The relative indicator of coordination is a ratio. Moscow State University of Printing Arts

Study economic processes, their analysis allows not only to draw conclusions about their current state, but also to predict development in the planned period. To do this, financial managers use a variety of methodologies. One of the simplest and most frequently used is the method that uses relative indicators. They allow you to compare several values, find their share of influence in common process, as well as purposefully optimize the object under study.

Without an assessment of relative indicators, it is unthinkable to carry out a financial and economic analysis.

general characteristics

Relative and absolute indicators are closely related. The analysis must examine each type of quantity.

Absolute indicators always have units of measurement. Relative indicators reflect the measure of the relationship between absolute values. This is a mathematical division (usually two) of signs that express the value of one or two factors.

A very important quality that makes relative values ​​so popular in analysis is their ability to abstract from differences in absolute values ​​in calculations. At the same time, it will be possible to look at the indicators from a different angle.

Absolute and relative indicators are inextricably linked, and should be used in combination to assess financial and economic processes.

Calculation formula

Relative indicators are calculated according to a certain formula. Its general form is as follows:

OP = absolute current (comparable) indicator / absolute baseline.

The relative indicator, the formula of which is given above, can have the same name of absolute indicators both in the numerator and in the denominator. The result in this case can be measured as a coefficient, percentage, ppm, etc.

If in the numerator and denominator the absolute indicators have different units measurements, then the result must be named, for example, speed - km / h.

Relative indicators, depending on their characteristics, may somewhat modify the formula, but its general principle is preserved.

Absolute and relative indicators can be considered for various quantities. Interaction analysis identifies factors:

• dynamics;
• structures;
• plan;
• implementation of tasks;
• coordination;
• intensity;
• comparisons.

Relative indicators of dynamics

Dynamic relative values ​​are comparisons of the same factor or event under consideration in the current period to the past.

If the resulting indicator is expressed in multiple form, it is called the growth factor. In the case when the result is in the form of percentages, it is called the growth rate.

When relative financial indicators presented for several periods, they are compared either in chain order or with a base value.

The product of all chain indicators of the dynamic study gives the base value for the analyzed period.

Dynamic indicators allow you to understand the trends in the development (or decline) of activities. With their help, the growth rates in the analyzed interval are monitored.

Structure indicators

Structural indicators compare the absolute indicator, which is part of the whole, with its total value.

The presented methodology is used for such calculations as relative indicators of financial stability. For example, to determine the part of the balance sheet in the structure equity. In this case, own sources of financing, which the company has put into circulation, are compared with current assets.

Other relative indicators of the structure are also used to analyze financial stability.

Also, to determine the correct structure of the analysis factors, the considered method is carried out. For example, relative measures of financial strength help improve a company's capital structure. One side, own funds ensure the stability of the enterprise. And it is permissible to expand your production capabilities with the involvement of borrowed capital. It is precisely the indicators of the structure that will help assess the compliance of each of these values ​​with the standard.

Indicators of coordination

Relative coordination indicators are similar to the previous variety, but allow not only to assess the degree of influence of one absolute indicator on the overall value, but also to determine the number of all factors.

Here the analyst will consider not only the degree of influence of one part, but of all components. This approach allows us to assess the comprehensively considered whole object of study.

In other words, it is possible to determine how many units of each factor are included in the structure of the overall indicator. This will reveal the harmony of the distribution of each part in the basic concept. For example, the indicator current liquidity shows that the company is solvent and can cover its obligations to investors. However, the analysis of absolute liquidity does not meet the standard and indicates the company's insufficient ability to pay off its debts quickly. This means that the structure of working capital is incorrect. The calculation of the relative indicators of each component of the second section of the balance will help to quickly determine this.

Intensity indicators

Indicators of the degree of intensity allow us to evaluate two qualitatively different, but related in the statistical totality of signs.

This approach makes it possible to determine the degree of distribution of factors in the studied environment.

For example, in terms of production, the presented methodology can be attributed to the profitability of labor in the context of production sites. To do this, compare the number of employees with the indicator net income each shop or department. This will make it possible to assess the degree of labor productivity of each employee in obtaining the total profit of his site. This will make it possible to determine where the receipt of net income was most ensured by the intensity of labor of workers.

