Examples of absolute indicators in statistics. Absolute and relative values in economic analysis. Types of absolute values
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 the quantitative ratios 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 are widely used in statistical research, because they make it possible to compare different indicators and make such a comparison visual.
Relative values are calculated as the ratio of two numbers. In this case, the numerator is called the compared value, and the denominator is the base of the relative comparison. Depending on the nature of the phenomenon under study and the objectives of the study, the basic value can take on different values, which leads to different forms of expression of relative values. Relative quantities are measured in:
Coefficients: if the base of comparison is taken as 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 of it is;
Percentage, if the base of comparison is taken as 100;
ppm, if the comparison base is taken as 1000;
Prodecimille, if the comparison base is taken as 10000;
Named numbers (km, kg, Ha), etc.
Relative values are divided into two groups:
Relative values obtained as a result of the ratio of the same statistical indicators;
Relative values representing the result of a comparison of dissimilar statistical indicators.
The relative values of the first group include: the relative values of the dynamics, the relative values of the planned task and the implementation of the plan, the relative values of the structure, coordination and visibility.
The result of comparing the same indicators is short relationship(coefficient), showing how many times the compared value is greater (or less) than the base value. The result can be expressed as a percentage, showing what percentage of the compared value is from the base.
Relative values of dynamics characterize the change of the phenomenon in time. They show how many times the volume of the phenomenon has increased (or decreased) over a certain period of time, they are called growth factors. Growth factors can be calculated as a percentage. To do this, the ratios are multiplied by 100. They are called growth rates, which can be determined with a variable or constant base.
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. Growth rates with a constant base of comparison are obtained by comparing the level of the phenomenon in each individual period with the level of one period taken as the base.
Percentage growth rate with variable base (chain growth rate):
where at 1 ; at 2 ; at 3; at 4;- levels of the phenomenon for the same consecutive periods (for example, output by quarters of the year).
Constant base growth rate (base growth rate):
; 
; . (4.2)
where at k is a constant base of comparison.
Relative value of the planned task- the ratio of the value of the indicator according to the plan ( y pl) to its actual value in the previous period ( at o) , i.e. u pl / u o.(4.3)
Relative value of plan execution is the ratio of the actual (reported) value of the indicator ( 1) to its planned value for the same period ( at pl), i.e. y 1 / y pl. (4.4)
The relative values of the planned task, the implementation of the plan and the dynamics are interconnected.
So, 
or ; . (4.5)
Relative values of the structure characterize the share of individual parts in the total volume of the population and are expressed in fractions of a unit or as a percentage.
Each relative value of the structure, expressed as a percentage, is called the specific gravity. This value has one feature - the sum of the relative values of the studied population is always equal to 100%, or 1 (depending on how it is expressed). Relative values of the structure are used in the study of complex phenomena that fall into a number of groups or parts, to characterize the specific gravity (share) of each group in the overall total.
Relative values of coordination reflect the ratio of the number of two parts of the whole, i.e. show how many units of one group account for an average of one, ten or one hundred units of another group of the studied population (for example, how many employees are there for 100 workers). Relative values of coordination characterize the ratio of individual parts of the population with one of them, taken as the basis for comparison. When determining this value, one of the parts of the whole is taken as the basis for comparison. With this value, you can observe the proportions between the components of the population. Coordination indicators 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 visibility and allow, if possible, to control the observance of optimal proportions.
Relative visibility values (comparisons) reflect the results of a comparison of indicators of the same name relating to the same period (or moment) of time, but to different objects or territories (for example, the annual labor productivity for two enterprises is compared). 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, countries. In this case, for example, the results of a particular enterprise, etc. are taken as a basis for comparison and 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 opposite statistical indicators, is called relative intensity values.
They are named numbers and show the total of the numerator per one, ten, one hundred units of the denominator.
This group of relative values includes indicators of production per capita; indicators of food consumption and non-food items per capita; indicators reflecting the provision of the population with material and cultural benefits; indicators characterizing the technical equipment of production, the rationality of spending resources.
Relative intensity values are indicators that determine the prevalence of a given phenomenon in any environment. They are calculated as the ratio of the absolute value of a given phenomenon to the size of the environment in which it develops. Relative intensity values are widely used in the practice of statistics. An example of this value can be the ratio of the population to the area on which it lives, capital productivity, the provision of the population with medical care (the number of doctors per 10,000 population), the level of labor productivity (output per worker or per unit of working time), etc.
Thus, the relative values of intensity characterize the efficiency of the use of various kinds of resources (material, financial, labor), the social and cultural standard of living of the country's population, and many other aspects of public life.
