average number of employees in large and medium-sized enterprises of the republic did not exceed 90.9% (Medvedevsky district). In urban districts alone, the average growth rate of this indicator was only 73.0%.

The negative dynamics of this indicator is due, first of all, to the reduction in the number of large and medium-sized enterprises and organizations on the territory of the Republic of Mari El, which in turn is due to the artificial fragmentation of larger enterprises in order to receive benefits or a lighter tax regime, as well as the redistribution of forms of ownership of enterprises in the region . The number of state-owned enterprises in the study period decreased from 861 to 746, of which the republican form of ownership - from 565 to 431.

The problems of small business development both in the country as a whole and in the republic have recently received quite close attention: decrees of the President of the Russian Federation, Government resolutions and decisions of local authorities are issued, various specialized funds and other infrastructure elements are created to support small businesses, since It is small enterprises that occupy a prominent place in the market for goods and services; they are most susceptible to changing conditions, to the introduction of new equipment, and the use of advanced technologies. With the help of individual entrepreneurship, social problems such as the creation of new jobs and other local problems are solved. Over the past ten years alone, the number of small businesses has grown by 542 units, while the average number of employees here has increased by 2.4 times over the same period.

The transition to market relations led to a transformation of the economy, the objective reflection of which is largely determined by the availability of general information about structural changes. The priority of studying structure indicators and their dynamics is determined by the need to present objective, high-quality, most complete information that adequately reflects the analyzed areas of employment to heads of government bodies for making effective management decisions.

At the same time, for adjacent periods of time, discrepancies in the structure of the total working population were interpreted for the most part as “identity of structures” in employment of the population in the context of municipalities, the V.M. index was used. Ryabtseva - integral coefficient of structural differences - criterion , :

(1)

where and are the specific gradations of the two structures; - number of gradations.

The advantage of this index over other methods for measuring changes in the number of employed people in the regions of the republic is that its value does not depend on the number of gradations of structures, that is, on the number of municipalities, therefore there is no overestimation of structural changes, and also in the presence of a scale for assessing the measure the significance of differences in structures by index (Table 1).

Table 1 - Scale for assessing the significance of differences in the number of employees according to the Ryabtsev index

Range of values	Characteristics of the measurestructural differencesin employment	Range of values	Characteristics of the measurestructural differencesin employment
	Identity of structures		Significant level of structural differences
			Very significant level of structural differences
			Opposite type of structures
		0.901 and above	Complete opposite of structures

In order to assess the significance of differences in the structure of employment of municipalities of the Republic of Mari El, calculations were made of the values ​​of Ryabtsev indices by year for the time interval from 2000 to 2010 for each of the previously considered employment indicators: number of employed population (total), people; average annual number of employees at large and medium-sized enterprises, people; average annual number of employees in small and micro enterprises, people.

Table 2 - Assessment of the significance of structural differences in employment in municipalities of the RME

Period	Ryabtsev index(employed population, total)	Interpretation	Ryabtsev index(employment in large and medium-sized enterprises)	Interpretation	Ryabtsev index(employment in small and micro-enterprises)	Interpretation
		Identity of structures		Identity of structures		Identity of structures
		Identity of structures		Identity of structures		Identity of structures
		Identity of structures		Identity of structures		Identity of structures
		Identity of structures		Identity of structures		Significant level of structural differences
		Low level of structure difference		Identity of structures		Identity of structures
		Identity of structures		Very low level of structure difference		Very low level of structure difference
		Identity of structures		Identity of structures		Very low level of structure difference
		Identity of structures		Identity of structures		Very low level of structure difference
		Identity of structures		Identity of structures		Very low level of structure difference
		Identity of structures		Identity of structures		Identity of structures
		Low level of structure difference		Low level of structure difference		Low level of structure difference

As follows from Table 2, the value of the criterion when comparing structural indicators of the number of employed population for the entire observation period (from 2010 and 2000) was 0.098, which indicates a low level of differences in structures in the number of employed population in the municipalities of the republic.