Relative intensity indicators will help to highlight the degree of distribution of the factor in the structure.

Comparison indicators

The presented approach makes it possible to determine how much the studied absolute indicator is greater than the base one. This will reveal which factor and how much more (less) the factor of the same name taken as the basis.

Since indicators of the same name are taken into account for the calculation, the result will be obtained as a percentage or coefficients.

For example, net profit enterprises last year was received in the amount of x. This year the company made a profit after deducting all taxes and deductions in the amount of y.

The types of relative indicators under consideration make it possible to compare these two indicators: K = x / y, which will determine how much more (less) the net profit in the current period is compared to the base one.

With the help of such an analysis, fixed, working capital, labor, production costs, income and profits, etc. are compared.

Plan performance indicators

In the process of planning its activities, the enterprise sets the expected indicators of costs, profits, etc. Planned relative indicators characterize the correspondence of real indicators to expected values.

Typically, the degree of order completion is presented as a coefficient. This helps to assess the degree of its implementation.

In this case, the base value will be the planned value of the indicator, and the compared value will be the actual figure.

The calculation of such varieties of key indicators plays a very important role in production area. They help to evaluate the quality of work of employees, as well as equipment, materials and other elements involved in the production process. finished products and its implementation.

The presented analysis will determine the degree of compliance of the fact with the plan. After that, it is necessary to conduct studies of the factors that influenced the deviations, both in a smaller and larger direction.

Indicators of the level of economic development

These indicators compare opposite absolute values ​​that are mutually related. The denominator is usually the factor value of the feature. The result number is the numerator.

Such an analysis is used to determine the production or economic potential, as well as the performance of the enterprise.

They are used to calculate, for example, the unit cost of production, labor productivity. Such values ​​allow us to determine the influence of a particular factor on the outcome of the work.

Having become acquainted with such a concept as the relative indicators of economic and financial analysis, it is possible to conduct comprehensive studies of the processes of the object under consideration. Properly applying this or that type of calculation, based on various features and data, it will be possible to identify the reasons for the growth or decline in performance. Based on the analysis performed, all factors influencing growth and development in the planning period are corrected.

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 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 standards financial reporting(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 Russian Federation in 2018 was 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 conditions market economy of 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 quantitative characteristics 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 given period 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 - Structure of gross domestic product RF 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 receive 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 level indicators 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 Russian GDP(in current prices) at the end of 2008 (41668034 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 federal budget amounted to 81.6 billion rubles, the 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?

Relative statistics is called a generalizing characteristic, expressed as a numerical measure of the ratio of two compared absolute values. These indicators are used to study the structure of the phenomenon under study, to compare its level of development with the level of development of another phenomenon, to assess the changes taking place in the phenomenon under study, etc.

A relative statistic is obtained by dividing one absolute value by another.

AT general view the relative statistic formula would look like this:

Relative indicators can be expressed as coefficients, percentages, ppm and decimille.

If the base of comparison is taken as one, then the relative indicator is expressed in the form of a coefficient. If the base of comparison is taken as one hundred units, then the relative indicator is expressed as a percentage. If the base of comparison is taken as a thousand units, then the relative indicator is expressed in ppm (a tenth of a percent), if for ten thousand - in a decimill (hundredth of a percent).

Speakers;

plan and execution of the plan;

structures;

coordination;

Intensity and level of economic development;

Comparisons.

Relative indicator of dynamics characterizes the change in the phenomenon under study over time and represents the ratio of indicators characterizing the phenomenon in the current period and the previous (or base) period.

OPD =

The indicator calculated in this way is called the coefficient of growth (decrease). It shows how many times the indicator of the current period is more (less) than the indicator of the previous (base) period. Expressed as a percentage, the relative indicator of dynamics is called the rate of growth (decrease).

T p \u003d (y i / y i-1) * 100%

T p \u003d (y i / y o) * 100%

Example: the population of the Russian Federation according to the 2002 census. amounted to 145181.9 thousand people, according to the 1989 census. - 147021.9 thousand people Determine the coefficient and rate of growth (decrease).

