Relative statistics are called values that express quantitative relationships between socio-economic phenomena or their signs.
They are obtained by dividing one quantity by another. Most often, relative values are the ratios of two absolute values.
The value with which the comparison is made (the denominator of the fraction) is usually called the base of the relative value, the base of comparison, or base value , and the one that is being compared is called the current, being compared, or reported value .
The relative value shows how many times the compared value is greater than the basic one, or what proportion the first is from the second.
With the help of relative values, many facts of social life are expressed: the percentage of plan fulfillment, the rate of growth and growth, etc.
The relative magnitude of the dynamics;
The relative size of the target;
The relative magnitude of the task completion;
The relative size of the structure;
The relative amount of coordination;
Relative comparison value;
The relative magnitude of the intensity.
Consider the procedure for determining relative values.
The relative magnitudes of the dynamics. They characterize the change in the studied phenomenon in time and reveal the direction of the development of the object. Received by dividing the actual level of the reporting period by the actual level of the base period:
Example... The machine-building plant produced 630 machine tools in 2000, and 500 machines in 1999. It is necessary to determine the actual dynamics of the production of machine tools.
Thus, the output of machine tools for 1 year increased by 1.26 times (growth rate, growth index) or in percentage terms - it is 126.0% (growth rate). In other words, in one year the production of machine tools increased by 26.0% (growth rate).
Relative value of the target ... It is obtained as a result of dividing the planned target of the reporting period by the actual level of the base period.
Example... The machine-building plant produced 500 machines in 2006, and in 2007 it planned to produce 693 machines. Determine the relative value of the planned production of machine tools.
So, according to the plan for 2007, it was supposed to increase the production of machine tools by 38.6% (the planned growth rate), i.e. by 1.386 times (planned growth rate), or by 138.6% compared to 2006 (planned growth rate).
The relative magnitude of the task completion. Received as a result of dividing the actually achieved level in the reporting period by the planned target for the same period:
Example... The machine-building plant planned to produce 693 machines in 2006, but actually produced 630 pieces. Determine the size of the plan.
Consequently, the planned target was underfulfilled by 9.1%.
The relative size of the structure. Characterizes the composition of the studied population (share, specific weights of elements). It is calculated as the ratio of the absolute value of a part of the population to the absolute value of the entire population:
Example... There are 27 students in the student group, 9 of them are men. Let's determine the relative size of the group structure.
In the group, 33.3% are men and 66.7% are women.
Relative magnitude of coordination ... They characterize the ratio of the parts of a given population to one of them, taken as a comparison base and show how many times one part of the population is larger than the other, or how many units of one part are in 1, 10, 100, 1000 ... units of another part.
Example... In 2001, fuel and energy resources (in standard fuel) were distributed as follows: conversion to other types of energy - 979.8 million standard fuel; production and other needs - 989.0 million USD; export - 418.3 million USD; the balance at the end of the year - 242.1 mln. Taking export supplies as the comparison base, we determine how much is for production:
That is, 2.363 times more resources are spent on production and other needs than they are exported.
Relative value of comparison (spatial). It characterizes the comparative sizes of indicators of the same name, but related to different objects or territories and having the same temporal definiteness. The interpretation of these values depends on the comparison base.
(4.6)
Example... The population of Moscow in 2001 was 8.967 million, and the population of St. Petersburg in the same year was 5.020 million.
That is, the population of Moscow is 1.79 times greater than the population of St. Petersburg.
The relative magnitude of the intensity. Shows how many units of one population fall on a unit of another population and characterizes the degree of distribution of the phenomenon in a certain environment:
Example... Determine the labor productivity of 100 workers if the total volume of finished products is 1200 items.
There are 12 parts for each worker, i.e. labor productivity is 12 parts per worker.
2.4.1. Known data on the production of garments
Table 2.4
Planned task for the production of garments
and its implementation
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Sewing products |
Total |
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Plan (thousand pieces) |
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Implementation of the plan (thousand pieces) |
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Monthly plan fulfillment,% |
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Cumulates of the plan |
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Cumulative plan execution |
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In% to the total for the half-year |
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Implementation of a plan |
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2.4.2. In the reporting period, the district canning enterprise produced
Table 2.5
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Types of products |
Weight or volume of cans, g |
Number of cans, thousand pieces |
|
Canned vegetables |
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|
1. Tomato sauce |
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2. Marrow caviar |
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3. Pickled cucumbers |
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4. Tomatoes are natural |
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Milk products |
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1. Condensed milk |
Determine the total volume of products produced in conventional natural units.