Relative intensity values are calculated by comparing opposite absolute values that are in a certain relationship with each other, and unlike other types of relative values, they are usually named numbers and have the dimension of those absolute values whose ratio they express. However, in some cases, when the calculated results are too small, they are multiplied for clarity by 1000 or 10,000, obtaining characteristics in ppm and decimille.
In the statistical study of social phenomena, absolute and relative values complement each other. If absolute values characterize, as it were, the statics of phenomena, then relative values make it possible to study the degree, dynamics, and intensity of the development of phenomena. For the correct application and 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 values (since the quantitative side of the phenomena characterized by these values is inextricably linked with their qualitative side);
To ensure the comparability of the compared and the basic absolute value in terms of the volume and composition of the phenomena they represent, the correctness of the methods for obtaining the absolute values themselves;
It is complex to use relative and absolute values in the analysis process and not to separate them from each other (because the use of relative values alone in isolation from absolute ones can lead to inaccurate and even erroneous conclusions).
10. The concept of absolute statistical values. Types of absolute values, their meaning. Units of measurement of absolute values.
Statistical data obtained during observation, as a result of a summary, grouping, are almost always absolute values, i.e., values that are expressed in physical units and obtained as a result of counting or direct measurement. Absolute values reflect the number of units of the studied populations, the sizes or levels of traits registered in individual units of the population, and the total amount of a quantitatively expressed trait as a result of summing up all its individual values.
Absolute values are of great cognitive importance.
Absolute values express the dimensions (levels, volumes) of socio-economic phenomena and processes, they are obtained as a result of statistical observation and summaries of initial information. Absolute values are used in the practice of trade, used in the analysis and forecasting of commercial activities. On the basis of these values, business contracts are drawn up in commercial activities, the volume of demand for specific products is estimated, etc.
Absolute values measure all aspects of social life.
Absolute values according to the way of expressing the sizes of the studied processes are divided into: individual and total, they in turn belong to one of the types of generalizing quantities. The sizes of quantitative features for each statistical unit characterize individual absolute values, and they are also the basis for a statistical summary for connecting individual units of a statistical object into groups. On their basis, absolute values are obtained, in which it is possible to distinguish indicators of the volume of signs of the population and indicators of the population size. If we study the development of trade and its condition in a certain area, then a certain number of firms can be attributed to individual values, and the volume of trade and the number of employees working in the firm are classified as total.
Absolute values are economically simple (the number of stores, employees) and economically complex (the volume of trade, the size of fixed assets).
Absolute values- always named numbers, have a certain dimension, units of measurement. In statistical science, natural, monetary (value) and labor units of measurement are used.
Units of measurement are called natural if they correspond to the consumer or natural properties of an object, product and are expressed in physical weights, measures of length, etc. In statistical practice, natural units of measurement can be composite. Conditionally natural units of measurement are used when summing up the number of dissimilar goods, products.
11. The concept of relative statistical values. Types of relative values. Ways of their calculation and forms of expression.
The relative statistic is the ratio of two absolute values and, if the latter are homogeneous, having the same dimension, then the relative value is dimensionless, taking the status of a coefficient. For example, capital productivity (turnover) as the ratio of the value of output to the value of fixed assets is a coefficient.
The most common is the relative value, coefficient or index of dynamics, which characterizes the change in a phenomenon over time, representing the ratio of the values of the same absolute value in different periods of time. That is
The criterion value of the dynamics index is one. If it is greater than it, there is an increase in the phenomenon; equal to one - stability; if it is less than unity, a decrease in the phenomenon is observed.
Another name for the index of dynamics is the index of change, subtracting one from which the rate of change with a criterion value of zero is obtained. If it is greater than zero, there is an increase in the phenomenon; equal to zero - stability; if less than zero, a decline is observed.
In some textbooks on Statistics, the index of change is called the growth rate, and the rate of change is called the growth rate, regardless of the result obtained, which may show stability or decline.
If the analyzed and base periods are not adjacent in the time series (for example, the year preceding the five-year period and its Last year), then the index of dynamics or change found by formula (1.1) will be general, therefore, the average index is additionally determined by the formula
where t is the number of periods in the time series (for example, in a five-year period t = 5).
As with the general index, the criterion value for the average index is one with the same conclusions about the nature of the change. By subtracting from the average index, the units obtain the average rate of change with a criterion value of zero and similar conclusions about the nature of the change in the phenomenon.
In production, relative values, coefficients or indices of the planned task and the implementation of the plan are used. The first is defined as the ratio of the values of the same absolute value according to the plan of the analyzed period and in fact the base one. That is
where X'1 - plan of the analyzed period; X0 - fact of the base period.
