The next type of relative values ​​is the relative value of comparison, or as it is also called the relative indicator of comparison. According to its status, the value of comparison is most likely the fifth among all relative values, after , and . But in terms of frequency of use, perhaps the first. In addition, in this part we will consider two more relative values, which can also be used for analytical purposes.

Relative comparison value

The thing is that the relative value of the comparison compares one indicator with another. We get that the comparison indicator is the relative value itself. What are relative values ​​​​and how it is calculated can be viewed.
The relative value of the comparison characterizes comparative sizes of different objects or absolute values, but related to the same phenomenon. For example, a package of milk with a volume of 1 liter in one store costs 50 rubles, and in another 60 rubles, then we can compare their cost and find out how many times one costs more than the other. 60:50 = 1.2. That is, a package of milk in the second store costs 1.2 times more.
Such a simple action is used to calculate the relative values ​​of the comparison, and the calculation process may consist not of one action, but of several at once. If several objects are used as compared values, and the base of comparison will naturally be one.
Given the above, determine the relative comparison value (RVR) can be obtained from the following formula

In this case, as in any relative value, the numerator (top) contains the compared value, and the denominator (bottom) contains the base value. The basic value may vary depending on the task and the purpose of the calculation. For example, it has data on meat production in the Moscow region, Tula region, Bryansk region, Smolensk region. If we take the Moscow region as the comparison base, then we will divide all the data for other regions by the data for the Moscow region. If, however, we take the Tula region as a comparison base, then, consequently, we will divide the data for all other regions by the data for the Tula region.
Example. Provisional data are available for milk production in four oblasts. Calculate the relative comparison indicator, taking the data for the Moscow region as the comparison base, and then the data for the Tula region.

Other variants of parts are also possible, for example 3 with 1 and so on.

Relative value of development intensity

The intensity value shows the degree of development of some indicator in some environment. The method of calculating the intensity index is classical, and is similar to calculating the comparison value.
Often the intensity value is calculated as a percentage, ppm.
Commonly used in population statistics to characterize demographics. For example, birth rates.
The number of people born in the city was 15 people for every thousand living. This is an example of the intensity of development.
In addition, this method of calculation is also used in the economy of the organization. Capital-labor ratio is an indicator characterizing the value of fixed assets per employee.
To return to the list of lectures .

The result of the analysis of processes and phenomena studied using statistical methods is a set of numerical characteristics that can be classified into absolute and relative indicators.

Absolute indicators

Absolute values ​​in terms of statistics are the number of units or amounts in the sample, which are the direct result of the summary and grouping of the analyzed data. Absolute indicators reflect, so to speak, the "physical" characteristics of the processes and phenomena under study (area, mass, volume, spatio-temporal parameters), which, as a rule, are recorded in primary accounting documents. Absolute values ​​always have a dimension. We also note that, in contrast to the mathematical interpretation, the statistical absolute value can be either positive or negative.

Classification of absolute indicators

Absolute values ​​are classified according to the method of presenting the dimensions of the phenomena under study into individual, group and general.

TO individual include absolute indicators expressing the numerical dimensions of individual units of the population. For example, the number of employees in the organization, the gross output of the enterprise, profit, etc.

group indicators are called parameters that determine the dimensional characteristics or the number of units in a certain part of the population. Such indicators are calculated by summing up the corresponding absolute parameters of individual units of the study group or by directly counting the number of units in a sample from the general population.

Absolute indicators that describe the size of a feature in all units of the population are called general. Such parameters are the result of a summary of the results of statistical studies. These indicators include the wage fund of enterprises in the region, wheat in the state, etc.

Definition of relative value

From the point of view of statistics, a relative value is a generalizing parameter that describes the quantitative ratio of two absolute values. In other words, relative indicators characterize the relationship and interdependence of two compared absolute parameters.

Application in socioeconomic research

Relative indicators play an important role in the analysis of socio-economic processes, since the absolute characteristics themselves do not always allow a correct assessment of the analyzed phenomenon. Often, their true significance is revealed only during comparison with another absolute indicator.