T p = 98, 7%

Consequently, the population decreased by 1.3%.

Relative indicator of the plan (forecast) (OPP) and the implementation of the plan (OPVP) are used by all subjects of financial and economic activities that carry out current and strategic planning and are calculated according to the formula:

The relative indicator of the plan characterizes the intensity of the plan task, and the relative indicator of the plan's implementation characterizes the degree of its implementation.

Example: the actual turnover of the company for 2008. amounted to 2 billion rubles. Market analysis showed that in 2009. it is possible to bring the turnover up to 2.6 billion rubles. Actual turnover for 2009 amounted to 2.5 billion rubles. Define AKI and OPVP.

OPP==130% or 1.3 times

OPVP==96%

Calculations show that the target for 2009 is 1.3 times higher than the actual level for 2008, but the plan for 2009 was only 96% fulfilled.

Relative indicators of the structure(OPS) characterize the shares (specific gravity) constituent parts aggregate in its total volume. They characterize the structure of the population and its structure.

OPS=(*100%)

OPVs are usually expressed in the form of coefficients or percentages. The sum of the coefficients should be 1, and the sum of the percentages should be 100%, since the specific weights are reduced to a common base.

The set of relative values ​​of the structure shows the structure of the set.

Relative indicators of coordination(OPK) characterize the ratio of parts of a given statistical population to one of them, taken as the basis for comparison. They show how many times one part of the population is larger than the other, or how many units of one part of the population fall into one, ten, one hundred, etc. units of another population.

For the base of comparison, the part that has the largest share is selected, or is a priority in this population.

Relative indicators of the intensity and level of economic development(OPI) characterize the degree of distribution or the level of development of the studied phenomena or processes in a certain environment. They are formed as a result of comparing oppositely named, but in a certain way interconnected quantities.

This indicator is calculated per hundred, thousand, ten thousand, etc. units of the studied population and is used in cases where it is impossible to determine the scale of the phenomenon by the value of the absolute indicator. For example, when studying demographic processes birth rates, death rates, natural increase(decrease) of the population as the ratio of the number of births (deaths) or the amount of natural increase per year to the average annual population of a given territory per 1,000 or 10,000 people.

K r =‰

K m=‰

to natural growth =‰

Relative indicators of the level of economic development characterize the efficiency of resource use and production efficiency. These are indicators of production output, unit costs, efficiency of use production assets etc.

Relative Comparison Index OPS r characterizes the comparative sizes of the same-named absolute indicators relating to different objects or territories, but for the same period of time.

They are obtained as private ones from the division of the absolute indicators of the same name characterizing different objects belonging to the same period or point in time.

OPS r=

These indicators can be used to compare labor productivity in different countries, compare prices of various goods and economic indicators for various enterprises.

Relative indicators of the structure (RPS) is the ratio of the part and the whole to each other

Relative indicators of the structure characterize the composition of the studied population and reflect the specific gravity (share) of each part as a whole. If OPS is expressed as a percentage, the sum of the specific weights is equal to 100%, if in the form of coefficients - to one.

Relative structure indicators can perform several analytical functions. First, they are in themselves informative and valuable for statistical analysis (they show the share of any part of the population in its total volume); secondly, they make it possible to identify the direction of development of the phenomenon by comparing its structure at the present stage of development with the structures of past years or periods (i.e., they allow us to identify the trend in the development of the phenomenon in time); thirdly, relative indicators of the structure can be used in cases where comparison of absolute indicators is impossible due to differences in the volumes of aggregates. For example, as of January 1, 2002, in the Central Federal District, there were, according to the data financial statements, 609,528 unprofitable enterprises, and in the Northwestern Federal District - 188,338. It is impossible to directly compare these two absolute indicators, since the total number of enterprises located in these territories is different. And if we find out what proportion of these territories is occupied by unprofitable enterprises in their total number, then the comparison of the obtained indicators will be correct: in the Central Federal District, the share of unprofitable enterprises amounted to 41.8% total number enterprises, and in the North-West - 39.7%. In this way, economic situation enterprises in the Central Federal District is worse than in the North-West.