The plan execution index is the ratio of the values of the same absolute value in fact and according to the plan of the analyzed period, determined by the formula
Multiplying the indices of the planned task and the execution of the plan, we obtain the dynamics index. That is
The relative value, coefficient or index of the structure is also widely used in the form of the ratio of any part of the absolute value to its entire value. In essence, this is the share mentioned above, specific gravity, frequency, determined by the formula
For example, if the number of females (fws) in a group of students is divided by the size of the entire group, then the fsw structure index will be obtained.
Similar is the relative value, coefficient or index of coordination as the ratio of any part of the absolute value to its other part, taken as a basis. Determined by the formula
For example, if we take as a basis the number of LSP in a group of students and divide by this number the number of males (LMP) in it, then we get the LMP coordination index relative to the LBP.
The next is the relative value, coefficient or index of comparison in the form of the ratio of the values of the same absolute value in one period or point in time, but for different objects or territories. Determined by the formula
where A, B are features of the compared objects or territories.
Another type of relative comparison values is obtained by comparing the indices of the dynamics of different phenomena. As a result, indexes of advance or lag in the development of one phenomenon in comparison with another are formed. So, if at the enterprise labor productivity increased by 12%, and the average salary only by 7.5%, then the growth in labor productivity outstrips the growth in wages by the index of change by 112/107.5=1.042 or by 4.2%, and in terms of the rate changes by 12/7.5=1.6 or 60%. These are the corresponding lead indexes. The index of wage growth lagging behind labor productivity growth will be the reciprocal.
The listed indices are dimensionless relative values, and the indicator having dimension is the relative value of intensity in the form of the ratio of the values of two heterogeneous absolute values for one period of time and one territory or object. To determine it, the formula is used
The indicators of intensity include the above-mentioned cost, price, energy intensity of products and other relative values with a fractional dimension.
Generalizing statistical indicators reflect the quantitative side of the studied set of social phenomena. They represent a statistical value expressed in the corresponding unit of measurement. Generalizing indicators characterize the volumes of the studied processes, their levels, ratio, etc.
The generalizing indicators reflect the results of cognition of the quantitative side of the studied phenomena.
Building statistical indicators This is one of the most important tasks of statistical science.
statistic is a quantitative characteristic of socio-economic processes and phenomena.
Statistical indicators have interrelated quantitative and qualitative aspects. The qualitative side of a statistical indicator is reflected in its content, regardless of the specific size of the feature. The quantitative side of an indicator is its numerical value.
A number of functions performed by statistical indicators are primarily cognitive, managerial (control and organizational) and stimulating functions.
Statistical indicators in the cognitive function characterize the state and development of the studied phenomena, the direction and intensity of the development of processes occurring in society
General indicators- this is the basis for the analysis and forecasting of the socio-economic development of individual districts, regions. regions and the country as a whole. The quantitative side of phenomena helps to analyze the qualitative side of the object and penetrates into its essence.
The managerial function is one of the most important elements of the management process at all its levels.
The indicators used to study statistical practice and science are divided into groups according to the following criteria:
1) according to the essence of the studied phenomena, these are volumetric, characterizing the size of processes, and qualitative, which express quantitative relationships, typical properties of the studied populations;
2) according to the degree of aggregation of phenomena - these are individual, which characterize single processes, and generalizing, reflecting the totality as a whole or its parts;
3) depending on the nature of the studied phenomena - interval and moment. Data reflecting the development of phenomena over certain periods of time are called interval indicators, that is, this is a statistical indicator that characterizes the process of changing signs. Momentary indicators include indicators that reflect the state of the phenomenon on a certain date (moment);
4) depending on the spatial certainty, indicators are distinguished: federal - characterize the object under study in the whole country; regional and local - these indicators refer to a certain part of the territory or a separate object;
5) depending on the properties of specific objects and the form of expressions, statistical indicators are divided into relative, absolute and average, these indicators will be discussed below.
For the correct reflection in the statistical indicators of the studied phenomena or ongoing processes, the following requirements must be met:
1) when constructing statistical indicators, it is necessary to rely on the provisions of economic theory, statistical methodology and the experience of statistical work of trade management; strive to ensure that the indicators express the essence of the phenomena being studied and give them an accurate quantitative assessment;
2) it is necessary to obtain complete statistical information both on the coverage of units of the object under study, and on a comprehensive display of all aspects of the ongoing statistical process;
3) ensure the comparability of statistical indicators through the uniformity of the initial data in spatial and temporal terms, as well as using the same units of measurement;
4) the degree of accuracy of the information received, on the basis of which the indicators will be calculated, should be increased. Statistical indicators are interdependent, therefore they are considered in a certain connection, since one indicator that characterizes one or more aspects of a statistical phenomenon cannot give a complete picture of the process under study.
To develop a system of indicators, it is necessary to deeply study the essence of the analyzed object and accurately formulate the target setting of the research process, highlighting the main link in the entire studied set of statistical indicators.
