The relative value of the planned task shows. Types of relative indicators

2.4.1. Known data on the production of garments

Table 2.4

Planned task for the production of garments
and its implementation

2.4.2. IN reporting period the enterprise of canning products of the region produced

Table 2.5

Determine the total volume of manufactured products in conditionally natural units.

Note. A conventional can is a can with a product weight of 400.0 and a volume (V) of 353.4 cm 3 .

2.4.3. Fuel consumption at heating plants in the reporting period is characterized by the following data

Table 2.6

Average caloric equivalents (coefficients) of conversion into reference fuel: Luchegorsky coal - 0.85 tons, Shakhtinsky coal - 0.8 tons, fuel oil - 1.35 tons.

Determine: 1) the total consumption of standard fuel according to the plan and actually;

2) the percentage of the plan for the total fuel consumption;

3) specific weight of actually consumed fuel by types.

2.4.4. The following data (conditional) on the sale of fish products are available, thousand rubles.

Table 2.7

Define:

1) the structure of the sale of fish products by quarters and for the 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. Trade turnover joint-stock company"Vladkhleb" for 2000 amounted to 20,260 million rubles. The trade turnover in the amount of 27,730 million rubles was planned for 2001. Determine the relative value of the planned target of the company in terms of turnover for 2001.

2.4.6. By construction company The plan for 2001 provides for a 3% increase in the labor productivity of builders. 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 the company's workers.

2.4.7. The plan of JSC "Vladkhleb" for 2001 in comparison with 2001 provided for a reduction in the cost of production by 3%. In fact, it was reduced by 2%.

Calculate the relative value of the implementation of the plan to reduce the cost of the company's products in 2001.

2.4.8. By industrial enterprise Monthly data available:

Table 2.8

2.4.9. The following data are known for the city of Nakhodka:

Table 2.9

Number of cars in personal ownership

The end of the table. 2.9

Determine the growth rate by the chain method, the share of each type of car by year, the coefficient of coordination between trucks and buses.

2.4.10. By travel company there is data on revenue for the reporting period:

Determine the percentage of implementation of the revenue plan as a whole for the travel company.

2.4.11. Food consumption per capita per year based on the materials of the survey of households in the city of Nakhodka is presented in Table. 2.10.

Table 2.10

Determine the dynamics of food consumption by the basic and chain methods, the structure of food consumption by years. compare figures and draw conclusions.

The implementation of the plan is an indicator that is very often used not so much in statistics as in the economy of an organization. The thing is that the analysis of the implementation of planned actions is the most important part of the analysis of sales revenue, productivity, cost and a number of others. key indicators enterprise activities. But to help calculate the level of implementation of the plan, and more often overfulfillment or underfulfillment helps the relative value of the plan.

As already noted, the three relative values ​​are interconnected. They are combined into a common block of mutually complementary relative values. The relationship formula in this case looks like this: ATS = OVPV x OVVP, but we will talk about this in more detail in the third part.

So, Relative value of plan execution , we will call it for short OVVP . In some textbooks, in particular Shmoylova's Theory of Statistics, this relative value has a slightly different name. Relative plan completion rate , well, the essence of the calculation itself and its principle, of course, will not change.

The relative value of the implementation of the plan shows how many times the actual level is more or less than planned. That is, by calculating this relative value, we can find out whether the plan is overfulfilled or underfulfilled, and what is the percentage of this process.
Similar to the calculation of the plan target, the execution of the plan is calculated based on two indicators. However, there is a fundamental difference here; for the calculation, indicators of the same period of time are used (in the planned task, these were two different periods). Included in the calculation:
Upl - the planned level for the current year.
Uf.t.g. - the actual level of the current year.

Calculation of the relative value of the implementation of the plan (RTI)

We will calculate the fulfillment of the plan, as well as the percentage of fulfillment and the percentage of overfulfillment, using similar formulas, as in the calculation of the planned target.
1. Coefficient form- characterizes how many times the actual value for the current period exceeds the planned indicator for the current period.

3. Growth rate form allows you to determine by what percentage the plan is overfulfilled or underfulfilled.

We will carry out calculations using the indicated formulas and analyze the results obtained.

Example. The output in 2015 actually amounted to 157 million rubles, while the planned figure for the same period was 150 million rubles. Determine the relative value of the plan, the percentage of the plan and the percentage of overfulfillment of the underfulfillment of the plan.

Given: Solution:
Upl 2015 - 150 million rubles. OVVP = 157 / 150 = 1.047

UV 2015 - 157 million rubles. % VP \u003d 1.047 x 100% \u003d 104.7%

Define:Δ% VP \u003d 104.% - 100% \u003d + 4.7%
ROVVP, %VP, Δ%VP
Thus, we get:
- The relative value of the implementation of the plan was 1.047, that is, the actual indicator exceeds the planned one by 1.047 times.
— The plan was fulfilled by 104.7%.
— The plan was exceeded by 4.7%.