Over adjacent periods of time, discrepancies in the structure of the total working population were interpreted for the most part as “identity of structures,” which indicates that transformations in the distribution of the number of employed within administrative units proceeded at a very slow pace (Fig. 2).

Rice. 2. Dynamics of structural changes in employment in the republic.

The most significant structural transformations during the period under study characterized small businesses in urban districts and municipal areas.

A “significant level of difference in the structures” employed in small businesses was noted in 2003-2004, when the growth rate of the average number of employees in small and large enterprises in the republic was 125.4%. The Gornomariysky district stood out especially strongly against the general background at that time, in which in just one year the average number of workers in this group increased by more than 8 times, while in the urban districts of the republic small businesses were stagnating.

In the last decade, most administrative units of the region have seen an unusually rapid increase in the number of small enterprises. Constantly changing (small businesses appear quickly, but can quickly go bankrupt), the small business system not only does not cease to exist, but is also constantly expanding, although, of course, the level of development of small businesses in the Republic of Mari El is still extremely low. Its formation is hampered by the current concentration of production, unstable economic situation, imperfection of the current tax legislation, and weak government support.

The need to increase the economic efficiency of municipalities poses new challenges for the territories, primarily related to the choice of a competitive model of the regional economy that makes it possible to make maximum use of the existing potential.

Reviewers:

• Katkov Nikolay Semenovich, Doctor of Economics, Professor, Professor of the Department of Economic Cybernetics of the Mari State University, Yoshkar-Ola.
• Shvetsov Mikhail Nikolaevich, Doctor of Economics, Professor, Rector of the ANO VPO “Interregional Open Social Institute”, Yoshkar-Ola.

Bibliographic link

Sarycheva T.V. STATISTICAL STUDY OF EMPLOYMENT DISPROPORTIONS AT THE MUNICIPAL LEVEL OF THE REPUBLIC OF MARI EL // Modern problems of science and education. – 2012. – No. 4.;
URL: http://science-education.ru/ru/article/view?id=6865 (access date: 12/20/2019). We bring to your attention magazines published by the publishing house "Academy of Natural Sciences"

The structure of a particular set does not remain constant either in time or in space. The need to analyze changes in structures arises either when comparing the structures of different periods of time, or the structures of different territorial objects. In the first case they talk about structural shifts, in the second - about structural differences.

The difference in the structures of the compared populations can be expressed in the difference in the specific weights of individual parts of these populations. All indicators characterizing changes in structures are divided into absolute and relative. Absolute indicators of changes in structures are based on the difference between the specific gravities of the corresponding parts of different structures. They are measured in percentage points, can be positive or negative, and their sum is zero. They show by how many percentage points the share of the analyzed part in one structure increased or decreased (positive or negative value, respectively) compared to its value in another structure. Relative indicators are calculated by the ratio of the corresponding specific weights: if the result is greater than one, then the share of this element in the compared structure is greater than in the basic structure; if it is less than one, then the share of the analyzed element of the compared structure is the corresponding part of the share of this element in the basic structure. It should be noted that when analyzing changes in two structures, in order to obtain an objective picture of these changes, it is necessary to use both absolute and relative indicators. Let's consider official statistical data on the structure of cash income of the population of the Russian Federation by source of income for 2000 and 2011. (Table 6.5).

Using the presented data, we will calculate indicators characterizing structural changes in 2011 compared to 2000.

Table 6.5

Statistical data on the structure of cash income of the population of the Russian Federation by source of income for 2000 and 2011.