The system of statistical indicators is formed by a set of interrelated indicators that have a single-level or multi-level structure. The system of statistical indicators is aimed at solving a specific problem.
Systems of statistical indicators have a different scale. For example, they characterize the activities of a store, association, trade of a district, region, etc. Subsystems of indicators are distinguished, with their help they study certain areas of activity of enterprises in the industry, for example, a subsystem of indicators for labor, material resources, financial resources, etc.
2. Absolute values, their main types
Statistical data obtained during observation, as a result of a summary, grouping, are almost always absolute values, i.e., values that are expressed in physical units and obtained as a result of counting or direct measurement. Absolute values reflect the number of units of the studied populations, the sizes or levels of signs registered in individual units of the population, and the total amount of a quantitatively expressed sign as a result of summing up all its individual values.
Absolute values are of great cognitive importance.
Absolute values express the dimensions (levels, volumes) of socio-economic phenomena and processes, they are obtained as a result of statistical observation and summaries of initial information. Absolute values are used in the practice of trade, used in the analysis and forecasting of commercial activities. Based on these values, business contracts are drawn up in commercial activity, the volume of demand for specific products is estimated, etc. All aspects of social life are measured by absolute values.
Absolute values according to the way of expressing the sizes of the processes under study are divided into: individual and total, they, in turn, belong to one of the types of generalizing values. The sizes of quantitative features for each statistical unit characterize individual absolute values, and they are also the basis for a statistical summary for connecting individual units of a statistical object into groups. On their basis, absolute values are obtained, in which it is possible to distinguish indicators of the volume of signs of the population and indicators of the population size. If we study the development of trade and its condition in a certain area, then a certain number of firms can be attributed to individual values, and the volume of trade and the number of employees working in the firm are classified as total.
Absolute values are economically simple (the number of stores, employees) and economically complex (the volume of trade, the size of fixed assets).
Absolute values- always named numbers, have a certain dimension, units of measurement. In statistical science, natural, monetary (value) and labor units of measurement are used.
Units of measurement are called natural if they correspond to the consumer or natural properties of an object, product and are expressed in physical weights, measures of length, etc. In statistical practice, natural units of measurement can be composite. Conditionally natural units of measurement are used when summing up the number of dissimilar goods, products.
Labor units of measurement (man-days, man-hours) are used to determine labor costs for the production of products, work, etc.
Absolute values are measured in cost units - prices. In cost units measure the income of the population, gross output, etc.
3. Relative values, their meaning and main types
Absolute statistical values alone are not enough to characterize the objects under study. To reflect the state of growth, the development of phenomena, their correlation in time and space in statistics, relative values are widely used.
Indicators obtained as a result of comparing absolute values are called in statistics relative values.
Relative values give an idea of how many times one absolute value is greater than another, or what part one absolute value is from another, or how many units of one set are per unit of another.
Relative values - this is an indicator that is a quotient of the division of two statistical values and characterizes the quantitative relationship between them.
To calculate relative values, the compared indicator is put in the numerator, which will reflect the phenomenon under study, and the denominator reflects the indicator with which this comparison will be made, it is the basis or base for comparison. The base of comparison is a kind of meter. The base has the result of a ratio depending on the quantitative (numerical) value, which is expressed in: coefficient, percentage, ppm or decimille.
If the base of comparison is taken as one, then the relative value is a coefficient and shows how many times the value under study is greater than the base. If the base of comparison is taken as 100%, then the result of calculating the relative value will be expressed as a percentage.
If the comparison base is taken as 1000, then the result of the comparison is expressed in ppm (%0). Relative values can also be expressed in decimilles if the base of the ratio is 10,000.
The form of the expression depends on: the quantitative ratio of the compared values; the semantic content of the result of the comparison. If the compared indicator is greater than the base, then the relative value is expressed as a coefficient or as a percentage, but if the compared indicator is less than the base, then it is better to express the relative value only as a percentage.
If the indicators being compared are comparable, then the calculation of relative values may be correct.
Depending on the purpose of the statistical study, relative values are divided into the following types: fulfillment of contractual obligations; relative values characterizing the structure of the population; relative values of dynamics; comparisons; coordination; relative intensity values.
The relative value of the fulfillment of contractual obligations is an indicator that characterizes the level of fulfillment by the enterprise of its obligations stipulated in the contracts.
The calculation of the indicator is made by the ratio of the volume of actually fulfilled obligations and the volume of obligations stipulated in the contract. It is expressed in the form of coefficients or as a percentage.
Relative indicators of the planned target (RPP) are used for long-term planning of the activity of a subject of the financial and economic sphere, etc.