It should be said that when calculating the growth rate, the resulting data can be negative , that is, there will be an underfulfillment of the plan.

As already noted, this relative value is a whole complex with two other relative values, you can view the link, and features.

Relative value of the planned task(planned target indicator) 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 base one).

The relative value of the planned task characterizes the prospects for the development of the phenomenon
OVTR = planned level for the future (next) period / actual level of the current (previous) period

Example: in 2007 the number of employees was 120 people. in 2008, it was planned to reduce production and bring the number to 100 people.
Solution:
OVTR =(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(plan implementation indicator) characterizes the degree of implementation of the plan.
TFR = actual level of the current period / plan of the current period

Example: in 2007 the number of employees was 120 people. in 2008, it was planned to reduce production and bring the number to 100 people. But the number of employees for the year increased to 130 people in a year.
Solution:
ROVP = (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 plan task and the relative value of the implementation of the plan, expressed in the formula: OVVP = OVD / OVPV

Example: the company planned to reduce the cost by 6%. The actual decrease compared to the previous year was 4%. How was the cost reduction plan implemented?
Solution:
ATS = (96 / 100) * 100% = 96% - 100% = - 4%
OVTR = (94 / 100)*100% = 94% - 100% = - 6%
RWP = 96% / 94% = 102.1% - 100% = -2.1% the actual level exceeded the planned one by 2.1%.

Example: Insurance Company in 1997, she entered into contracts in the amount of 500 thousand rubles. In 1998, she intends to conclude contracts for the amount of 510 thousand rubles. The relative value of the target will be equal to 102% (510 / 500).

Suppose the influence of various factors led to the fact that in 1998 the insurance company concluded expensive deals 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 task and the fulfillment of the plan are related by the following relationship:

In our example: 1.02*0.784=0.8

The relative values ​​of the dynamics are also called "growth rates", denoted as "Tr" or indices. The period in which the phenomenon is taken as the basis for comparison in statistics is usually called "basic" and denoted as "x0". The period in which the compared phenomenon occurs is called the "reporting", "current" and is designated as "x1". The relative value of the dynamics is calculated using the following formula:

The level of the compared phenomenon can also be called the "actual level", that is, the level actually achieved in the reporting period, it has the designation "xf". Then, the relative value of the dynamics will take the following form:

The relative value of the planned target. In statistics, the values ​​of the characteristics of the phenomenon under study, which must be achieved in the coming period, are called planned values.

The relative value of the planned task (ORp.z.) is calculated as a correlation of the planned level of the phenomenon (xpl) with the level of the same phenomenon, which is taken as the basis for comparison (x0). As a basis for comparison, the actually achieved value of the attribute of the phenomenon under study in the period preceding the planned one is taken, and not necessarily the immediate precedence, any previous period can be taken as the basis for comparison. Thus, the relative value of the planned task has the form:

That is, this relative value determines, in percentage terms, how many times the planned level of the phenomenon differs from the level of the phenomenon achieved in the previous period.

Relative value of plan implementation. The concept of "implementation of the plan" implies a comparison of the planned target and the actual result. Consequently, the relative value of the implementation of the plan (Rvv.p.) is a correlation of the actually achieved level of the phenomenon in the study period (хф,х1) with the planned level of this phenomenon (хpl): That is, this relative value shows how many times the actual level of the phenomenon under study in the reporting period differs from the planned level of the phenomenon for this period.

The relationship between the relative values ​​of the dynamics, the plan task, the implementation of the plan. If there is a planned level in the construction of relative values ​​that reflect changes in the phenomenon over time, three levels are analyzed: basic, planned and actual. Sequential calculation of the change in the first planned value relative to the base, then the actual value relative to the planned one, makes it possible to judge the change in the phenomenon for the period under study as a whole, i.e. change in the actual level relative to the baseline or characterizes the relative magnitude of the dynamics.

The product of the relative values ​​of the planned task and the fulfillment of the plan is equal to the relative value of the dynamics. Really:

This expression reflects the relationship between the relative values ​​of the planned task, the implementation of the plan and dynamics.

Relative indicators characterizing the structure of the object. The structure in statistics is understood as information about the division of the population under study into separate groups, about the size of each of the groups and about their significance for the population as a whole. Therefore, the relative value of the structure (d) in statistics is the correlation of a part of the phenomenon (f) and the phenomenon as a whole (the sum of all parts, f):

That is, the relative value of the structure shows what proportion (or how many percent) is part of the population in the total volume of the population. The concept of "relative size of the structure" is also synonymous with the concepts of "specific gravity", "share".

It is necessary to note a feature of the data for which the relative value of the structure can be calculated: the data must be grouped, that is, they must undergo primary processing after observation.