It is obvious that there were changes in the structure of cash income of the population of the Russian Federation in 2011 compared to 2000: the share of income from business activities and income from property decreased, and the share of other income items increased. This is confirmed by the signs of absolute change (pluses and minuses). Based on the results obtained, we can say that in terms of absolute changes, the largest changes occurred in the shares of income from business activities, social benefits and wages, and in relative terms, the most significant changes are observed for the shares of other income and income from property. The relative change is more clearly visible by the relative increase (decrease). Relative increase (decrease) is calculated from relative change (multiplying by 100 and subtracting 100%). This means that the share of income from business activities decreased by 6.3 percentage points in 2011 compared to 2000, or amounted to 41% in 2011 of its value in 2000; the share of wages in 2011 compared to 2000 increased by 4.3 percentage points, or 1.07 times, or 7%. Similarly, conclusions can be drawn about other sources of income. The different degrees of changes in absolute and relative indicators are explained by differences in the size of the share of individual elements. An increase in the share of other income by 0.8 percentage points gave the maximum increase in relative change, since the very value of the share of this source of income generation is the smallest. At the same time, the increase in the share of wages by 4.3 percentage points amounted to the smallest relative change of 1.07, or an increase of 7%. It is worth paying attention to the content of the changes that have occurred over the past 10 years, reflected in this example. In the structure of income of the population of the Russian Federation, the shares of wages and social payments have increased and the shares of income from business activities, income from property and other income have decreased.

Absolute and relative indicators of change in individual parts of the whole are disproportionate to each other: smaller absolute changes may correspond to larger relative changes, and larger absolute changes may correspond to smaller relative ones. That is why, when analyzing changes in the structure of any population, both absolute and relative indicators of changes in structures should be calculated in order to obtain a more accurate idea of ​​the structural changes in the compared structures.

Moving on to general indicators, let us pay attention to the following point. If the total volume of the population under study grows, then the relative indicators of change for individual elements of the population may be greater or less than unity, i.e. they can grow and contract. Moreover, if the relative indicator of change in an individual element is greater than the relative change in the entire aggregate, this means that the specific weight of this element in the aggregate is growing. Accordingly, if the relative indicator of change for any element or part of the population is less than the same indicator for the entire population as a whole, this means that the share of this part in the total volume is decreasing. Thus, a change in the structure of the whole is a consequence of the uneven intensity of change in its individual parts, i.e. differences in relative changes in specific gravity.

When analyzing changes in structures, a generalized description of these changes is often required. The following indicators can be used for this.

1. Sum of absolute changes in specific gravity

where are the proportions of individual elements of the two populations being compared; n- the number of elements (groups) in total.

The sum of absolute changes in specific weights is expressed in percentage points. This value characterizes the total volume of deviations of one structure from another.

.

The difference index, calculated through specific gravities expressed as percentages, can take values ​​from 0 to 100%; approaching zero means no change; approaching maximum indicates a significant change in the structure.

3. Integral coefficient of structural shifts K. Gateva. The above indicators do not provide an idea of ​​changes in the shares of individual elements of the population. This indicator takes into account the intensity of changes in individual groups in the compared structures:

.

The number of groups into which the population under study is divided affects the final assessment of structural changes.

4. Salai Structural Difference Index. This indicator also takes into account the number of groups or elements in the compared structures:

.

Both last presented coefficients (or indexes) can take values ​​from zero to one. The closer the resulting value is to unity, the more significant the structural changes that have occurred. The Szalai coefficient takes values ​​close to one when the total number of units is large.

5. Ryabtsev index. The values ​​of this indicator do not depend on the number of gradations of structures. The assessment is made on the basis of the maximum possible value of discrepancies between the components of the structure; the actual discrepancies of individual components of the structures are compared with the maximum possible values:

.

This coefficient (index) also takes values ​​from zero to one. An advantage of this indicator can be considered the presence of a scale for assessing the obtained indicator values ​​(Table 6.6).

Table 6.6

Scale for assessing the significance of structural differences using the Ryabtsev index

Thus, the listed indicators represent a generalized characteristic of structural changes, but do not give an idea of ​​the magnitude of these changes.

The following indicators give this idea.

6. Average linear change in shares

.

7. Mean square change

.