The CVPP is calculated using the following formula:
Relative values of the structure- these are indicators characterizing the share of the composition of the studied populations. The relative value of the structure is determined by the ratio of the absolute value of an individual element of the statistical population to the absolute value of the entire population, that is, as the ratio of the part to the general (whole), and characterizes the share of the part as a whole, in the form of a percentage.
In the analysis of the commercial activities of trade and the service sector, relative values make it possible to study the entire composition of the turnover in terms of its assortment, the composition of the company's employees - according to certain characteristics (length of service, gender, age), the composition of the enterprise's expenses and other factors affecting commercial activity enterprises.
Relative Structural Indicators (RSI) = level of a part of the population / total level of the population as a whole
The relative values of the dynamics characterize the change in the phenomenon under study over time, reveal the direction of development, and measure the intensity of development. The relative value of the dynamics is calculated as the ratio of the level of a feature in a certain period or point in time to the level of the same feature in the previous period or point in time, that is, it characterizes the change in the level of a certain phenomenon over time. The relative values of the dynamics are called growth rates:
Relative comparison values characterize the quantitative ratio of similar indicators related to different objects of statistical observation.
To compare the level of prices for the same product sold through state stores and on the market, relative comparison values are used. The state price is taken as the basis for comparison. Relative values of coordination are a kind of comparison indicators. They are used to characterize the relationship between the individual parts of the statistical population. Relative values of coordination characterize the structure of the studied population. Relative intensity values demonstrate how widespread the studied phenomenon is in a certain environment; they are characterized by the ratio of oppositely named and interconnected absolute values.
Named values are expressed in relative intensity values:
Relative intensity value \u003d absolute value of the phenomenon under study / absolute value characterizing the volume of the medium in which the phenomenon propagates
The relative value shows how many units of one statistical population account for a unit of another statistical population.
The condition for the correct use of generalizing indicators is the study of absolute and relative values in their unity. The complex use of absolute and relative values gives a comprehensive description of the phenomenon under study.
Relative indicators of coordination (RIC) is the ratio of one part of the population to another part of the same population:
OPC = level characterizing the i - th part of the population / level characterizing the part of the population chosen as the basis of comparison
The result of the analysis of processes and phenomena studied using statistical methods is a set of numerical characteristics that can be classified into absolute and relative indicators.
Absolute indicators
Absolute values in terms of statistics are the number of units or amounts in the sample, which are the direct result of the summary and grouping of the analyzed data. Absolute indicators reflect, so to speak, the "physical" characteristics of the processes and phenomena under study (area, mass, volume, spatio-temporal parameters), which, as a rule, are recorded in primary accounting documents. Absolute values always have a dimension. We also note that, in contrast to the mathematical interpretation, the statistical absolute value can be either positive or negative.
Classification of absolute indicators
Absolute values are classified according to the method of presenting the dimensions of the phenomena under study into individual, group and general.
TO individual include absolute indicators expressing the numerical dimensions of individual units of the population. For example, the number of employees in the organization, the gross output of the enterprise, profit, etc.
group indicators are called parameters that determine the dimensional characteristics or the number of units in a certain part of the population. Such indicators are calculated by summing up the corresponding absolute parameters of individual units of the study group or by directly counting the number of units in a sample from the general population.
Absolute indicators that describe the size of a feature in all units of the population are called general. Such parameters are the result of a summary of the results of statistical studies. These indicators include wages enterprises of the region, wheat in the state, etc.
Definition of relative value
From the point of view of statistics, a relative value is a generalizing parameter that describes the quantitative ratio of two absolute values. In other words, relative indicators characterize the relationship and interdependence of two compared absolute parameters.
Application in socioeconomic research
Relative indicators play an important role in the analysis of socio-economic processes, since the absolute characteristics themselves do not always allow a correct assessment of the analyzed phenomenon. Often, their true significance is revealed only during comparison with another absolute indicator.
Relative indicators include parameters that determine the structure of the phenomenon, as well as its development over time. With their help, it is easier to trace the trends in the development of the process under study and to make a forecast of its further evolution.
The main feature of relative values is that they make it possible to perform processes that are incomparable in absolute terms, which, in turn, opens up opportunities for comparing the levels of development or the prevalence of various social phenomena.
The principle of calculating the relative value
In relation to absolute indicators, which are input data for statistical analysis, relative values are derived from them, or secondary. Calculation of relative indicators in general view is performed by dividing one absolute parameter by another. In this case, the value in the numerator is called the compared, or current, and the indicator in the denominator with which the comparison is made is the basis (base) of comparison.
Obviously, it is possible to perform a comparison even of seemingly completely unrelated absolute values. Relative indicators necessary for statistical analysis should be chosen based on the objectives of a particular study and the nature of the primary data available. At the same time, it is necessary to be guided by the principles of visibility and ease of perception.