The relative indicator of coordination (RIC) is calculated as the ratio of two parts of the whole to each other and shows how many units of the part in the numerator of the formula are per unit of the other part in the denominator

In this case, if the set consists of several parts, then one of them is taken as the base of comparison.

Example 5.3. Let us determine the structure of candy production for 2005 and 2006. according to the table.

Table 5.5. Candy production structure in 2005 and 2006

Candy production volume	2005		2006
	thousand roubles.	%	thousand roubles.	%
"Bear"	280	28	350	29
"Sweet"	200	20	310	26
"Snowball"	520	52	540	45
Total	1 000	100	1 200	100

Thus, more than half of the total output (52%) in 2005 accounted for "Snezhok" sweets. In 2006, there was a change in the structure of output: the share of the first two varieties of sweets increased and the share of Snezhok sweets decreased.

According to the example, we will determine the ratio between the release of different varieties of sweets in 2005.

Consequently, in 2005, in the composition of the issue for every 1 thousand rubles. sweets "Slastena" accounted for sweets "Snezhok" by 2.6 thousand rubles, sweets "Mishka" - by 1.4 thousand rubles.

In some cases, when calculating the relative value of coordination, it is more convenient to present it in a form indicating how many units of the indicator in the numerator fall on 100 units of the indicator in the denominator (by multiplying by 100), or per 1000 units of the indicator in the denominator (by multiplying by 1000), etc. So, if, for example, as of January 1, 2006, the ratio between the number of unprofitable and non-unprofitable enterprises in the region was equal to 0.769, then it is incorrect to interpret this value as "0.769 unprofitable enterprises account for one non-unprofitable one". The fraction should be multiplied by 1000, then we get: 769 unprofitable enterprises account for every 1000 unprofitable ones.

5.2.3. Relative intensity measures and comparisons

The relative intensity index (RII) characterizes the density of propagation of the phenomenon in specific environment. Such indicators are the demographic rates of fertility, mortality, natural increase, marriage rate, etc. Thus, the birth rate is calculated as the ratio of the number of births per year to the average annual population

The mortality rate is calculated by the formula

As you can see, the birth and death rates, as well as most other demographic factors, are expressed in ppm and characterize the level of the phenomenon (the number of births, the number of deaths, etc.) per 1000 inhabitants. The transition to ppm is based on the considerations that it is inconvenient to measure these quantities in the form of coefficients, since the dimension of the resulting number will be thousandths. GPIs can also be named numbers. For example, population density, being a relative indicator of intensity, has a unit of measure people / km 2.

Relative intensity indicators are widely used in statistical analysis. These include indicators of labor productivity, capital productivity and capital-labor ratio; production of GDP per capita; volume of investments per capita; security of the population medical care; the amount of distribution costs per 100 rubles. turnover; costs per ruble of manufactured products; profitability; productivity, etc.

Example 5.4. The following data are available for home contents insurance by an insurance company in 2006:

• number of insurance contracts - 8305;
• number of insured events - 86;
• the amount of the insured property - 2,558,029,010 rubles;
• amount paid insurance compensation- 102,447,000 rubles.

Let's calculate the relative intensity indicators:

Among the relative values ​​of intensity, the relative values ​​of the level of economic development, which represent the size of production or consumption of GDP, various types of products per capita, are distinguished into a separate group. These indicators are used in territorial and international comparisons; they are used to judge the degree of economic development of a region or country.

Relative Comparison Index (RPC) is the ratio of similar indicators related to the same moment or period of time, but different territories or objects. In this case, the compared values ​​must have the same calculation methodology.

Example 5.5. The amount of attracted credit organizations deposits and deposits at the end of 2002 amounted to 503,411.3 million rubles in Moscow and 70,160.9 million rubles in St. Petersburg. Let's define the relative indicator of comparison

Thus, at the end of 2002, the amount of deposits and deposits attracted by credit institutions in Moscow was 7.2 times higher than in St. Petersburg.

