Development of plan targets is the process of justifying approved indicators based on calculations and logical analysis of factors that have a significant impact on their value.
This process is creative in nature, since formalized procedures constitute only a certain part, and final decisions are made on the basis of an expert analysis of the results of calculations and the totality various factors, which can only be qualitative assessment. Strictly speaking, in accordance with the previously given classification, this kind of solutions belongs to the category of semi-creative ones. Moreover, there is a tendency to improve that part of the planning decision-making process that lends itself to formalized calculations.
One of the main formalized methods for justifying plan targets is direct calculation. This method involves a scrupulous calculation of each quantifiable factor in accordance with the scheme of their relationship (technological, cost estimates, etc.). At first glance, it seems that this method gives the most reliable results. However, this impression is deceptive, since direct calculations (such as costing) provide reliable data only regarding accomplished events. As for planned calculations for the future, then the uncertainty inherent in future events significantly depreciates the value of direct calculations.
An alternative to direct calculations is the normative method, which allows you to predict future values key indicators planning based on significantly simpler calculations than when using direct accounting. This method is based on multiplying the standard indicator (always relative) by the value determined by the basic reference indicator. The standard indicator is determined based on an analysis of the current situation and adjustments for the future using expert assessments. The basic indicator is determined on the basis of statistical data or a forecast of their expected value for the planning period.
The balance sheet method occupies a special place in the system of formalized planned calculations. Its meaning is to compare the results of two calculations performed using different methods and for different purposes. The first is the calculation of the need for any resource (material or financial) necessary to fulfill planned target. The second is the calculation of the possibility of providing required type resource to complete the same task. This calculation is made on the basis of an analysis of planned tasks for the production of relevant products or for the formation of the revenue side of the budget. Next, a comparison of needs and opportunities is carried out (as an option - a comparison of the expenditure and revenue parts of the budget).
If capacity equals or exceeds demand, then the plan is considered balanced. In this case, the excess of capabilities compared to needs is called a surplus. In those cases when needs exceed capabilities, the plan is considered deficient.
If the deficit (the difference between need and opportunity) is comparable to errors caused by inaccurate prediction of future events (usually no more than 3-4%), then such a plan can be considered balanced. A plan with a significantly larger deficit is obviously impossible to implement. If such a plan is approved, then as it is implemented, adjustments are inevitable depending on the actual situation. Such a plan cannot be considered scientifically sound. Therefore, its adoption usually has the character of a kind of compromise in the hope that life itself will tell you what will need to be cut and what will have to be abandoned as the plan is implemented, since a priori it is not always possible to predict this with sufficient accuracy.
The most complex method of formalizing planning calculations is the use of economic and mathematical models to optimize planning decisions. This method has many various options depending on the use of different mathematical models. They are united by the fact that during the calculations a large number of options are calculated and the best one is determined from the perspective of a given criterion. Moreover, the volume of calculations is such that they can only be performed using electronic computers. The effectiveness of such calculations directly depends on the compliance mathematical model assigned tasks.
A formalized planning method also includes “network planning”. In this case, planned calculations are combined with decision-making on operational management. All the work and events that must take place to achieve ultimate goal, are depicted as a network graph in accordance with their natural sequence. The duration in time and the amount of funding for each activity are usually estimated using the previously described method of expert assessment. As a result, using a network graph, a “critical path” is identified that requires increased attention in terms of operational regulation and ensuring the established deadline for completing the entire volume of planned work.
Along with absolute values, one of the most important forms of generalizing indicators in statistics are relative values - these are generalizing indicators that express a measure of quantitative relationships inherent in specific phenomena or statistical objects. When calculating a relative value, the ratio of two interrelated values (mainly absolute) is measured, which is very important in statistical analysis. Relative values widely used in statistical research because they allow you to compare different indicators and make such comparisons clear.
Relative values are calculated as the ratio of two numbers. In this case, the numerator is called the value being compared, and the denominator is called the basis of relative comparison. Depending on the nature of the phenomenon being studied and the objectives of the study, the basic quantity can take on different values, which leads to different forms of expression of relative quantities. Relative values are measured in:
— coefficients: if the comparison base is taken to be 1, then the relative value is expressed as an integer or fractional number showing how many times one value is greater than the other or what part it makes up;
— percent, if the comparison base is taken as 100;
— ppm, if the comparison base is taken to be 1000;
— prodecimal, if the comparison base is taken to be 10000;
- named numbers (km, kg, ha), etc.
Relative values are divided into two groups:
— relative values obtained as a result of the ratio of statistical indicators of the same name;
— relative values representing the result of comparison of different statistical indicators.
The relative values of the first group include: relative values of dynamics, relative values of the plan task and plan implementation, relative values of structure, coordination and visibility.
The result of a comparison of indicators of the same name is a short ratio (coefficient) showing how many times the compared value is greater (or less) than the base one. The result can be expressed as a percentage, showing what percentage the compared value is of the base.