The average estimate of the measure of change (per one group, population unit) is represented by the average linear change in shares or the root mean square of these changes. The obtained values ​​show how many percentage points on average the specific weights of the compared structures deviate from each other. The analytical content of these two indicators is the same. However, the square mean is always greater than the arithmetic mean, so the value of the root mean square change will be greater than the linear mean. Two indicators will be equal if the absolute changes in the specific weights of all parts of the whole are equal in absolute value. In the absence of changes in structures, these indicators are equal to zero. Since the degree of the average linear change corresponds to the degree of the indicator itself, this estimate should be considered more accurate, however, the mean square change is more often used, since it reacts more sensitively to weak fluctuations in the structure.

When using the listed indicators, the analysis of changes in structures occurs without taking into account the size of the base from which this change occurred. A more accurate assessment can be made by using relative rather than absolute changes. In particular, the average relative linear change can be calculated as the average of the relative linear deviations (i.e., growth rates) taken modulo:

.

The result multiplied by 100 can be expressed as a percentage and easily evaluated.

An example of solving problem 3.

According to the sample survey, the following distribution of the organization’s employees by salary was obtained:

Define:

1. Average salary.

2.Coefficient of variation.

3.Mode and median

1. The task condition is represented by an interval variation series with equal intervals. Therefore, to calculate indicators, you must first determine the value of the averaged characteristic (X) as the middle of each interval and obtain a discrete distribution series.

2. The coefficient of variation characterizes the measure of fluctuation of individual variants of a characteristic (x) around the average value. It represents the percentage ratio of the standard deviation (σ) and the arithmetic mean () , that is

To calculate the standard deviation, we first calculate the dispersion (σ 2) using the formula:

The calculation can be done using the auxiliary table

x	m	X-	(x- ) 2	(x- ) 2 m
		12500-15095
		13500-15095
		14500-15095
		15500-15095
		16500-15095
Total		-	--

Standard deviation - is the square root of the variance:

σ = ±√ σ 2 = ± ±1100.443 rub.

The coefficient of variation will be:

If the value of the coefficient of variation does not exceed 33.3%, then the population is considered homogeneous, and the average value can be considered typical for a given distribution. In our example, the average value is typical.

3. Mode (dominant) is the most common value of the attribute x; in an interval series, the modal interval will be the interval that has the highest frequency (frequency).

In this task, the interval 15,000 - 16,000 rubles has the highest frequency (65), therefore, the mode will be in this interval.

Consequently, the largest number of workers had a salary of 15,280 rubles.

Median is the value of the attribute for that unit of the ranked series that is in its middle. First, let's determine the serial number of this unit. To do this, add one to the sum of all frequencies of the series () and divide the result in half, that is

The median salary value will be the one that is half the sum of the salaries of the 100th and 101st employees. They fall into the fourth interval (10+20+58+65=153) according to the sum of accumulated frequencies, that is, from 15,000 to 16,000 rubles.

Consequently, half of the workers have a salary of no more than 15,184.6 rubles, and the other half - no less than 15,184.6 rubles.

To compare the structure of statistical aggregates, compare actual and normative structures, and to quantify dynamic structural changes (structural shifts), indicators of structural differences can be used. A generalizing quantitative assessment is given by integral indicators of structural differences:

Salai index:
V. Ryabtsev index:

where d 1i and d 0i are the structural components being compared,

n – number of structural gradations (distinguished groups).

Graphical comparative analysis of structure

In socio-economic research, situations often arise in which it is necessary to analyze the structures of phenomena or processes over a number of periods. One of the methods of analysis in this case is to consider structural diagrams.

The most common structural diagram is the pie or pie

Figure - Composition and structure of the unemployed by education in 2003, %

This type of diagram is most convenient to use when illustrating the structure of a phenomenon for one, two or three periods, but in practice a situation may arise when it is necessary to compare the structure for 5 or more periods. In this case, you need to use a donut chart.

Figure - Composition and structure of the unemployed by education in 1992. and 2003, %

Figure - Composition and structure of the unemployed by education in 1992, 1998, 2002-2003, %

To assess changes in the structure of the population over time and determine the structures of individual groups, indicators of structural differences and shifts are used. The simplest indicators of structural differences are [page 37, Timofeeva]:

Linear coefficient of structural differences (shifts) or Re index:

Where d1, do- structure of the reporting and base periods, %

P - number of lines.