Relative statistic is called a generalizing characteristic, expressed as a numerical measure of the ratio of two compared absolute values. Such indicators are used for various purposes: they allow comparison of various indicators and make such a comparison visual; serve as a tool for monitoring the progress of the plan; help to identify production reserves; are essential tool in the process of management.

Unlike absolute relative indicators, they are always derived (secondary) values, and they can only be obtained by calculation on the basis of absolute indicators. An important property of a relative magnitude is that it abstracts differences in absolute magnitudes and makes it possible to compare phenomena whose absolute magnitudes are not directly comparable.

A relative indicator is obtained by dividing one absolute indicator by another. The scheme for calculating the relative indicator (RP) is as follows:

where the comparison value is the absolute value that is being compared; base (base) of comparison - the absolute value with which the comparison is made;

P - degree value.

Choice forms of expression relative values ​​depends on the nature of the analytical task, which consists in expressing the relationship with the greatest clarity in each specific case.

As a result of comparing the absolute values ​​of the same name, unnamed relative values ​​are obtained. In this case, the relative value shows how many times the compared value is greater or less than the base value, or what proportion the first is in relation to the second. In this case, relative indicators can be expressed as shares, multiples, percentages, as ppm, etc.

If the base of comparison is taken as one (P= 0), then the relative indicator is expressed in the form coefficient. For example, in 2003, 40.3 thousand children were born in St. Petersburg, and in 2002 - 37.2 thousand children. The growth rate of the number of births will be 1.083 (40.3:37.2).

If the comparison base is taken as 10 units (P= 1), then the relative indicator is expressed in decile form. For example, in social statistics, important indicators of population differentiation are the decile indicator and the coefficient of funds.

If the base of comparison is taken as 100 units (u = 2), then the relative indicator is expressed in percents(%). According to previous data, the increase in the number of births will be 108.3% (1.083 x 100).

Percentage, as a rule, is used in cases where the compared absolute indicator exceeds the base one by 2-3 times. Percentages over 200-300 are usually replaced by a multiple ratio, a coefficient. So, instead of 550%, they say that the compared indicator exceeds the base one by 5.5 times.

If the comparison base is taken as 1000 units (n = 3), then the relative indicator is expressed in ppm(tenth of a percent, %o). Promille are widely used in demographic statistics. Thus, the indicator of the natural movement of the population - the birth rate, is calculated in ppm and shows the number of births or deaths per year per 1000 people. For example, the birth rate in St. Petersburg in 2003 was 8.9%o, which means 8.9 births per thousand population.

If the base of comparison is taken as 10,000 units (u = 4), then the relative indicator is expressed as decimille(hundredth of a percent). Thus, the number of doctors, the number of hospital beds, the number of places in higher educational institutions, etc. are calculated per 10,000 inhabitants. The decimille is resorted to in order to give relative values ​​​​more comfortable view, freeing them from fractional numbers, from a large number of decimal places in decimal fractions.

The result of a comparison of dissimilar quantities are named relative quantities. They have a complex natural unit of measurement. Their name is formed by a combination of compared and basic absolute values. In this case, the relative value shows how many units of one quantity fall on a unit of another. For example, the relative indicator "population density" characterizes how many people live in 1 km 2 of the territory, and has a unit of measurement - a person per 1 km 2.

For economic purposes relative values ​​are divided into four groups: 1) for the analysis of the plan; 2) to characterize changes in social phenomena in time and space; 3) to characterize the internal structure of the phenomenon; 4) to calculate intensity indicators; 5) to analyze the level of development.

1 group. The indicators characterizing the plan (forecast) include: the relative value of the planned (forecast) task and the relative value of the plan (forecast) fulfillment. These indicators are used by all subjects of financial and economic activity that carry out current and strategic planning. Usually these figures are calculated as a percentage.

Relative value of the planned task is used to calculate the percentage increase (decrease) in the value of the plan indicator compared to its base level in the previous period, for which formula 3.3 is used

where U pl - the level of the planned task;

Y o - the level of the base (past) period.

Relative value of plan execution calculated according to formula 3.4

where Y1 is the level of the reporting period.