Relative dynamics characterize changes in a phenomenon over time. They show how many times the volume of a phenomenon has increased (or decreased) over a certain period of time; they are called growth coefficients. Growth rates can be calculated as percentages. To do this, ratios are multiplied by 100. They are called growth rates, which can be determined on a variable or constant basis.
Growth rates (T p) with a variable base are obtained by comparing the level of the phenomenon of each period with the level of the previous period. Constant growth rate comparison base obtained by comparing the level of the phenomenon in each individual period with the level of one period taken as the base.
Growth rate in percentage with variable base (chain growth rate):
Where y 1; y 2; y 3; y 4;- levels of the phenomenon for the same consecutive periods (for example, product output by quarter of the year).
Growth rate on a constant basis (baseline growth rate):
; 
; . (4.2)
Where y k– a constant base of comparison.
— ratio of the indicator value according to the plan ( y pl) to its actual value in the previous period ( y o), i.e. at pl / at o.(4.3)
– the ratio of the actual (reported) value of the indicator ( at 1) to its value planned for the same period ( at pl), i.e. y 1 / y pl. (4.4)
The relative values of the planned target, plan implementation and dynamics are interconnected.
So, 
or ; . (4.5)
Relative magnitudes of structure characterize the share of individual parts in total volume aggregates and are expressed as fractions of a unit or as a percentage.
Each relative value of the structure, expressed as a percentage, is called specific gravity. This value has one feature - the sum of the relative values of the population being studied is always equal to 100%, or 1 (depending on how it is expressed). Relative values of structure are used in the study of complex phenomena that fall into a number of groups or parts, to characterize the specific weight (share) of each group in the overall total.
Relative coordination values reflect the ratio of the numbers of two parts of the whole, i.e. show how many units of one group are on average per one, ten or one hundred units of another group of the population being studied (for example, how many employees are there per 100 workers). Relative coordination values characterize the relationship between individual parts of the population and one of them, taken as the basis of comparison. When determining this value, one of the parts of the whole is taken as a basis for comparison. Using this value, you can maintain the proportions between the components of the population. Indicators of coordination are, for example, the number of urban residents per 100 rural; the number of women per 100 men, etc. Characterizing the relationship between the individual parts of the whole, the relative values of coordination give them clarity and allow, if possible, to control the observance of optimal proportions.
Relative values of visibility (comparisons) reflect the results of a comparison of indicators of the same name that relate to the same period (or moment) of time, but to different objects or territories (for example, annual labor productivity is compared for two enterprises). They are also calculated in coefficients or percentages and show how many times one comparable value is greater or less than another.
Relative comparison values are widely used in the comparative assessment of various performance indicators of individual enterprises, cities, regions, and countries. In this case, for example, the results of the work of a particular enterprise, etc. are taken as a basis for comparison and are consistently correlated with the results of similar enterprises in other industries, regions, countries, etc.
The second group of relative values, which is the result of a comparison of different statistical indicators, is called relative intensity values.
They are named numbers and show the total of the numerator per one, ten, per hundred units of the denominator.
This group of relative values includes indicators of production per capita; indicators of food consumption and non-food food products per capita; indicators reflecting the provision of the population with material and cultural benefits; indicators characterizing the technical equipment of production and the rational use of resources.
Relative intensity values are indicators that determine the degree of prevalence of a given phenomenon in any environment. They are calculated as the ratio of the absolute magnitude of a given phenomenon to the size of the environment in which it develops. Relative intensity values are widely used in statistical practice. An example of this value can be the ratio of the population to the area on which it lives, capital productivity, the provision of medical care to the population (the number of doctors per 10,000 population), the level of labor productivity (output per employee or per unit of working time), etc.
Thus, relative intensity values characterize the efficiency of using various types of resources (material, financial, labor), the social and cultural standard of living of the country’s population, and many other aspects of social life.
Relative intensity values are calculated by comparing opposite absolute quantities that are in a certain relationship with each other, and, unlike other types of relative quantities, they are usually named numbers and have the dimension of those absolute quantities whose ratio they express. However, in some cases, when the obtained calculation results are too small, they are multiplied for clarity by 1000 or 10,000, obtaining characteristics in ppm and prodecimal.
In the statistical study of social phenomena, absolute and relative values complement each other. If absolute values characterize the static nature of phenomena, then relative values make it possible to study the degree, dynamics, and intensity of development of phenomena. For correct application and the use of absolute and relative values in economic and statistical analysis it is necessary:
- take into account the specifics of phenomena when choosing and calculating one or another type of absolute and relative quantities (since the quantitative side of phenomena, characterized by these quantities, is inextricably linked with their qualitative side);
- ensure the comparability of the compared and basic absolute values in terms of the volume and composition of the phenomena they represent, the correctness of the methods for obtaining the absolute values themselves;
— comprehensively use relative and absolute values in the analysis process and not separate them from each other (since the use of relative values alone in isolation from absolute ones can lead to inaccurate and even erroneous conclusions).