Relative indicators include parameters that determine the structure of the phenomenon, as well as its development over time. With their help, it is easier to trace the trends in the development of the process under study and to make a forecast of its further evolution.

The main feature of relative values ​​is that they make it possible to carry out processes that are incomparable in absolute terms, which, in turn, opens up opportunities for comparing the levels of development or the prevalence of various social phenomena.

The principle of calculating the relative value

In relation to absolute indicators, which are input data for statistical analysis, relative values ​​are derived from them, or secondary. The calculation of relative indicators in general terms is performed by dividing one absolute parameter by another. In this case, the value in the numerator is called the compared, or current, and the indicator in the denominator with which the comparison is made is the basis (base) of comparison.

Obviously, it is possible to perform a comparison even of seemingly completely unrelated absolute values. Relative indicators necessary for statistical analysis should be chosen based on the objectives of a particular study and the nature of the primary data available. At the same time, it is necessary to be guided by the principles of visibility and ease of perception.

As current and basic indicators for calculation, you can use not only absolute, but also relative characteristics. Relative parameters obtained by comparing absolute characteristics are called first-order indicators, and relative parameters are called higher-order indicators.

Dimensions of relative values

Statistical analysis allows you to calculate relative indicators for both the same and opposite values. The result of the comparison of the parameters of the same name are unnamed relative values, which can be expressed in multiplicity factors, representing how many times the current indicator is greater or less than the base one (in this case, one is taken as the basis for comparison). Often in statistical studies, the comparison base is taken equal to 100. In this case, the dimension of the obtained relative indicators will be percentages (%).

When comparing dissimilar parameters, the ratio of the corresponding dimensions of indicators in the numerator and denominator is taken as the dimension of the obtained relative value (for example, the indicator of GDP per capita has the dimension of million rubles / person).

Classification of relative values

Among the variety of relative parameters, the following types are distinguished:

• indicator of dynamics;
• indicators of the plan and implementation of the plan;
• intensity indicator;
• structure index;
• indicator of coordination;
• comparison index.

Dynamic indicator (OPD)

This parameter describes the ratio of the current level of development of the phenomenon under study to some, taken as a base, the level of its development in the previous period. Expressed as a multiple ratio, the relative indicator of dynamics is called the growth factor, and as a percentage - the growth rate.

Plan Indicators (PPI) and Plan Implementation Indicators (PIP)

Such indicators are used by all economic entities involved in current and strategic planning. They are calculated as follows:

The characteristics discussed above are related by the following relationship:

OPD \u003d OPP * OPP.

The relative indicator of the plan determines the intensity of the task compared to the previous period, and the implementation of the plan determines the degree of its implementation.

Structural Index (SIR)

This relative indicator shows the structural composition of the population and is expressed in relation to the size of the absolute attribute of the structural part of the object under study to the size of the attribute of the population as a whole. In other words, the calculation of structure indicators consists in calculating the specific weight of each part of the population:

OPS are usually expressed as fractions of a unit (coefficients) or percentages. The sum of the specific weights of the structural parts of the studied population should be equal to one or one hundred percent, respectively.

Such coefficients are used in the study of the structure of multicomponent complex phenomena, for example, in the study of emissions of harmful substances by vehicles of a traffic flow, separating them by the type of fuel used (gasoline, diesel, gas) or by purpose (cars, trucks, buses), etc.

Index of Coordination (CPI)

This parameter characterizes the ratio of the characteristics of some part of the statistical population to the characteristics of the base part. The relative indicator of coordination is used in statistical analysis for a more visual representation of the relationship between the individual parts of the population under study.

The part of the population with the maximum specific gravity or being a priority is chosen as the basic one.

Intensity Index (IIR)

This characteristic is used to describe the propagation of the phenomenon (process) under study in its own environment. Its essence lies in the comparison of oppositely named quantities related to each other in some way.

An example is indicators of the level of GDP per capita, demographic indicators of natural increase (decrease) of the population per 1000 (10000) people, etc.