This indicator characterizes the degree of fulfillment of the planned task for the reporting period.

Consider tasks to analyze the level of execution of the plan.

Example 3.1. The plan provided for the release of products in the amount of 105 thousand units, in fact, 110.25 thousand units were produced. Determine the percentage of the plan for the release of products.

Implementation of the plan: 110.25: 105 = 1.05 (105%).

Conclusion: the plan was fulfilled by 105%, or the plan was overfulfilled by 5%.

In statistical analysis, there are situations when it is necessary to evaluate the degree of implementation of the plan by an indicator, the value of which was planned to be reduced (labor intensity, cost, etc.). In such situations, one has to move away from the usual approach (“more is better”), since an increase in labor intensity and cost indicates a deterioration in work. Let us illustrate this point with the following example.

Example 3.2. The association has a plan for reducing the labor intensity of a unit of production: the labor intensity should be reduced to 93 hours per unit of production, but in fact it was reduced to 97 hours. It is necessary to determine the relative magnitude of the plan.

The relative value of the implementation of the plan will be: 93:97 x 100 = = 95.9%.

Conclusion: the implementation of the plan was 95.9% or the plan was underfulfilled by 4.1%.

2 group. Indicators that characterize changes in social phenomena in time and space include indicators: the relative magnitude of the dynamics and the relative magnitude of the comparison.

Relative magnitude of dynamics calculated by formula 3.5

This indicator characterizes changes in social phenomena over time. The indicator calculated in this way is called the coefficient of growth (decrease). It shows how many times the indicator of the current period is more (less) than the indicator of the previous (base) period.

The relative indicator of dynamics expressed as a percentage is called the rate of growth (decrease).

There is a relationship between the three indicators expressed by formulas 3.3, 3.4, 3.5:

Thus, knowing any two quantities, you can always find the third.

Relative comparison value is obtained as a result of comparing the levels of the same name related to different objects or territories, but to the same time:

This indicator characterizes changes in social phenomena in space and is calculated as a coefficient or percentage.

An example of this kind of relative magnitude is the comparison of prices for basic foodstuffs in different regions.

3rd group. The indicators characterizing the internal structure of the phenomenon include: the relative value of the structure and the relative value of coordination.

The relative size of the structure is calculated as the ratio of the volume of a part of the population to the absolute value of the entire population, thereby determining the share (specific gravity) of the part in the total volume of the population:

Usually this indicator is calculated as a percentage.

Relative amount of coordination characterizes the ratio between two parts of the studied population, one of which acts as a comparison base (formula 3.9):

The basis of comparison is usually taken to be the part that has the greatest weight in the aggregate, or is more significant than the others. An example of the relative value of coordination is: the number of engineering and technical personnel per 100 workers of the enterprise, thereby controlling the observance of the optimal proportions of the ratio of workers in the enterprise.

The relative values ​​of coordination complement the indicators of the structure, they make it possible to analyze the observance of the necessary proportions between the individual parts of the population.

Let us consider an example of calculating the relative value of the structure and the relative value of coordination.

Example 3.3. The entire population of the region is 635 thousand people, including urban - 419 thousand people, rural - 216 thousand people.

The relative value of the structure is an indicator that characterizes the share of urban and rural population in the total population of the region.

If the entire population of the region is taken as 100%, then the urban population will be 419: 635 = 0.66 (66%), and the rural population - 216,635 = 0.34 (34%), or 100 - 66 = = 34%.

The relative size of the structure expressed the specific gravity (or share) of each part of the population in the total.

Conclusion: the urban population is 66%, and the rural population is 34% of the total population.

To calculate the relative value of coordination, we will choose the size of the urban population as a comparison base. As a result, we get: 216: 419 \u003d 1: 2 \u003d 5: 10.

The relative value of coordination shows how many units of a part of the phenomenon fall on 10 (100,1000...) units of the part that is chosen as the base of comparison.

Conclusion: for every 10 people in the urban population, there are 5 people living in the countryside.

4 group. Relative indicators can analyze intensive, demographic and socio-economic development.