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Development of plan targets is the process of justifying approved indicators on the basis of calculations and logical analysis of factors that have a significant impact on their value.
This process is creative in nature, since formalized procedures constitute only a certain part, and final decisions are made on the basis of an expert analysis of the results of calculations and a combination of various factors that can only be assessed qualitatively. Strictly speaking, in accordance with the previously given classification, this kind of solutions belongs to the category of semi-creative ones. Moreover, there is a tendency to improve that part of the planning decision-making process that lends itself to formalized calculations.
One of the basic formalized methods for justifying plan targets is direct calculation. This method involves a scrupulous calculation of each quantifiable factor in accordance with the scheme of their relationship (technological, budget, etc.).
Relative values.
At first glance, it seems that this method gives the most reliable results. Moreover, this impression is deceptive, since direct calculations (such as calculations) provide reliable data only regarding accomplished events. As for planned calculations for the future, the uncertainty inherent in future events significantly depreciates the value of direct calculations.
An alternative to direct calculations is the normative method, which allows you to predict future values of key planning indicators based on significantly simpler calculations than when using direct calculations. The root of this method is the multiplication of a standard indicator (always relative) by the value determined by the basic reference indicator. The standard indicator is determined on the basis of an analysis of the current situation and adjustments for the future using expert assessments. The basic indicator is determined on the basis of statistical data or a forecast of their expected value for the planned period.
The balance sheet method occupies a special place in the system of formalized planned calculations. Its meaning is to compare the results of two calculations performed using different methods and for different purposes. The first is the calculation of the need for any resource (material or financial), which is extremely important for achieving the planned target. The second is the calculation of the possibility of providing an extremely important type of resource to complete the same task. This calculation is made on the basis of an analysis of planned tasks for the production of relevant products or for the formation of the revenue side of the budget. Next, a comparison of needs and opportunities is carried out (as an option - a comparison of the expenditure and revenue parts of the budget).
If the possibilities are equal to or exceed the need, the plan is considered balanced. In this case, the excess of capabilities compared to needs is called a surplus. In those cases when needs exceed capabilities, the plan is considered deficient.
If the deficit (the difference between need and opportunity) is comparable to errors caused by inaccurate prediction of future events (usually no more than 3-4%), then such a plan should be considered balanced. A plan with a significantly larger deficit is obviously impossible to implement. If such a plan is approved, then as it is implemented, adjustments are inevitable based on the actual situation. Such a plan cannot be considered scientifically sound. For this reason, its adoption usually has the character of a kind of compromise in the hope that life itself will tell you what will need to be cut and what will have to be abandoned as the plan progresses, since a priori it is not always possible to predict this with sufficient accuracy.
The most complex method of formalizing planning calculations is the use of economic and mathematical models to optimize planning decisions. This method has many different options based on the use of different mathematical models. They are united by the fact that during the calculations a large number of options are calculated and the best one is determined from the perspective of a given criterion. Moreover, the volume of calculations is such that they can only be performed using electronic computers. The effectiveness of such calculations directly depends on the correspondence of the mathematical model to the assigned tasks.
A formalized planning method also includes “network planning”. In this case, planned calculations are combined with decision-making on operational management. All work and events that must be accomplished to achieve the final goal are depicted in the form of a network graph in accordance with their natural sequence. The duration in time and the amount of funding for each activity are usually estimated using the previously described method of expert assessment. As a result, with the help of a network graph, a “critical path” is identified, which requires increased attention in terms of operational regulation and ensuring the established deadline for completing the entire volume of planned work.
Absolute and relative statistical quantities
The concept of absolute values
Absolute values- these are the results statistical observations. In statistics, unlike mathematics, all absolute quantities have a dimension (unit of measurement), and can also be positive and negative.
Units of measurement absolute values reflect the properties of units of the statistical population and can be simple, reflecting 1 property (for example, the mass of the cargo is measured in tons) or complex, reflecting several interrelated properties (for example, tonne-kilometer or kilowatt-hour).
Units of measurement absolute values can be 3 types:
- Natural- used to calculate quantities with homogeneous properties (for example, pieces, tons, meters, etc.). Their disadvantage is that they do not allow the summation of heterogeneous quantities.
- Conditionally natural- are applied to absolute quantities with homogeneous properties, but manifesting them differently. For example, the total mass of energy resources (firewood, peat, coal, petroleum products, natural gas) is measured in t.u.t. - tons of standard fuel, since each type has a different calorific value, and 29.3 mJ/kg is taken as the standard. Similarly, the total number of school notebooks is measured in standard units. - conventional school notebooks size 12 sheets.
Relative values of the planned target and plan implementation
Similarly, canning production products are measured in u.c.b. - conventional cans with a capacity of 1/3 liter. Similar products detergents is reduced to a conditional fat content of 40%.
- Cost units of measurement are expressed in rubles or other currencies, representing a measure of the value of an absolute value. They make it possible to summarize even heterogeneous values, but their disadvantage is that it is necessary to take into account the inflation factor, therefore statistics always recalculate cost values in comparable prices.