Note. For a conditional jar, a jar with a product weight of 400.0 and a volume (V) of 353.4 cm 3 is taken.
2.4.3. Fuel consumption for heating plants in the reporting period is characterized by the following data
Table 2.6
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Type of fuel |
|||
|
actually |
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Luchegorsky coal |
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Shakhtinsky coal |
|||
Average caloric equivalents (coefficients) of conversion to conventional fuel: Luchegorsky coal - 0.85 tons, Shakhtinsky coal - 0.8 tons, fuel oil - 1.35 tons.
Determine: 1) the total consumption of the equivalent fuel according to the plan and actually;
2) the percentage of the plan for the total fuel consumption;
3) specific gravity of actually consumed fuel by type.
2.4.4. There is the following (conditional) data on the sale of fish products, thousand rubles.
Table 2.7
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Products |
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Total |
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smoked |
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Define:
1) the structure of the sale of fish products by quarters and per year;
2) the dynamics of sales for each type and for all products, together with a constant and variable base of comparison. Draw conclusions.
2.4.5. The turnover of the Vladkhleb Joint Stock Company in 2000 amounted to 20,260 million rubles. The planned turnover for 2001 was 27,730 million rubles. Determine the relative value of the company's planned target for turnover for 2001.
2.4.6. According to the construction firm, the plan for 2001 envisages an increase in the productivity of builders by 3%. In fact, during the reporting period, it increased by 5% compared to 2000. Determine the relative value of the implementation of the plan for the growth of labor productivity of workers in the company.
2.4.7. The plan of Vladkhleb JSC for 2001 compared to 2001 provided for a 3% reduction in production costs. In fact, it has been reduced by 2%.
Calculate the relative value of the plan to reduce the cost of production of the firm in 2001.
2.4.8. There are monthly data for an industrial enterprise:
Table 2.8
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Average payroll |
General fund |
Average monthly |
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according to plan |
actually |
percentage completed plan,% |
according to plan |
actually |
percentage completed plan,% |
according to plan |
actually |
percentage completed plan,% |
|
|
Total for the enterprise |
912,89 |
1420 |
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2.4.9. The following data are known for the city of Nakhodka:
Table 2.9
Number of cars in personal ownership
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Including |
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freight |
passenger cars |
buses |
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The end of the table. 2.9
Determine the growth rate by the chain method, the proportion of each type of car over the years, the coordination coefficient between trucks and buses.
2.4.10. For the travel company, there is data on revenue for the reporting period:
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Tour destinations |
Actual revenue |
Percent |
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China – Harbin |
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Turkey – Istanbul |
||
Determine the percentage of fulfillment of the revenue plan as a whole for the travel company.
2.4.11. Per capita consumption of food products according to the household survey in Nakhodka per year is presented in Table. 2.10.
Table 2.10
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Product type (kg) |
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1950 |
1960 |
1970 |
1980 |
1990 |
1999 |
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Bread products |
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Potato |
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Fish and fish products |
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Meat and meat products |
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Determine the dynamics of food consumption by the basic and chain method, the structure of food consumption by years. to equalize the indicators and draw conclusions.
Relative value of the target(indicator of the planned target) is the ratio of the planned level of the indicator to its level achieved in the previous period (or in the period considered as the baseline)
The relative value of the planned target characterizes the prospect of the development of the phenomenon
ORP = planned level for the future (next) period / actual level of the current (previous) period
Example: in 2007 the number of personnel was 120 people. in 2008 it was planned to reduce production and bring the number to 100 people.
Solution:
ORP = (100/120) * 100% = 83.3% - 100% = -16.7%.
The company planned to reduce the number of personnel by 16.7%.
Relative value of plan execution
Relative value of plan execution(indicator of implementation of the plan) characterizes the degree of implementation of the plan.
ORP = actual level of the current period / plan of the current period
Example: in 2007 the number of personnel was 120 people. in 2008 it was planned to reduce production and bring the number to 100 people. But the number of employees increased over the year to 130 people.
Solution:
ORVP = (130/100) * 100% = 130% - 100% = 30%.
The actual number of employees exceeded the planned level by 30%.
There is a relationship between and the relative value of the planned target and the relative value of the plan's fulfillment, expressed in the formula: OVVP = OVD / OVPZ
Example: the company planned to reduce the cost by 6%. The actual decrease compared to last year was 4%. How was the cost reduction plan implemented?
Solution:
ATS = (96/100) * 100% = 96% - 100% = - 4%
ORP = (94/100) * 100% = 94% - 100% = - 6%
ORVP = 96% / 94% = 102.1% - 100% = -2.1% the plan for cost reduction was not fulfilled because the actual level exceeded the target by 2.1%.