Comparison indicator (CFR)

This parameter describes the ratio of the same absolute characteristics of different objects:

The relative comparison indicator can be used for comparative analysis, for example, the population of different countries, prices for the same goods of different brands, labor productivity at different enterprises, etc.

The calculation of relative characteristics is an important step in statistical analysis, however, considering them regardless of the primary absolute indicators, one can come to unreliable conclusions. Consequently, a correct assessment of various socioeconomic processes and phenomena should be based on a system of parameters, which includes both absolute and relative indicators.

By itself, the absolute value does not give a complete picture of the phenomenon under study, does not show its structure, the relationship between individual parts, development over time. It does not reveal correlations with other relative indicators. These functions perform relative indicators determined on the basis of absolute values.

Relative indicator- this is a generalizing indicator, which is the result of dividing one absolute indicator by another and expresses the ratio between the quantitative characteristics of socio-economic processes and phenomena:

current / compared

index

base / comparison base

Relative indicators can be expressed in coefficients, percentages, ppm, decimilles, or named numbers. If the base of comparison is taken as 1, then the relative indicator is expressed in coefficients, if the base is taken as 100, 1000 or 10,000, then the relative indicator is respectively expressed as a percentage ( % ), ppm ( %O) and prodecimille ( %oo).

All relative statistical indicators used in practice can be divided into the following types:

Relative indicator of dynamics(OPD) is the ratio of the level of the process or phenomenon under study in a given period of time to the level of the same process or phenomenon in the past and shows how many times the current level exceeds the previous one, or what proportion of it is:

Moreover, if the level of the phenomenon at the initial moment of time (basic) is chosen as the basis of comparison, then we get basic indicator, if the level of the phenomenon for the previous moment of time is chosen as the base, then we get chain index.

If this indicator is expressed as a multiple ratio, it is called growth rate, multiplying this factor by 100% gives growth rate.

Relative target indicator(HPP) is calculated as the ratio of the level planned for the future period ( y sq.), to the level actually formed in the past ( y 0):

Relative indicator of plan implementation(OPRP) - is defined as the ratio of the level actually achieved in the current period ( y 1) to that planned for the same period ( y sq.):

There is the following relationship between the relative indicators of the planned target, the implementation of the plan and the dynamics:

OPPP ´ OPRP = OPD.

Relative structure index(OPS) characterizes the share or specific gravity of a part of the population in its total volume:

OPS is expressed as a simple multiple ratio (in fractions of a unit) or as a percentage.

Relative indicators of coordination(OPK) reflect the ratio of individual parts of the whole to each other:

As a result, it is determined how many units of each structural part account for 1 unit of the basic structural part.

Relative intensity indicator(OPI) is always a named value and characterizes the degree of distribution of the process or phenomenon under study in its inherent environment:

OPI are calculated by comparing opposite quantities that are in a certain relationship with each other and are usually determined per 100, 1000, etc. units of the studied population (for example, the number of births per 1000 people, agricultural production per 1 hectare of agricultural land, etc.).

A variety of OPIs are relative indicators of the level of economic development characterizing production per capita.

Relative Comparison Index(OPSr) is the ratio of absolute indicators of the same name characterizing different objects (enterprises, firms, districts, regions, countries, etc.), but related to the same point in time (for example, the ratio between the cost levels of one type of product, issued by different companies):

Despite the great importance of relative values ​​in statistics, they cannot be considered in isolation from absolute indicators. Only the complex application of these quantities provides reliable information about the phenomena or processes under study.

Average values

When analyzing and planning, it is necessary to rely not on random facts, but on indicators expressing the main, typical. This characteristic is given by average values.

average value- this is a general indicator that characterizes the typical level of a variable trait per unit of a homogeneous population in specific conditions of place and time.

When calculating the average value, the individual values ​​of a characteristic are replaced by one average value. At the same time, random deviations of the value of the attribute for individual units in the direction of increasing or decreasing mutually balance and cancel each other, and the average value shows the typical size of the attribute characteristic of this group or population as a whole, which makes it possible to identify patterns inherent in mass social phenomena that are invisible in single occurrences.