Absolute values can be momentary or interval. Momentary absolute values show the level of the phenomenon or process being studied at a certain point in time or date (for example, the amount of money in your pocket or the value of fixed assets on the first day of the month). Interval absolute values are the final accumulated result for a certain period (interval) of time (for example, salary for a month, quarter or year). Interval absolute values, unlike moment ones, allow subsequent summation.
The absolute statistical value is denoted X, and their total number in the statistical aggregate is N.
The number of quantities with the same attribute value is indicated f and is called frequency(repetition, occurrence).
By themselves, absolute statistical values do not provide a complete picture of the phenomenon being studied, since they do not show its dynamics, structure, and relationships between parts. Relative statistical values are used for these purposes.
Concept and types of relative quantities
Relative statistic is the result of the relationship between two absolute statistical quantities.
If absolute quantities are correlated with the same dimension, then the resulting relative quantity will be dimensionless (the dimension will be reduced) and is called coefficient.
Often used artificial dimension of coefficients. It is obtained by multiplying them:
- for 100 - get interest (%);
- for 1000 - get ppm (‰);
- for 10,000 - get prodecimal(‰O).
The artificial dimension of coefficients is used, as a rule, in colloquial speech and when formulating results, but it is not used in the calculations themselves. Most often, percentages are used, in which it is customary to express the obtained values of relative values.
More often instead of a name relative statistic a shorter synonymous term is used - index(from lat. index- indicator, coefficient).
Depending on the types of correlated absolute values when calculating relative values, different results are obtained. types of indexes: dynamics, plan task, plan implementation, structure, coordination, comparison, intensity.
Dynamics index
Dynamics index(growth coefficient, growth rate) shows how many times the phenomenon or process being studied has changed over time. It is calculated as the ratio of the absolute value in the reporting (analyzed) period or point in time to the base (previous):
The criterion value of the dynamics index is “1”, that is: if iD>1 - there is an increase in the phenomenon over time; if iD=1 - stability; if iD
For example, a car dealership sold 100 cars in January, and 110 cars in February. Then the dynamics index will be iD = 110/100 = 1.1, which means an increase in car sales by a car dealership by 1.1 times or 10%
Schedule task index
Schedule task index is the ratio of the planned absolute value to the basic value:
For example, a car dealership sold 100 cars in January, and planned to sell 120 cars in February. Then the plan target index will be iпз= 120/100 = 1.2, which means planning sales growth by 1.2 times or 20%
Plan execution index
Plan execution index is the ratio of the actual absolute value obtained in the reporting period to the planned one:
For example, a car dealership sold 110 cars in February, although it was planned to sell 120 cars in February. Then the plan fulfillment index will be iвп= 110/120 = 0.917, which means the plan is 91.7% fulfilled, that is, the plan is underfulfilled by (100%-91.7%) = 8.3%.
Multiplying the indices of the planned task and plan execution, we obtain the dynamics index:
In the previously discussed example about a car dealership, if we multiply the obtained values of the indices of the planned task and the implementation of the plan, we obtain the value of the dynamics index: 1.2 * 0.917 = 1.1.
Structure index
Structure index(share, specific gravity) is the ratio of any part of a statistical aggregate to the sum of all its parts:
The structure index shows what proportion a particular part of the population makes up of the entire population.
For example, if in the group of students under consideration there are 20 girls and 10 young men, then the structure index (proportion) of girls will be equal to 20/(20+10) = 0.667, that is, the proportion of girls in the group is 66.7%.
Coordination index
Coordination index- this is the ratio of one part of the statistical population to another part of it, taken as the basis of comparison:
The coordination index shows how many times more or what percentage one part of the statistical population is compared to another part taken as the basis of comparison.
For example, if in a group of students of 20 girls and 10 young men, we take the number of girls as a basis for comparison, then the coordination index of the number of young people will be 10/20 = 0.5, that is, the number of young people is 50% of the number of girls in the group.
Comparison index
Comparison index is the ratio of values of the same absolute value in the same period or point in time, but for different objects or territories:
where A, B are characteristics of the objects or territories being compared.
For example, in January 2009, the number of residents in Nizhny Novgorod was approximately 1280 thousand people, and in Moscow - 10527 thousand people.
Let’s take Moscow as object A (since it is customary to put a larger number in the numerator when calculating the comparison index), and Nizhny Novgorod- for object B, then the comparison index for the number of residents of these cities will be 10527/1280 = 8.22 times, that is, in Moscow the number of residents is 8.22 times greater than in Nizhny Novgorod.
Intensity index
Intensity index- this is the ratio of the values of two interrelated absolute quantities with different dimensions, relating to one object or phenomenon.
For example, a bread store sold 500 loaves of bread and earned 10,000 rubles, then the intensity index will be 10,000/500 = 20 [rubles/loaf of bread], that is, the selling price of bread was 20 rubles. for a loaf.