Example: an insurance company in 1997 entered into contracts in the amount of 500 thousand rubles. In 1998 she intends to conclude an agreement in the amount of 510 thousand rubles. The relative value of the planned target will be equal to 102% (510/500)
Suppose the influence of various factors led to the fact that the insurance company actually entered into contracts in 1998 in the amount of 400 thousand rubles. In this case, the relative value of the execution fee will be equal to 78.4% (400/510)
The relative values of the dynamics, the planned target and the fulfillment of the plan are related by the following relationship:
ОВП / ОВРП = ОВД
In our example: 1.02 * 0.784 = 0.8
The development of planned targets is the process of substantiating the approved indicators based on calculations and logical analysis of factors that have a significant impact on their value.
This process is of a creative nature, since formalized procedures make up only a certain part, and the final decisions are made on the basis of an expert analysis of the results of calculations and a combination of various factors that lend themselves only to a qualitative assessment. Strictly speaking, in accordance with the previously given classification, such decisions are classified as semi-creative. 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 substantiating planned targets is direct calculation. This method assumes a scrupulous calculation of each quantifiable factor in accordance with the scheme of their relationship (technological, estimate, etc.). At first glance, it seems that this method gives the most reliable results. However, this impression is misleading, since direct calculations (such as calculation) provide reliable data only in relation to the events that have happened. As for the planned calculations for the future, the uncertainty inherent in future events significantly devalues the value of direct calculations.
An alternative to direct calculations is the normative method, which makes it possible to predict the future values of key planning indicators on the basis of significantly simpler calculations than using direct account. This method is based on multiplying the standard indicator (always relative) by the amount determined by the basic reference indicator. In this case, the normative indicator is determined on the basis of an analysis of the current situation and adjustments for the future using expert assessments. The base figure is determined on the basis of statistical data or a forecast of their expected value for the planning period.
The balance method occupies a special place in the system of formalized planned calculations. Its meaning lies in comparing 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 the planned task. The second is the calculation of the possibility of providing the required type of resource to perform the same task. This calculation is done on the basis of an analysis of the planned targets for the release of the corresponding 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 side of the budget).
If the possibilities are equal or exceed the need, then the plan is considered balanced. At the same time, the excess of opportunities in comparison with the needs is called a surplus. In those cases, when the needs exceed the possibilities, the plan is recognized as scarce.
If the deficit (the difference between the need and the opportunity) is comparable to the errors caused by the inaccuracy of foreseeing future events (usually no more than 3-4%), then such a plan can be considered balanced. A plan with a significantly large deficit value is obviously impracticable. If such a plan is approved, then in the course of its implementation, adjustments are inevitable, depending on the actual situation. Such a plan cannot be considered scientifically sound. Therefore, its acceptance usually bears the character of a kind of compromise in the expectation that life itself will tell you what will need to be cut and what will have to be abandoned during the execution of the plan, since a priori it is not always possible to predict with sufficient accuracy.
The most difficult method of formalizing planned calculations is the use of economic and mathematical models to optimize planning decisions. This method has many different options depending on the use of different mathematical models. They are united by the fact that in the calculations a large number of options are calculated and the best one is determined from the position of a given criterion. At the same time, the volumes of calculations are such that they can be performed only with the use of electronic computers. The effectiveness of such calculations directly depends on the correspondence of the mathematical model to the tasks set.
The formalized planning method also includes "network planning". In this case, planned calculations are combined with decision-making on operational management. All works and events that must be accomplished in order to achieve the final goal are depicted in the form of a network graph in accordance with their natural sequence. The duration and amount of funding for each work are usually estimated using the peer review method previously described. As a result, using the network graph, a "critical path" is identified, requiring increased attention in terms of operational regulation and ensuring the set deadline for the implementation of the entire volume of planned work.
Relative values in statistics represent the quotient of dividing two statistical values, and characterize the quantitative relationship between them, expressed either in the form of a coefficient or as a percentage (Fig. 18.).
When calculating relative values, the numerator always contains an indicator that reflects the phenomenon under study, and in the denominator there is an indicator with which a comparison is made.
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Rice. 18. Types of relative values.
Relative value of fulfillment of contractual obligations- an indicator characterizing the level of fulfillment by an enterprise of its contractual obligations. In connection with the transition of the country's economy to market relations, the statistical reporting will not contain planned indicators, instead of them, the relative values of the fulfillment of contractual obligations will be calculated by the ratio of the actually fulfilled obligations and the volume of obligations provided for in the contract, expressed either in the form of a coefficient or as a percentage ...