Calculation of the change in the relative value of the structure over time. For a full-fledged analysis, it is not enough to study only the structure of the phenomenon; it is necessary to compare the distribution of the phenomenon by groups in the period under study with the distribution that existed in previous periods. The construction of the relative values ​​of the structure of the phenomenon for several periods makes it possible to identify changes in the structure of the phenomenon that occur over time. Such changes in statistics are called "structural shifts". Calculation structural changes phenomena in time () is determined by the ratio of the change in part of the phenomenon in time () with the change in time of the phenomenon as a whole ():

Relative value of coordination. The relative value of coordination characterizes the ratio of the parts of the whole to each other. That is, in addition to determining the specific gravity of the various parts in comparison with the whole set, relative values ​​are also used, reflecting the comparison of various parts with each other.

The relative value of coordination (RC) has a form based on its essence - a comparison of one part of the studied population (fх) with another part of the same population (fу):

The value shows how many units of the compared part fall on 1, 10, 100 or 1000 units of the part taken as the basis for comparison. For example, how many women are there for every 1,000 men.

Relative comparison value. The relative value of the comparison reflects the correlation of indicators that have the same content, units of measurement, period or point in time, but calculated for different objects. That is, this relative value is allocated in separate view, because it allows you to compare different objects according to the characteristics under study. The form of the relative value of comparison (RBC) is determined by its content: the correlation of a certain characteristic of the object A (XA) with the same characteristic of the object B for the same period (XB):

The following indicators can be cited as an example of calculating relative comparison values:

1) the ratio of oil production for 1999 in the United States with the volume of oil production for 1999 in the Russian Federation,

2) comparison of the average annual gross domestic product per capita in Germany for the period from 1995 to 2000 with the average annual gross domestic product per capita in Russian Federation for the same period; etc.

Relative statistics name quantities expressing quantitative relationships between socio-economic phenomena or their features.

They are obtained by dividing one value by another. Most often, relative values ​​are ratios of two absolute values.

The quantity with which the comparison is made (the denominator of a fraction) is usually called the base of the relative quantity, the base of comparison, or base value , and the one that is compared is called the current, compared, or reporting value .

The relative value shows how many times the compared value is greater than the base value or what proportion the first is from the second.

Many facts are expressed with the help of relative values. public life: percentage of plan implementation, growth and growth rates, etc.

The relative magnitude of the dynamics;

The relative value of the planned task;

Relative value of task completion;

The relative magnitude of the structure;

Relative value of coordination;

Relative comparison value;

Relative value of intensity.

Consider the procedure for determining relative values.

Relative values ​​of dynamics. They characterize the change of the studied phenomenon in time and reveal the direction of development of the object. Obtained by dividing the actual level of the reporting period by the actual level of the base period:

Example. Machine building plant in 2000 produced 630 machines, and in 1999 - 500 machines. 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 factor, growth index) or in percentage terms - this is 126.0% (growth rate). In other words, in one year the output of machine tools increased by 26.0% (growth rate).

Relative value of the planned task . It is obtained as a result of dividing the planned task of the reporting period by the actual level of the base period.

Example. The machine-building plant produced 500 machine tools in 2006, and planned to produce 693 machines in 2007. Determine the relative value of the planned task for the production of machine tools.

Thus, 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 reach 138.6% compared to 2006 (planned growth rate).

The relative amount of task completion. Obtained as a result of dividing the level actually achieved in the reporting period by the planned task of the same period:

Example. The machine-building plant planned to produce 693 machine tools in 2006, but actually produced 630 units. Let's determine the value of the plan.

Consequently, the planned task was underfulfilled by 9.1%.

The relative size of the structure. Characterizes the composition of the studied population (share, specific gravity 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 people in the student group, 9 of them are men. Let us determine the relative value of the group structure.

In the group 33.3% are men and 66.7% are women.

Relative amount of coordination . They characterize the ratio of the parts of a given set to one of them, taken as the base of comparison, and show how many times one part of the set is larger than the other, or how many units of one part account for 1, 10, 100, 1000 ... units of the other part.

Example. In 2001, fuel and energy resources (in reference fuel) were distributed as follows: conversion into other forms of energy – 979.8 million reference fuel; production and other needs - 989.0 mln. export – 418.3 mln. balance at the end of the year - 242.1 mln. taking export deliveries as the base of comparison, we determine how much falls on production:

That is, 2.363 times more resources are spent on production and other needs than they are exported.

Relative value of comparison (territorial-spatial). It characterizes the comparative sizes of indicators of the same name, but related to different objects or territories and having the same temporal certainty. The interpretation of these values ​​depends on the basis of comparison.

(4.6)

Example. The population of Moscow in 2001 amounted to 8.967 million people, and the population of St. Petersburg in the same year amounted to 5.020 million people.

That is, the population of Moscow more population St. Petersburg by 1.79 times.

Relative value of intensity. Shows how many units of one set fall on a unit of another set 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 finished products 1200 items.

There are 12 parts for each worker, i.e. labor productivity is 12 parts per 1 worker.