Most fractional quantities are intensity indices.
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Relative indicators
Relative value (indicator)- a statistical quantity that is a measure of the quantitative relationship of statistical indicators and reflects the relative sizes of socio-economic phenomena. This could be: the ratio of the numbers of different sets of phenomena, their individual characteristics; sizes of different features of the same population; the ratio of the planned and actual values of an indicator or the value of an indicator for the current and past time.
A relative quantity is obtained as the quotient of dividing one quantity, usually called current or reporting, to another, which is called basic value, basis of comparison or basis of relative magnitude. The base of a relative value is equal to one or any number that is a multiple of 10 (100, 1000, etc.). In the first case, the relative value is presented in the form of a multiple ratio, showing how many times the current value is greater than the base value, or what proportion the first is in relation to the second. In other cases - as a percentage, ppm (per thousand), etc. The compared values can be either the same name or different names (in the latter case, the relative values have names derived from the name of the compared values, for example, rub/person; rub/sq.m).
The following types of relative quantities are distinguished: plan target; implementation of the plan; speakers; intensity; coordination; structures; comparisons; level economic development.
Relative value of the planned target- the ratio of the value of the target indicator to the value of the same indicator in the base year.
Relative level of plan implementation- the ratio of the value of an indicator achieved over a period of time (or at some point in time) and its value established according to the plan for the same time. She has great value as a means of monitoring and analyzing the implementation of plans. The relative amount of plan implementation is usually expressed as a percentage. The difference between the relative value of plan completion and 100% can be zero, have a positive or negative sign. A difference equal to zero indicates the exact implementation of the plan. If the planned indicator is such that its increase is a positive phenomenon (for example, production), then a difference with a positive sign indicates an overfulfillment of the plan, and a negative difference indicates an underfulfillment. If the nature of the indicator is such that a decrease in its size is positive (for example, labor costs, material consumption per unit of production), then the excess of the actual value over the planned value indicates a failure to fulfill the plan, and if it is less than the planned value, then an overfulfillment of the plan.
The plan target can be expressed in the form of absolute or relative values. In the first case, the relative value of plan implementation is calculated as the ratio of the actual (reported) value to the planned value. In the second, to determine the relative value of plan implementation, it is necessary to find the ratio of the reported value to the one that was accepted as the base value when establishing the plan target, and relate (divide) the resulting relative value to the planned relative value.
Relative magnitude of dynamics- ratio of the indicator value for given time and its value for any similar previous time, taken as the basis of comparison. The relative magnitude of the dynamics characterizes the degree and rate of change of the indicator over time, in particular the growth rate. The relative magnitude of the dynamics is expressed as a multiple or as a percentage. If there is a series of dynamics of absolute values, then the relative value of the dynamics can be calculated as the ratio of the value of the indicator (the level of the dynamics series) for each subsequent time to its value for the time immediately preceding it or as the ratio to its value for the same time, taken as the base comparisons. In the first case, the relative magnitude of the dynamics is called relative magnitude of dynamics with a variable comparison base, or chain, in the second - with a constant comparison base, or basic The first show how the value of the indicator changes between individual periods of time, and the second show how the gradual change in its value occurs, starting from the initial (basic). Chain and basic relative quantities are widely used to study the rate of development of a phenomenon, to identify its trends and patterns.
If the levels of a series of dynamics are denoted by ( - the serial number of levels from 1 to n ), then the chain relative dynamics are:
 |
basic:
or in general 
Relative intensity value- the ratio of the sizes of two qualitatively different phenomena.
One of them is the environment (its size) in which the development of any process, phenomenon occurs or which are generated by it, the other is the process or phenomenon being studied (their magnitude). The relative intensity value characterizes the degree of development (distribution) of a particular process or phenomenon in a certain environment. For example, the ratio between the number of births during the year in a country and the average annual population. When calculating the relative intensity value, the base is equal to 1, 100, 1000, etc. The relative magnitude of intensity is often called intensity factor. For example, fertility rate, marriage rate. They show how many units of one value are in 1, 100, 1000, etc. units of another quantity with which comparison is made. Relative intensity values are also called relative magnitudes of degree or frequencies.
Relative magnitude of coordination- the ratio of the sizes of the parts to each other. It shows how many units of one part of the whole there are in 1, 100, 1000, etc. units of its other part. For example, how many women are there per 1000 men (in a country or in a particular region), office workers per 100 workers (at an enterprise, in a certain industry? national economy). Relative values of coordination make it possible to identify the discrepancy between individual parts of a single whole, between the sizes of heterogeneous but closely interrelated characteristics, and disproportions in the national economy.
Relative comparison value— the ratio of the values of indicators of the same name relating to different objects or different territories. For example, comparing the cost of similar products produced at two enterprises by dividing data for one enterprise by data for another enterprise. Relative comparison values provide a visual representation of the relationship between the compared values and a comparative assessment of objects and regions of the country according to the compared indicator. Relative comparison values are sometimes called relative values of visibility. Relative comparison values are expressed as a multiple ratio (in times, fractions of a unit) or as a percentage.