The relative value of the fulfillment of contractual obligations is nothing more than relative size of plan execution , since in the conditions of market relations the level stipulated by the contract will be planned, i.e.:
Have a dog. = At pl.
Relative value of plan execution = 
In addition, for enterprises, relative value of the target , which shows how many times or by how many percent the value of the indicator according to the plan (according to the contract) should increase or decrease in comparison with its actual level in the previous period.
The relative value of the planned target =. 100%, where:
Upl- the planned level of the indicator for the reporting period;
Whoo- the actual level in the base period.
The relative value of the dynamics characterizes the change in the studied phenomenon over time, shows a decrease or increase in the indicator in comparison with any previous period. As a rule, the analysis relies on data for a number of periods.
In this case, the comparison base can be constant (basic growth rates) or variable (chain growth rates)
There is a relationship between the relative values of the dynamics, the fulfillment of the plan and the planned target:
That is, the relative magnitude of the dynamics can be obtained by the product of the relative values of the fulfillment of the plan and the planned target (the relative values must be taken in the form of coefficients, that is, without converting them into percentages).
Relative structure size characterizes the composition of the studied population. It is calculated as the ratio of the absolute value of each of the elements of the set to the absolute value of the whole set; those. as the ratio of a part to a whole, and represents the specific gravity of a part as a whole. As a rule, it is expressed as a percentage (the comparison base is taken as one hundred%), but it can also be expressed in fractions (comparison base 1).
Relative comparison value the quantitative ratio of indicators of the same name related to different objects of statistical observation. For example: the number of different cities can be compared with each other price levels in state stores (base) and in markets, etc.________________________________________________________________
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Relative magnitude of coordination one of the types of comparisons. Shows how many times the compared part of the population is more or less than the part taken as the comparison base (base), i.e. essentially characterize the structure of the studied population, sometimes more expressively than the relative size of the structure. For example: there is one specialist with a higher education for every two specialists with a secondary specialized education.
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Relative intensity value shows how widespread a particular phenomenon is in a particular environment. They represent the ratio of unlike but related absolute values. ___________________________________
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Unlike other relative values, the relative intensity values are always expressed by named values and show how many units of one population are per unit of another population.
For example: food consumption per capita; provision of the population with durable household items per hundred families or per thousand people, etc.
Questions and tasks
1. What are the absolute values? ___________________________________________
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2. What is the relationship between the relative magnitude of the plan, the relative magnitude of the planned target and the relative magnitude of the dynamics? _______________
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3. How to determine the relative size of the structure? __________________________________
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Task number 6
I. Use the data of periodicals and give the absolute and relative values that characterize any phenomenon of socio-economic life.
II. Solve the problems.
To obtain an "excellent" grade you need to solve all 5 problems, if the first two problems (6.1 and 6.2.) Are solved - you apply for "good", and, finally, if only problem No. 6.1 is solved. - Your knowledge of Topic 6 “Absolute and Relative Values” will be rated as “Satisfactory”.
Problem number 6.1
The supply of milk and dairy products for the reporting period is characterized by the following data: Table 5.
Determine the fulfillment of the supply agreement:
1) for each product;
2) for all products in a conditionally natural measurement (in terms of milk).
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Problem number 6.2
Based on the given data, calculate for each store and in general, the relative values of the plan, target and dynamics. Is there a relationship between the calculated indicators? Table 6.
Problem number 6.3
The actual turnover of the trading company for the reporting period amounted to 270 thousand rubles. The company fulfilled its turnover plan for this period by 102.4%. Determine the plan for the turnover in thousand rubles.
Problem number 6.4
The planned target for the store in terms of retail turnover for the year is set at 4,700 thousand rubles. The store exceeded the plan by 3.7%. Calculate the actual turnover of the store in thousand rubles.
Problem number 6.5
The plan for the reporting period was to increase the trade turnover by 3%. The planned target was exceeded by 600 thousand rubles, which is 2.5%. Calculate the increase in turnover (in thousand rubles and in%) in the reporting period compared to the base period.
Conclusions:
Absolute and relative values are widely used in the study of socio-economic phenomena of social life. Absolute values can be natural and value (monetary). Relative values are used to characterize the fulfillment of contractual obligations, dynamics and structure of statistical populations.
To achieve the intended goals, students were asked:
Study the materials of the supporting synopsis, supplement them with personal examples;
Answer questions for self-control;
Complete practical task number 6.