As current and basic indicators for calculation, you can use not only absolute, but also relative characteristics. Relative parameters obtained by comparing absolute characteristics are called first-order indicators, and relative parameters are called higher-order indicators.
Dimensions of relative values
Statistical analysis allows you to calculate relative indicators for both the same and opposite values. The result of comparing the parameters of the same name are unnamed relative values, which can be expressed in multiplicity factors, representing how many times the current indicator is greater or less than the base one (in this case, one is taken as the basis for comparison). Often in statistical studies, the comparison base is taken equal to 100. In this case, the dimension of the obtained relative indicators will be percentages (%).
When comparing different parameters, the ratio of the corresponding dimensions of the indicators in the numerator and denominator is taken as the dimension of the obtained relative value (for example, the indicator of the level of GDP per capita has the dimension of million rubles / person).
Classification of relative values
Among the variety of relative parameters, the following types are distinguished:
- indicator of dynamics;
- indicators of the plan and implementation of the plan;
- intensity indicator;
- structure index;
- indicator of coordination;
- comparison index.
Dynamic indicator (OPD)
This parameter describes the ratio of the current level of development of the phenomenon under study to some, taken as a base, the level of its development in the previous period. Expressed as a multiple ratio, the relative indicator of dynamics is called the growth factor, and as a percentage - the growth rate.
Plan Indicators (PPI) and Plan Implementation Indicators (PIP)
Such indicators are used by all economic entities involved in current and strategic planning. They are calculated as follows:
The characteristics discussed above are related by the following relationship:
OPD \u003d OPP * OPP.
The relative indicator of the plan determines the intensity of the task compared to the previous period, and the implementation of the plan determines the degree of its implementation.
Structural Index (SIR)
This relative indicator shows the structural composition of the population and is expressed in relation to the size of the absolute attribute of the structural part of the object under study to the size of the attribute of the population as a whole. In other words, the calculation of structure indicators consists in calculating the specific weight of each part of the population:
OPS are usually expressed as fractions of a unit (coefficients) or percentages. The sum of the specific weights of the structural parts of the studied population should be equal to one or one hundred percent, respectively.
Such coefficients are used in the study of the structure of multicomponent complex phenomena, for example, in the study of emissions of harmful substances by vehicles of a traffic flow, separating them by the type of fuel used (gasoline, diesel, gas) or by purpose (cars, trucks, buses), etc.
Index of Coordination (CPI)
This parameter characterizes the ratio of the characteristics of some part of the statistical population to the characteristics of the base part. The relative indicator of coordination is used in statistical analysis for a more visual representation of the relationship between the individual parts of the population under study.
The part of the population with the maximum specific gravity or being a priority is chosen as the basic one.
Intensity Index (IIR)
This characteristic is used to describe the propagation of the phenomenon (process) under study in its own environment. Its essence lies in the comparison of oppositely named quantities related to each other in some way.
An example is indicators of the level of GDP per capita, demographic indicators of natural increase (decrease) of the population per 1000 (10000) people, etc.
Comparison indicator (CFR)
This parameter describes the ratio of the same absolute characteristics of different objects:
The relative comparison indicator can be used for comparative analysis, for example, the population of different countries, prices for the same goods of different brands, labor productivity at different enterprises, etc.
The calculation of relative characteristics is an important step in statistical analysis, however, considering them regardless of the primary absolute indicators, one can come to unreliable conclusions. Consequently, a correct assessment of various socioeconomic processes and phenomena should be based on a system of parameters, which includes both absolute and relative indicators.
A statistical indicator is a quantitative characteristic of a socio-economic process or phenomenon.
A set of interrelated statistical indicators, having a single-level or multi-level structure, forms a system of statistical indicators.
Distinguish indicators - categories and specific statistical indicators. Indicator - the category reflects the essence, the general distinctive properties of specific statistical indicators. But after binding to a specific place (object), it becomes specific. For example, the population is a qualitative definition, and the population of Leninogorsk on 01.01.2010. is a specific statistic.
According to the coverage of population units, indicators can be individual and consolidated. The summaries are divided into:
Volumetric - obtained by adding the values of the attribute of individual units of the population
Calculated - calculated according to various formulas and serve to measure the relationship, variation, characteristics of structural changes, etc.
According to the time factor, indicators can be momentary - for the date and interval - for the period, from ... to ...
On a spatial basis, indicators can refer to the federal, regional and local levels.
From the point of view of specific objects and forms of expression, indicators can be absolute, relative, average.
Statistical indicators expressing the dimensions (volumes, levels) of socio-economic phenomena in units of measure, weight, volume, length, area, cost, etc. called absolute statistics. They always have a certain dimension, certain units of measurement.