Relative magnitude of structure- the ratio of the size of a part of a whole and the size of this whole. For example, the ratio of the number of a group of population units possessing a certain characteristic to total number units of this population (the ratio of the number of women and the number of men separately to the total population; the ratio of the number of different categories of industrial production personnel to its total number), or the ratio parts a certain amount to this amount (the ratio of family expenses on food to the total amount of the expenditure part of its budget; the ratio of costs of materials to the total amount of costs for the production of any product).
The relative value of the structure characterizes the composition, structure of the population, the structure of the process being studied, i.e. their internal structure according to one or another characteristic. Calculated over several periods (instants) of time, they give an idea of changes in the structure, called structural changes, about the patterns of its change.
Topic 3. Absolute, relative and average values
The relative value of the structure is calculated in fractions of a unit or as a percentage.
Relative values of structure are also called relative values of the share, specific gravity.
Relative value of the level of economic development- ratio of the magnitude of the most important economic indicators(country, region, sector of the national economy) and population. For example, the ratio of the annual volume of national economic production and the average annual population. Sometimes relative values of the level of economic development are called relative values of intensity.
Types of absolute quantities, their meaning
Types of relative quantities, methods of their calculation and forms of expression
The essence and meaning of average values. Average power quantities
Average structural values
Types of absolute quantities, their meaning
As a result of statistical observation and summaries, generalized indicators are obtained that reflect the quantitative side of phenomena.
All indicators used in statistical practice by form of expression classified into absolute, relative and average.
The initial form of expression for statistical indicators is absolute values. Absolute values characterize the absolute sizes of the phenomena being studied, and also give an idea of the volumes of aggregates.
Absolute value- an indicator reflecting the dimensions of social phenomena and processes in specific conditions of place and time. It characterizes the social life of the population and the economy of the country as a whole (gross domestic product (GDP), national income, industrial production, population, etc.).
In practice, there are two types of absolute values: individual and total.
Individual values show the size of the attribute of individual units of the population (for example, the weight of one person, the salary of an individual employee, the size of a deposit in a particular bank).
Total values characterize the final value of the attribute for a certain set of subjects covered by statistical observation (for example, the size of the wage fund, the total amount of deposits in banks).
Absolute statistical indicators- always named numbers, i.e. have units of measurement.
Absolute values are expressed:
V natural units(kilograms, grams, centners, units, pieces, etc.), which are used in the case of characterizing the size of one phenomenon (for example, the volume of milk sales);
V conventionally natural units(feed units, equivalent fuel units, etc.), which are used to characterize the size of homogeneous phenomena (for example, the volume of feed in feed units);
V value units(rubles, dollars, euros, etc.) used in determining the size of heterogeneous phenomena (for example, the cost of purchasing a variety of food products);
V labor units(man-hours, man-days, etc.), which express the amount of working time spent.
Types of relative quantities, methods of their calculation and forms of expression
Absolute values do not always fully characterize phenomena. In order to correctly evaluate a particular absolute indicator, it is necessary to compare it with a plan or indicator relating to another period. For this, relative values are used.
Relative value- the result of dividing one absolute indicator by another, expressing the relationship between the quantitative characteristics of socio-economic phenomena and processes. By the relative value, one can judge how much the compared indicator is greater than the base one or what share it makes up of the base level.
When calculating relative values, the absolute indicator found in the numerator is called compared (current), and located in the denominator - base of comparison. IN Depending on the comparison base, the resulting relative indicator can take the form of an expression or be a named value.
The following are distinguished: forms of expression relative values:
coefficient , if the comparison base is taken as 1;
percent, if the comparison base is taken to be 100;
ppm, if the comparison base is taken to be 1000;
prodecimal, if the comparison base is taken to be 10,000.
If the relative value is obtained by dividing different indicators, then it will be expressed using units of measurement, which reflect the relationship between the compared and basic indicators.
OVPP - relative value of the planned target;
OVVP - relative value of plan implementation;
OVD - relative magnitude of dynamics;
RVS - relative value of the structure;
RVC - relative magnitude of coordination;
OVSR - relative comparison value;
RVI - relative intensity value;
OVUER is the relative value of the level of economic development.
Relative value of the planned target (RPT) represents the ratio of the value of the indicator established for the planning period to its actual value achieved for the previous period or for any other period taken as the basis of comparison.
Where is the level planned for the upcoming period.
The indicator level achieved in the past (previous, base) period.
OVPP characterizes the growth or reduction of the phenomenon under study in the planning period compared to the achieved level in the previous period.
Relative value of plan implementation (RPV) represents the result of comparing the actually achieved level of the indicator with its planned level.
,
where , is the level of the indicator achieved in the reporting period.
OVVP characterizes the growth or reduction of the phenomenon under study, actually achieved in the reporting period, compared to the plan.