The average value is always named, it has the same unit of measurement as the attribute of individual units of the population.

In statistics, two categories of averages are used:

1. Power Averages – arithmetic mean, harmonic mean, geometric mean and mean square.

2. Structural averages – mode and median.

Power Averages

Power averages, depending on the presentation of the initial data, can be simple and weighted.

simple average calculated on ungrouped data and has the following form:

,

n is the number of population units.

Weighted average is calculated from the grouped data and has the form:

,

where х i is the value of the feature for the population unit i,

m is the exponent of the average,

f i - frequency showing how many times the i-th value of the feature occurs.

Power mean formulas have a common exponent m. Depending on what meaning it takes, there are the following types of power means :

1. Arithmetic mean (m=1) - the most common type of medium.

simple	weighted

Note . If the values ​​of the averaged feature are given in the form of intervals, then when calculating the arithmetic mean value, the midpoints of these intervals are taken as the values ​​of the features in groups, resulting in a discrete series. In this case, the values ​​of open intervals are conditionally equated to the intervals adjacent to them.

Properties of the arithmetic mean:

a) if all individual values ​​of the feature (all variants) are reduced or increased by m times, then the average value will decrease or increase by m times, respectively.

b) if all variants of the averaged attribute are reduced or increased by the number A, then the arithmetic mean will respectively decrease or increase by the same number A.

c) if the frequencies (weights) of all averaged options are reduced or increased by k times, then the arithmetic mean will not change.

2. Average harmonic (m=-1) - is the reciprocal of the arithmetic mean and is used when the statistical information does not contain frequencies for individual population options, but is presented as their product xf.

simple	weighted
	, Where w = xf

3. Geometric mean (m=0) - is used to determine the average for values ​​that have a large scatter, or in cases of determining the average value for relative indicators, for example, the average annual growth rate in the series of dynamics, where the individual values ​​of the attribute are growth coefficients.

The relative indicator is the result of dividing one absolute indicator by another and expresses the ratio between the quantitative characteristics of socio-economic processes and phenomena. Therefore, in relation to absolute indicators, relative indicators or indicators in the form of relative values ​​are derivative, secondary. Without relative indicators, it is impossible to measure the intensity of the development of the phenomenon under study over time, to assess the level of development of one phenomenon against the background of others interconnected with it, to carry out spatial and territorial comparisons, including at the international level.

When calculating a relative indicator, the absolute indicator that is in the numerator of the resulting ratio is called current or compared. The indicator with which comparison is made and which is in the denominator is called basis or base of comparison. Thus, the calculated relative value shows how many times the compared absolute indicator is greater than the base one, or what proportion it is, or how many units of the first fall on 1,100,1000, etc. units of the second.

Relative indicators can be expressed in coefficients, percentages, ppm, decimilles, or named numbers. If the base of comparison is taken as 1, then the relative indicator is expressed in coefficients, if the base is taken as 100, 1000 or 10,000, then the relative indicator is respectively expressed in percent (%), ppm (% 0) and prodecimille (% 00).

The relative indicator obtained as a result of the correlation of opposite absolute indicators, in most cases, should be named. Its name is a combination of the names of the compared and basic indicators (for example, the production of any product in the corresponding units of measurement per capita).

All relative statistical indicators used in practice can be divided into the following types:

• 1) speakers;
• 2) plan;
• 3) implementation of the plan;
• 4)structure;
• 5) coordination;
• 6) intensity and level of economic development;
• 7) comparisons.

The relative indicator of dynamics is the ratio of the level of the process or phenomenon under study for a given period of time (as of a given point in time) 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 made with the same base level, for example the first year of the period under consideration, one obtains relative indicators of dynamics with a constant base (basic). When calculating relative indicators of dynamics with a variable base (chain) comparison is carried out with the previous level, i.e. the base of the relative magnitude changes sequentially.

For example, let's use the data in Table. 5.1.