Shows how much, on average, the structure of the reporting period does not correspond to the structure of the base period. A disadvantage of the indicator is the fact that its value depends on n. If n is small, then the index takes small values ​​and vice versa.

Quadratic coefficient of structural changes:

0 £ d£100 or £0 s£100 (if data measured in %).

The closer the value of the indicators is to 0, the smaller the differences in the structures of the populations being studied; or the smaller the changes that have occurred in the structure of the population in dynamics.

Linear and quadratic coefficients are used mainly to study the dynamics of structure indicators, because clearly allow one to draw conclusions about the intensity of changes in structures in certain periods of time.

Gateva Index(Gatev index) distinguishes structures with equal sums of squared deviations.

Ryabtsev index(Ryabtsev index) differs slightly from the Gatev index and takes lower values:

Salai Index(Szalai index) was introduced when studying differences in the structure of time budget use among different population groups:

The Salai index differs from all the indices of this group discussed above. It takes values ​​close to one when the total is a large number of units.

The given indices take values ​​in the range from 0 to 1. If one or another index is equal to zero, then complete similarity of structures is observed, if one is a complete difference. If more than 0.5, then the differences in the structure of the reporting and current periods are considered significant.

The following conditional data are available on the structure of cash incomes of the population of the region, in percentage:

It is necessary to draw a conclusion about changes in the structure of cash incomes of the population.

Solution.

Based on the above indicators, we can conclude that in the composition of the population’s cash income, the share of wages decreased (from 60% in the base period to 42% in the reporting period) with an increase in the share of income from property and business activities (from 24% to 44%, respectively) .

A generalizing characteristic of the measure of structural changes is given by integral indicators of structural differences, the calculation of which is illustrated in the table:

The magnitude of the calculated indicators of structural differences indicates significant changes in the structure of monetary incomes of the population of the region.

Problems 5-6 involve studying the dynamics of indicators, i.e. the intensity of changes in phenomena over time, which are carried out using the following indicators: absolute growth, growth rates, growth rates, the absolute value of one percent of growth, as well as average generalizing indicators.

Depending on the research objective, indicators can be calculated with a variable base of comparison (chain) and with a constant base of comparison (basic).

1. Absolute increase is the difference between the level being compared and the previous or baseline:

chain absolute increase:

base absolute increase: .

The sum of chain absolute increases is equal to the basic absolute increase for the corresponding period of time.

2. Growth rate– a relative indicator characterizing the intensity of development of the phenomenon; it is equal to the ratio of the level being studied to the previous or basic level and is expressed in coefficients or percentages.

chain growth rate: 100;

base growth rate: .

The product of the corresponding chain growth rates calculated in coefficients is equal to the base one.

3. Rate of increase determined in two ways:

a) as the ratio of absolute growth to the previous level (chain) or basic level (basic):

chain growth rate:

base growth rate: .

b) as the difference between the growth rate and 100%:

T pr = T r -100%.

4. Absolute value of one percent increase is defined as the ratio of the chain absolute increase to the chain growth rate (%) or for each subsequent level - as 0.01 of the previous level of the dynamics series:

5. Average absolute increase calculated using the simple arithmetic average, that is, dividing the sum of chain absolute increases by their number

Average growth rate found using the geometric mean formula:

Average growth rate found by subtracting 100% from the average growth rate:

Calculation methods mid-level Some dynamics depend on its type and completeness of information.

1) in interval series with equal time intervals, the average level is determined by the simple arithmetic mean formula:

2) in interval series with unequal time intervals - according to the weighted arithmetic mean formula (based on the size of the intervals):

3) in moment series with comprehensive data on changes in the moment indicator, the calculation is made using the arithmetic mean of the series levels that remained unchanged for certain periods of time, weighted by the value of the corresponding intervals;

4) in moment series of dynamics with equally spaced levels, the average chronological simple formula is used.