Relative magnitude of dynamics (RSD) is calculated as the ratio of the current indicator to the previous or basic one, i.e. characterizes changes in certain phenomena over time.
.
ATS is called growth rates and is expressed as coefficients or percentages.
The last three quantities are interconnected as follows:
OVD = OVPZ x OVVP
This relationship appears only if relative values are expressed in coefficients.
ATS is calculated using a chain or basic method. At chain calculation method each subsequent reporting level is compared with the previous level, with basic calculation method- with the first level taken as the basis of comparison.
If the level of each subsequent period (U n) is compared with the level of the previous period (U n -1), then the ATS is calculated chain method .
If the level of each subsequent period (U n) is compared with the level taken as the basis of comparison (U 0), then the ATS is determined in a basic way .
Relative magnitude of structure (RVS) shows the specific gravity of a part of the population in its total volume:
,
Where fi – the number of units of a part of the population,
∑ fi - total volume totality.
OBC expressed in coefficients or percentages and used to characterize the structure of a phenomenon.
Relative Coordination Magnitude (RCM) characterizes the relationship between individual parts of the whole. In this case, the part that has the greatest share or is a priority from an economic, social or other point of view is selected as a basis for comparison.
,
Where fi- number of units i- parts of the totality;
fj- number of units j- parts of the totality.
Relative coordination values show how many times one part of a population is larger than another or how many units of one part are per 1,10,100,1000,10000 units of another part.
Relative comparison value (RCV) is a ratio of absolute indicators of the same name that characterize different objects (enterprises, regions, countries, etc.), but corresponding to the same period or point in time.
The form of expression for OVSR can be taken in terms of coefficients or percentages.
Relative intensity value (RIM) shows the degree of distribution of a phenomenon in its inherent environment and is the result of a comparison of opposite, but in a certain way related absolute values (population density, labor productivity, unit cost of production, etc.). Calculated per 100, 1000, etc. units of the population being studied.
A special case of relative intensity magnitude is relative value of the level of economic development (LVED), which represents the volume of production of any product per capita. This value has a unit of measurement (kilograms, centners, tons, etc. per capita).
Comparison of statistical data is carried out in various forms and in different directions. According to various tasks and directions of comparison of statistical data are applied various types relative quantities, the classification of which is presented in Figure 1.
According to the nature, purpose and essence of the expressed quantitative relationships, the following types of relative quantities are distinguished:
1. Implementation of the plan;
2. Planned task;
3. Speakers;
4. Structures;
5. Coordination;
6. Intensity;
7. Comparisons.
Figure 1 - Classification of relative quantities
Relative indicators of the planned target (RPI) are used for purposes forward planning activities of subjects of the financial and economic sphere. They are usually expressed as a percentage.
Example. In the first quarter, the trade association's retail turnover amounted to 250 million rubles; in the second quarter, retail turnover is planned at 350 million rubles. Determine the relative value of the planned target.
Solution: GPZ = 
. Thus, in the second quarter it is planned to increase retail turnover trade association by 40%.
Relative plan performance indicators (RPI) express the degree of fulfillment of planned tasks over a certain period of time. It is calculated as the ratio of the actually achieved level to the planned target as a percentage. They are used to evaluate the implementation of the plan.
Example. According to the plan, the enterprise was supposed to produce products during the quarter in the amount of 200 thousand rubles. In fact, it produced products worth 220 thousand rubles. Determine the degree to which the company's production plan is fulfilled for the quarter.
Solution: OPVP = 
Consequently, the plan was completed 110%, i.e. the plan was exceeded by 10%.
When the plan is given in the form of a relative indicator (compared to the base level), the implementation of the plan is determined from the ratio of the relative value of the dynamics with the relative value of the plan target.
Example. According to the plan for 1999, labor productivity in the region's industry was supposed to increase by 2.9%. In fact, labor productivity increased by 3.6%. Determine the degree of implementation of the labor productivity plan by the region.
Solution: OPVP = 
Consequently, the level of labor productivity achieved in 1999 is 0.7% higher than planned.
If the planned target provides for a decrease in the level of the indicator, then the result of comparing the actual level with the planned one, which is less than 100% in value, will indicate that the plan has been exceeded.
Relative dynamics indicators (RDI) are called statistical quantities that characterize the degree of change in the phenomenon being studied over time. They represent the ratio of the level of the process or phenomenon under study for a given period of time and 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) one or what proportion of the latter it constitutes. This indicator can be expressed as shares or percentages.
Example. The number of telephone exchanges in Russia in 1996 was 34.3 thousand, and in 1997 - 34.5 thousand. Determine the relative magnitude of the dynamics.
Solution: OPD = times or 100.6%. Consequently, the number of telephone exchanges in 1997 increased by 0.6% compared to 1996.
If data is available for several periods of time, comparison of each given level can be made either with the level of the previous period, or with some other one taken as the basis of comparison (base level). The first ones are called relative indicators of dynamics with a variable comparison base, or chain, the second - relative indicators of dynamics with a constant base of comparison, or basic. Relative dynamics indicators are also called growth rates and growth rates.