Table 5.1. Production of passenger cars in Russia in 2005-2009

Relative indicators of dynamics with a variable and constant base of comparison are interconnected as follows: the product of all relative indicators with a variable base is equal to the relative indicator with a constant base for the period under study. So, for the calculated indicators (after converting them from percentages to coefficients), we get:

1,102- 1,098- 1,136-0,408 = 0,561.

Relative performance indicators are also called growth rates. The averaging of these indicators for several successive periods is considered in Chap. 8.

Relative indicators of the plan and implementation of the plan are used by all subjects of financial and economic activity, from small individual private enterprises to large corporations, for the purpose of operational and strategic planning, as well as comparing actual results achieved with previously planned ones:

The first of these indicators characterizes the relative height of the planned level, i.e. how many times the planned volume indicator will exceed the achieved level or how many percent of this level it will be. The second indicator reflects the actual volume of production or sales as a percentage or ratio compared to the planned level.

Let's assume that at the end of 2010, the proceeds from the sale of a trading enterprise amounted to 4.5 million rubles. Based on the analysis of the emerging trends in the market, the management of the company considers it realistic to bring the turnover to 5.4 million rubles next year. In this case, the relative indicator of the plan, which is the ratio of the planned value to the actually achieved one, will be 5.4 / 4.5 x 100% = 120%. Suppose now that the actual turnover of the company for 2011 amounted to 4 million rubles. Then the relative indicator of the implementation of the plan, defined as the ratio of the actually achieved value to the previously planned one, is 4/5.4 100% = 74.1%.

Between the relative indicators of the plan, the implementation of the plan and dynamics, there is the following relationship:

In our example:

1.2 0.741 = 0.89, or 4/5 = 0.89.

Based on this relationship for any two known quantities, if necessary, it is always possible to determine the third unknown quantity.

Relative structure index is the ratio of the structural parts of the object under study and their whole:

The relative indicator of the structure is expressed in fractions of a unit or percentage. The calculated quantities, respectively called shares or specific gravity, show what share has or what specific gravity this or that part has in the total.

Consider the structure of Russia's GDP by types of primary income in 2010 (Table 5.2).

The percentages calculated in the last column of this table are relative indicators of the structure (in this case, specific weights). The sum of all specific gravity must always be strictly equal to 100% or 1.

Table 5.2. The structure of the gross domestic product of the Russian Federation by type of primary income in 2010

Relative indicator of coordination is the ratio of one part of a population to another part of the same population:

In this case, the part that has the largest share or is a priority from an economic, social or any other point of view is selected as the basis for comparison. As a result, it is calculated how many times this part is greater than the basic one, or how many percent of it is, or how many units of a given structural part fall into one unit (sometimes 100, 1000, etc.) of the basic structural part. So, based on the data in Table. 5.2 it can be calculated that for every 100 rubles. GDP income received in the form of remuneration of employees accounts for 35.9 rubles. net taxes on production and imports (8017/22,334.9) and 63.3 rubles. gross profit of the economy and gross mixed income (14,138.5/22,334.9).

The relative indicator of the intensity and level of economic development characterizes the degree of distribution of the process or phenomenon under study and represents the ratio of the indicator under study to the size of its inherent environment:

This indicator is obtained by comparing the levels of two phenomena interrelated in their development, therefore, most often it is a named value, but it can also be expressed as a percentage, ppm, decimille.

Usually, the relative intensity indicator is calculated in cases where the absolute value is insufficient to formulate reasonable conclusions about the scale of the phenomenon, its size, saturation, and distribution density. For example, to determine the level of provision of the population with housing, the number of square meters per inhabitant is calculated, to determine the population density, the number of people per 1 km2 is calculated.

So, according to social statistics, in 2009 the total number of unemployed in Russia was 6162 thousand people, and the economically active population - 75 524 thousand. It follows that the unemployment rate was 8.2% (6162/75 524 "- 100 %).

Relative indicators of the level of economic development are a kind of intensity indicators. They characterize production per capita and play an important role in assessing the development of the economy of a state or region. Since the volume indicators of production are by their nature intervals, and the population indicator is momentary, the average population for the period (suppose the average annual) is used in the calculations.