In statistical practice, the indicators of this group are used in the study of the degree of volume of a phenomenon in relation to the volume of the environment in which this phenomenon propagates. Relative values ​​of development show how many units of one set (numerator) account for one, ten, one hundred units of another set (denominator).

Indicators of this group:

• 1) characterize the ratio of heterogeneous, but interconnected statistical indicators;
• 2) always named quantities. Sometimes they are calculated in ppm;
• 3) are calculated according to a special methodology.

Relative magnitude of development calculated by formula 3.10

This group of indicators characterizes the degree of spread or development of the phenomenon under study in a certain environment, i.e. the ratio of two levels of different, but interconnected phenomena is considered.

When calculating the relative values ​​of development, the problem of choosing an adequate comparison base (environment for the propagation of the phenomenon) may arise. The criterion for the correctness of the calculation is the comparability of the developed methodology for calculating the compared indicators used in statistical practice. For example, when determining the population density indicator, one cannot take as a basis for comparison overall size territory of this or that state, in this case, only the territory of 1 km 2 can be the basis for comparison.

Intensity indicators characterize a progressive phenomenon per unit of another, i.e. indicators of the level of technical development of production. For example: the return on assets shows how much output falls on a unit cost of fixed production assets, and is measured in rubles. for 1 rub.; labor productivity characterizes the value of output per unit of labor costs and is measured in rubles. per 1 man-hour or in pieces per 1 man-hour.

An example of an indicator of demographic development is population density . The unit of measurement of the indicator is a person per 1 km 2. Other indicators are, for example, birth and death rates, measured in ppm.

Socio-economic development is characterized by such indicators as GDP per capita (rubles per 1 person), average per capita consumption of products per capita (kg per 1 person), as well as indicators of the level of well-being of citizens, indicators of the provision of the population with the media, cultural -household purposes, etc.

By themselves, relative values ​​do not give a clear idea of ​​the phenomena under study, so their use without connection with absolute values ​​can lead to erroneous conclusions.

For a correct characterization of a social phenomenon, it should be taken into account that:

• - the growth of indicators, expressed as a percentage, depends on the absolute size of the compared indicators;
• - small phenomena in percentage terms change much faster than similar phenomena with significant sizes;
• - with a small initial level of the phenomenon, an increase of several units can give the same or even higher percentage growth than thousands of units with a significant entry level;
• - the smaller the indicator with which the comparison is made, the greater the relative indicator will be, and vice versa. Hence, the same percentage may contain different absolute values.

Example 3.4. Increase wages in the public sector by 20%

leads to following results: an employee who has a salary

a fee of 1,000 rubles, the increase will be 20 rubles, and if the employee receives 10,000 rubles, then the increase will be 1,000 rubles.

Consider basic rules for the use of absolute and relative values:

• 1) the need for deep qualitative analysis indicators, allowing to reveal their essence, specific features, relationships with other phenomena;
• 2) ensuring comparability of values: a) by content; b) the boundaries of the object; c) units of measurement; d) territories; e) time; e) calculation methodology, etc.;
• 3) the need for integrated use in the statistical study of absolute and relative values. Relative values ​​do not replace absolute indicators, but supplement information about a given phenomenon.

Applying these rules, consider the following economic problems.

Example 3.5. If you reduce the price of a unit of goods by 20%, and then increase it by 20%, what will happen to the price in the end: will it be less, more or equal to the previous one?

Before the reduction, the price of a unit of goods was, for example, 100 units, after the reduction it became 80 units. The subsequent increase of 20% will be made from 80 units, i.e. from a base less than before the reduction: 20% of 80 units will be 16. Thus, the price will be 96% of the old price.

Conclusion: the price will be less than the original one by 4%.

Example 3.6. The price of item "A" is more than the price of item "B" by 25%. By what percent is the price of item B less than the price of item A?

To solve this problem, it is necessary to take into account the change in the comparison base:

Conclusion: the price of product "B" is less than the price of product "A" by 20%.

Thus, only observance of all the rules makes it possible to comprehensively characterize the quantitative side of mass qualitatively defined social phenomena.