The choice of units for measuring absolute values is determined by the essence, properties of the phenomenon under study, as well as the objectives of the study. In statistics, a large number of the most diverse units of measurement are used. In the most general classification, they can be reduced to three types: natural, monetary (value) and labor.
natural it is customary to call such units of measurement, which are expressed in measures of weight, volume, length, area, etc. Such units of measurement are used to characterize the volume of various types of products, the size of the sale of goods, the power of power plants, etc. These are the production of fabrics - in linear and (or) square meters, the production of gas - in cubic meters, electricity - in kilowatt-hours.
In some cases, apply conditionally natural units. They are used to bring together several varieties of the same use-value. One of them is taken as a standard, while others are converted using special coefficients into units of measure of this standard. Thus, in the practice of our statistics, all types of fuel are recalculated into equivalent fuel with a calorific value of 29.3 MJ/kg (7000 kcal/kg).
Soap with different content of fatty acids is recalculated to 40% fatty acid content, canned goods of different volumes - to conditional cans with a volume of 353.4 cm3, freight cars - to biaxial, etc.
If, for example, there are 100 tons of soap with a fatty acid content of 40% and 100 tons with a fatty acid content of 60%, then, counting for 40% soap, we get 100 + 100. 60/40 = 250 conditional tons of soap.
Labor units of measurement such as man-hours, man-days, etc., are used to determine the labor costs for the production of products, for the performance of some work, for taking into account the labor intensity of individual operations of the technological process.
In conditions market economy important and widely used cost units of measurement that give a monetary assessment of socio-economic phenomena and processes.
These are: gross domestic product, trade turnover, incomes and expenses of the population, etc.
Absolute statistical indicators are subdivided into volume indicators and level indicators.
Volume indicators allow us to characterize the magnitude of the entire population or its parts. Thus, the economically active population in Russia in 1998 amounted to 72,572 thousand people, including 38,355 thousand men and 34,217 thousand women. They can also express the total value of any feature of the entire population or part of it.
Level indicators characterize the value of the load of a unit of one population by elements of another population (for example, in Russia in 1999 the number of inhabitants per 1 km2 of territory was 8.6 people). They can also determine the degree of saturation of a particular set of elements of some feature of this or another set. (in Russia in 1998 the average subsistence minimum per capita per month was 493.3 rubles; in 1998 in Moscow the average retail price for a women's demi-season coat made of woolen and semi-woolen fabrics amounted to 2128.16 rubles. a piece).
There are also difference absolute figures. They represent the absolute size in the difference between two absolute indicators in time or space. An example of the absolute display of the gel of the difference in time (called the absolute growth rate) is the difference between the production of confectionery and Russia in 1998 (1310 thousand tons) and in 1992 (1829 thousand tons), equal to 519 thousand tons. The absolute size of the production of confectionery products in Russia has decreased over this six years
Relative indicators are called statistical indicators, defined as the ratio of the compared absolute value to the base of comparison. The value with which the comparison is made (the denominator of the fraction) is usually called the base, base of comparison, or base value. The numerator is the value being compared. It is also called the current or reporting value.
For example, dividing the urban population by the entire population of the country, we obtain the indicator "share of the urban population".
Compared values can be of the same name and opposite names. If the same-name values are compared, then the relative indicators are expressed in abstract numbers. As a rule, the base of comparison is taken equal to 1,100,1000 or 10000. If the base is 1, then the relative value shows what proportion of the base value is the current value. If the base of comparison is 100, then the relative value is expressed as a percentage (%), if the base of comparison is 1000 - in ppm (% o), 10000 - in decimilles (% oo).
When comparing dissimilar values, the names of relative values are formed from the names of the compared values (population density of the country: people / km2; productivity: q / ha, etc.).
Depending on the tasks, content and meaning of the expressed quantitative ratios, there are relative indicators of the plan of the new task, the implementation of the plan, dynamics, structure, coordination, comparison, intensity, level of economic development.
Relative indicators of the planned target(OPPP) are used for the purpose of long-term planning of the activities of subjects of the financial and economic sphere, as well as for comparing the actual results achieved with those previously planned.
Example In the first quarter, the retail turnover of the trade association amounted to 250 million rubles; in the second quarter, retail turnover of 350 million rubles is planned. Determine the relative value of the planned task.
Solution: HPP * 100% = 140%. Thus, in the second quarter, it is planned to increase retail trade trade association by 40%.