For example, considering only the absolute size of Russia's GDP in 2009 (38,797,184.7 million rubles), it is difficult to estimate or "feel" this value. In order to draw a conclusion about the level of economic development on the basis of this figure, it is necessary to compare it with the average annual population of the country (141.9 million people), which in the simplest case is calculated as half the sum of the population at the beginning and at the end of the year. As a result, the annual GDP per capita will be 38,797,184.7 million rubles/141.9 million people = 273.4 thousand rubles.

The relative comparison indicator is the ratio of the absolute indicators of the same name characterizing different objects (enterprises, firms, districts, regions, countries, etc.):

To express this indicator, both coefficients and percentages can be used.

For example, according to official statistics, investments in fixed assets in the Russian Federation in 2010 at the expense of the federal budget amounted to 642.1 billion rubles, the budgets of the constituent entities of the Russian Federation. 127.8 billion rubles. Off-budget funds - 1591.8 billion rubles . Thus, we can conclude that investments from extra-budgetary funds were 2.5 times higher than investments from the federal budget and three times higher than investments from the budgets of the constituent entities of the Russian Federation.

Absolute indicators

original, primary form expressions of statistical indicators are indicators in absolute terms or absolute values. Statistical indicators in the form of absolute values ​​characterize the absolute dimensions of the processes and phenomena studied by statistics, namely their mass, area, volume, length, reflect their temporal characteristics, and can also represent the volume of the population, i.e. the number of its constituent units.

Individual absolute indicators (values), as a rule, they are obtained directly in the process of statistical observation as a result of measuring, weighing, counting and evaluating a quantitative trait of interest. In some cases, individual absolute indicators have a difference character: the difference between the number of employees of the enterprise at the end and at the beginning of the year, the difference between the proceeds from the sale of the enterprise and the total amount of costs, etc.

Summary absolute indicators, characterizing the volume of a feature or the volume of the population, both as a whole for the object under study, and for any part of it, are obtained as a result of a summary and grouping of individual values. Such indicators include the total number of people employed in the industry, the total assets of commercial banks in the region, etc.

Absolute statistical indicators are always named numbers. Depending on the socio-economic essence of the phenomena under study, their physical properties, they expressed in natural, value or labor units of measure.

In international practice, such natural units measurements , How tons, kilograms, square, cubic and simple meters, miles, kilometers, gallons, liters, pieces etc.

Example: According to International Financial Reporting Standards (IFRS), Rosneft increased oil production by 2.6% in 2018, to 216.3 mln t.; according to (TASS) data, the actual consumption of electricity in the Russian Federation in 2018 amounted to 1076.2 billion kWh(according to UES of Russia 1055.6 - billion kWh); export of liquefied natural gas (LNG) from Russia to the countries of the Asia-Pacific region (APR) grew in 2018 by 58.6% year-on-year and amounted to 26 bcm m.

The natural group also includes conditionally natural meters, used in cases where a product has several varieties and the total volume can be determined only on the basis of a common consumer property for all varieties. For example, various types of fossil fuels are converted into conventional fuel ((c.f.) - a unit of accounting for fossil fuels used to compare the efficiency of various types of fuel and their total accounting. 1 kg of fuel with a calorific value of 7000 kcal is taken as units of c.f. /kg (29.3 MJ/kg)); soap of different varieties - into conditional soap with a 40% content of fatty acids; canned food of various sizes - in conditional cans with a volume of 353.4 cubic meters. see etc.

Conversion into conventional units of measurement is carried out on the basis of special coefficients calculated as the ratio of consumer properties of individual varieties of the product to the reference value. So, for example, 100 tons of peat, the calorific value of which is 24 MJ / kg, will be equivalent to 81.9 tons of reference fuel (100 × 24.0/29.3), and 100 tons of oil with a calorific value of 45 MJ/kg will be estimated at 153.6 tons of reference fuel (100 × 45,0/29,3).