There is the following relationship between the relative indicators of the plan target, plan implementation and dynamics: OPPP * OPVP = OPD. Based on this relationship, from any two known indicators it is always possible to determine a third unknown value. To prove this, let us actually denote achieved level the current period through , the base period - as , the level provided for by the plan - . Then - the relative indicator of plan implementation, - the relative indicator of the planned task, - the relative indicator of dynamics and, obviously, 
Relative structure indicators (RSI) represent the relationship between the part and the whole. Relative indicators of the structure characterize the composition of the population being studied and show what proportion (what proportion) each part of the totality constitutes. They are obtained by dividing the value of each part of the population by their total, taken as the basis for comparison.
Typically, relative indicators of this type are expressed in fractions of a unit or percentage.
Relative indicators of structure make it possible to establish structural shifts, changes that occur over a certain period of time, as well as their direction and trend. They are used when studying the composition of employees, when studying production costs, when studying the composition of trade turnover, etc.
Example. The organization's retail turnover for the year amounted to 1,230.7 thousand rubles, including the turnover of food products - 646.1 thousand rubles, turnover non-food products— 584.6 thousand rubles.
Solution: The share of turnover of food products in the entire turnover of the organization for the year was:
The share of turnover of food products in the entire turnover of the organization for the year was:
.
Sum specific gravity will be 100%. The structure of the organization’s retail turnover shows the predominance in the implementation of this retail commodity enterprise food products.
Relative Coordination Indicators (RCI) represent the ratio of one part of a population to another part of the same population.
Expressed as coefficients.
As a result of this division, we get how many times this part of the totality is greater (less) than the base one, or what percentage of it it is, or how many units of this structural part are per 1 unit, per 100, per 1000, etc. units of another part taken as the basis of comparison.
Example. According to the Russian statistical collection in 1996. V Russian Federation the number of men was 69.3 million people. And 78.3 million women. We determine how many women there were per 100 men.
In 1990 There were 114 women per 100 men. This means that the number of women per 100 men in 1996 was compared to 1990 decreased by 1 person.
Relative coordination values include capital productivity, capital intensity, labor productivity, product consumption per capita, etc.
The concept of relative magnitude for statistical and economic science very important. Or rather, not even the concept itself, but the process of calculating the relative value. How many times is one phenomenon greater or less than another, by what percentage did the increase occur, how the planned indicator changed or how the plan was fulfilled; relative values help to find out all this. We have already discussed the general essence of relative quantities. This part of the topic will introduce the concept of a specific relative quantity and examples of its calculation.
In the first of three blocks, we will analyze the relative value of the plan target.
Relative value of the planned target
(hereinafter we will call it OVPP for short) - allows it to determine the planned task of the organization for the next year in comparison with what we have already done in the past period.
Simply put, the relative value of the planned target shows
how the production plan will change next year compared to actually achieved results this year.
In different textbooks this relative value has a little different name. Sometimes she is called Relative target indicator
. But this does not change the essence of the quantity.
The basis for calculating the GPZ is the levels of the phenomenon being studied. In this situation it is:
Upl – planned level for the current period;
Ufact – the actual level achieved last year.
Calculation of the relative value of the planned target
1. Form for calculating the growth rate – shows how many times the planned indicator exceeds the actual indicator of the previous year.
2. Growth rate calculation form
– shows what percentage of the planned target for the next year will be in comparison with the actual value of the past year.
3. Form for calculating the growth rate – shows by what percentage they would like to increase output compared to the previous year; if the indicator turns out to be negative, then by how many percent they would like to reduce the target target.
Three forms of calculating indicators are necessary, since on the basis of them it is much easier to draw a conclusion about what should happen to the plan in the current year compared to the achieved indicators of the past year.
Example . Product output in value terms in 2014 amounted to 143 million rubles. In 2015, it is planned to increase the cost of production to 150 million rubles. determine the relative value of the planned target, the percentage of the planned target and by what percentage it is planned to increase the cost of production.
Given
Solution
Uf.p.g. – 143 million rubles. 1.
OVPP = Upl2015 / Uf.p.g.2014 - 150 / 143 - 1.049
For pl - 150 million rubles. 2. %PV = OVPP x 100% = 1.049 x 100% = 104.9%
Define 3.Δ%PZ = OVPP x 100% - 100% = 1.049 x 100 - 100 = +4.9%
OVPP, %PZ, Δ%PZ Answer: OVPP=1.049, %PV=104.9%, Δ%PV=+4.9%
Thus, it has a GPZ of 1.049, or it is planned to increase the cost of issue by 1.049 times.
The percentage of the planned target (%PZ) for 2015 will be 104.9% or it is planned to increase the cost of production (Δ%PZ) by 4.9% in 2015 compared to 2014.
The relative value of the plan target in combination with two other relative values forms an interconnected unity. You can read more about the essence of the relationship in the article about. What is the relative magnitude of plan implementation?
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