Relative performance of the plan(OPVP) express the ratio between the actual and planned levels of the indicator. They are usually expressed as a percentage. The method of calculating the relative performance indicators of the plan depends on how and in what form the plan indicators are given. Planned indicators can be set in the form of absolute and average values. If the target is set in the form of absolute and average values, the degree of fulfillment of the plan is determined by dividing the actually achieved value of the indicator by the value provided for by the plan
When the plan is set as a relative indicator (compared to the baseline), the implementation of the plan is determined from the ratio of the relative value of the dynamics to the relative value of the target
If the planned task 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 size, will indicate that the plan has been overfulfilled.
Relative indicators of dynamics(OPD) are called statistical quantities that characterize the degree of change in the studied phenomenon 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) level or what proportion of the latter it is. This indicator can be expressed in shares or percentages.
When data are available for multiple time periods, comparing 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 (basic level). The former are called relative indicators of dynamics with a variable base of comparison, or chain, the second - relative indicators of dynamics with a constant base of comparison, or basic. Relative indicators of dynamics are otherwise called growth rates and growth rates.
There is the following relationship between the relative indicators of the planned target, the fulfillment of the plan and the dynamics: OPPZ. OPVP = OPD. Based on this relationship, for any two known indicators, it is always possible to determine the third unknown value.
Relative indicators of the structure(OPS) represent the relation of the part and the whole. They characterize the structure, the composition of a particular set of socio-economic phenomena. From the definition of the relative indicators of the structure, it follows that when they are calculated, the value of the whole (the total for any indicator) is taken as the basis for comparison, and the values of the indicators of individual parts of this whole are compared.
Relative indicators of coordination(OPK) are the ratio of one part of the population to another part of the same population
As a result of this division, they get how many times this part of the population is more (less) than the base one, or how many percent of it is, or how many units of this structural part fall into 1 unit, 100, 1000, etc. units of the other -th part taken as the base of comparison.
Relative intensity indicators(OPI) characterize the degree of saturation or development of this phenomenon and represent the ratio of the indicator under study to the size of its inherent environment
A kind of relative intensity indicators are relative indicators of the level of economic development (OPUER). They characterize the output per capita and are very significant in assessing the state of the economy of the state.
Since the volume indicators of production are by their nature intervals, and the population indicator is momentary, the average population for the period (for example, the annual average) is used in the calculation:
Relative Comparison Indicators(OPSr) are the ratio of similar values related to different objects (enterprises, firms, districts, regions, countries, etc.):
With the help of such an indicator, one can compare the population, the size of the territory, the amount of sown area by country, region, district, etc.
Averages are the most common in statistics. They represent a generalized quantitative characteristic of a trait in a statistical aggregate. They give a generalized description of the same type of phenomena according to one of the varying features.
The most important property of averages is the ability to reflect the common inherent in all units of the population. The average value reflects the typical level of the trait when it is calculated from a qualitatively homogeneous population. If the population is not homogeneous, the general average value should be supplemented with group averages, which are calculated as a result of preliminary grouping of the population data.
The most common types of averages used in statistics include:
Arithmetic, which can be simple and weighted.
Simple arithmetic mean used when the calculation is based on ungrouped data. To do this, the sum of the values of the varying indicators is divided by their total number.
Arithmetic mean weighted, used when the value of a variable feature is repeated. In this case, the frequency of repetition of such a value is determined and the average is calculated from the grouped data using the formula:
or by the formula:
When calculating the weighted average according to the data of the interval series, it is necessary to move from the interval values to the median values.
Harmonic weighted mean - is used when the numerator of the original ratio of the average is known, but its denominator is not known. In this case, the calculation is carried out according to the formula:
Where w i = x i m i
A weighted place can be used in cases where the values w i for population units are equal to (planned duration of the working day). It is calculated by the formula:
Unweighted geometric mean calculated by the formula:
Average harmonic weighted calculated by the formula:
The most commonly used statistics are the mode and the median. Fashion represents the value of the studied feature, which is repeated with the greatest frequency.
The median is the value of the feature that falls in the middle of the ranked (ordered) population. The main property of the median is that the sum of the absolute deviations of the attribute values from the median is less than from any other value.
According to the grouped data, the mode is determined from the table.
The median value of the attribute is calculated by the formula:
Where P- the volume of the population.
In the interval series, the mode is calculated by the formula:
where, X 0 - the lower limit of the modal interval (the interval with the highest frequency), h - the width of the modal interval; mMo is the frequency of the modal interval;
T Mo-1 - the frequency of the interval preceding the modal;
T Mo+1 - the frequency of the interval following the modal.
In the interval series, the median is calculated by the formula:
Where: x0 is the lower limit of the median interval (the first interval in which the accumulated frequency exceeds half total amount frequencies); h is the width of the median interval; T i - frequency of the i-th interval;
S M e -1 - the accumulated frequency of the interval preceding the median;
T Me - the frequency of the median interval.