In some cases, to characterize a phenomenon or process, one unit of measurement is not enough, and it is used product of two units. An example of this can be such indicators as cargo turnover and passenger turnover, estimated respectively at ton-kilometers And passenger kilometers, electricity generation measured in kilowatt-hour ah, etc.

In a market economy, the greatest importance and application are stop bridge units , allowing to obtain a monetary assessment of socio-economic phenomena and processes. Thus, one of the most important cost indicators in the system of national accounts, characterizing the overall level of development of the country's economy, is the gross domestic product, which in Russia, according to the Federal State Statistics Service for 2018, amounted to 103,875.8 billion rubles.

When analyzing and comparing cost indicators, it must be borne in mind that in conditions of high or relatively high inflation rates, they become incomparable. Thus, it is hardly advisable to compare the export of the Russian military-industrial complex in 2018 with its value, for example, in 1998, since the content of the ruble has changed significantly over this period. In order to make such comparisons, where possible, conversion to comparable prices is carried out.

TO labor units , allowing to take into account both the total labor costs at the enterprise, and the labor intensity of individual operations of the technological process, include man-days and man-hours.

Relative indicators

Relative indicator (value) represents the result of dividing one absolute indicator by another and expresses the relationship between the quantitative characteristics of socio-economic processes and phenomena.

That's why , with respect to abs. fierce indicators, relative indicators or indicators in the form of relative values are derivative, secondary.

Without relative indicators, it is impossible to measure the intensity of the development of the phenomenon under study over time, to assess the level of development of one phenomenon against the background of other phenomena interconnected with it, to carry out spatial and territorial comparisons, including at the international level.

Relative indicators can be expressed in coefficients, percentages, mille, ppm, decimille or be named numbers . If the base of comparison is taken as 1, then the relative indicator is expressed in coefficients, if the base is taken as 100, 1000, then the relative indicator is respectively expressed as a percentage (%), ppm (‰), etc.

All relative statistical indicators used in practice can be divided into the following types:

1. Relative indicator of dynamics

2. Relative indicator of the plan (OPP);

3. Relative indicator of plan implementation (OPRP);

4. Relative structure index(OPS);

5. Relative indicator of coordination (RIC);

6. Relative intensity indicator (OPI);

7. Relative comparison indicator(OPSr).

Consider below the formulas and examples of the above indicated relative values.

1) Relative indicator of dynamics is the ratio of the level of the process or phenomenon under study for a given period of time (as of a given point in time) to the level of the same process or phenomenon in the past (formula 8.1):

• Calculation example (OPD). Suppose the foreign trade turnover of the company in 2017 amounted to 3.0 million rubles, and in 2018 it amounted to 3.8 million.

Solution. In this case, the relative indicator of dynamics, which is the ratio of the current level to the previous one or the base of comparison, will be (3.8 / 3.0 \u003d 1.27 x 100 \u003d 126.7%)

All subjects of financial and economic activity, from small individual private enterprises to large corporations, to one degree or another, carry out both operational and strategic planning, and also compare the actual results achieved with those previously planned.

For this purpose are used Relative Plan Scores (PRP) and Relative Plan Execution Rates (PRPRs)(formulas 8.2 and 8.3):

2) Relative indicator of the plan (OPP) characterizes the relative height of the planned level, i.e. how many times the planned volume indicator will exceed the achieved level or how many percent of this level will be :

3) Relative indicator plan implementation (OPRP) reflectsthe actual volume of production or sales as a percentage or coefficients compared to the planned level:

• Calculation example (Relative Plan Index (PPI)).

The foreign trade turnover of the company in 2017 amounted to 3.0 million rubles. Based on the analysis of the emerging trends in the market, the company's management considers it realistic to bring the turnover to 3.6 million rubles in the next 2018. In this case (opp), which is the ratio of the planned value to the actually achieved, will be (3.6/ 3.0=1.2 x 100 =120%) .

• Calculation example (Relative Plan Implementation Rate (PRRP)).

The actual turnover of the company for 2018 amounted to 3.8 million rubles. Then the relative indicator of the implementation of the plan, defined as the ratio of the actually achieved value to the previously planned one, will be (3.8 / 3.6 \u003d 1.056 x 100 \u003d 105.6%).

• Between the relative indicators of the plan, the implementation of the plan and the dynamics, there is the following relationship: OPP X OPRP = OPD .

• In our example: 1.20x 1.056 \u003d 1.267 or 3.8 / 3.0 \u003d 1.267. Based on this relationship, for any two known quantities, if necessary, it is always possible to determine the third unknown quantity.

4) Relative structure index(OPS) represents the ratio of the structural parts of the object under study and their whole:

Example calculations ( OPS-relative indicator of the structure) consider in Table 8.1.

Table 8.1 - The structure of the gross domestic product of the Russian Federation in 2018 (conditional figures)

The percentages calculated in the last column of this table are relative indicators of the structure(OPS)(in this case, specific gravity). The sum of all specific gravity must always be strictly equal to 100% or 1.

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

In this case, the part that has the largest share or is a priority from an economic, social or any other point of view is selected as the basis for comparison. As a result, they get how many times this part is greater than the base part or how many percent of it it is, or how many units of this structural part fall on 1 unit (sometimes 100, 1000, etc. units) of the basic structural part.

Calculation example ( relative measure of coordination(OPK)). Based on the data in Table 8.1 above, we can calculate (OPK), i.e. for every ruble of goods produced, RUB 4.84 services rendered (59417/32928,6) And 0.35 rub. net taxes on products (11530,2/32928,6) .

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

This indicator is obtained comparison levels two interrelated phenomena in their development. Therefore, most often it is a named value, but it can also be expressed as a percentage, ppm, decimille.

Usually, the relative intensity indicator is calculated in cases where the absolute value is insufficient to formulate reasonable conclusions about the scale, phenomenon, its size, saturation, distribution density. So, For example, to determine the level of provision of the population with cars, the number of cars per 100 families is calculated; to determine the population density, the number of people per 1 sq. km.

Calculation Examples (Relative Intensity Index)

Example 1 (OPI). Thus, according to social statistics at the end of 2008, the total number of registered unemployed in the Russian Federation was 1.552 million people, and the economically active population was 75.892 million people.

It follows that the unemployment rate (UIR) was (1552/75892 x 100 = 2.05%).

A variety of relative intensity indicators are relative indicators of the level of economic development characterizing production per capita and playing an important role in assessing the development of the economy of a state or region. Since the volume indicators of production are by their nature intervals, and the population indicator is momentary, the average population for the period (suppose the average annual) is used in the calculations.

Example 2 (OPI). Considering only the absolute size of Russia's GDP (in current prices) at the end of 2008 (41,668,034 million rubles), it is difficult to estimate this value. In order to draw a conclusion about the level of economic development on the basis of this figure, it is necessary to compare it with the average annual population of the country (142.1 million people), which in the simplest case is calculated as half the sum of the population at the beginning and at the end of the year. As a result, the annual GDP per capita (GPI) will be:

(293.2 thousand rubles = 41668034 million rubles / 142.1 million people

7) Relative comparison indicator(OPSr)represents the ratio of the same-name absolute indicators characterizing different objects (enterprises, firms, districts, regions, countries, etc.):

To express this indicator, both coefficients and percentages can be used.

Calculation example (Relative Comparison Index (RCR).

According to official statistics, investments in fixed capital in the Russian Federation in 2002 at the expense of the federal budget amounted to 81.6 billion rubles, budgets of the subjects of the Federation and local budgets - 184.5 billion rubles, funds of enterprises - 653.1 billion rubles Let's calculate the OPSr (653.1/81.6=8 and 653.1/184.5=3.5).

Conclusion: investments at the expense of enterprises were 8 times higher than investments from the federal budget and 3.5 times higher than investments from the budgets of the subjects of the Federation and local budgets.

Control tasks

1. List what the statistical indicators characterize in the form of absolute values.
2. What is the role of relative values ​​in statistics?
3. Name all kinds of relative values.
4. Describe the forms of expression of relative values?