General index of physical volume of products. Medium indices

Composite index - This is a complex relative indicator that characterizes the average change in the socio-economic phenomenon consisting of directly incommensurable elements. The source form of the consolidated index is an aggregate.

When calculating aggregate index For heterogeneous aggregate, such a general indicator is found in which all its elements can be combined. Example, fold prices of various goods implemented in retail, To fold is unlawful, however, from an economic point of view, it is quite acceptable to summarize the turnover for these goods. Accordingly, S. water index Commodity This turnover in the current period classified to its magnitude in the baseline:

Consolidated price index, reflects the price changes that have had:

· by the method of Paashe:

Index Numerator - the actual turnover of the current period. The denominator shows no matter how commodity turnover in the current period, subject to the maintenance of prices at the basic level.

The magnitude of economy:

The difference sign shows "-" savings, "+" - overrun.

· according to the method of Laspeyres:

Complement index of physical sales, characterizes the change in the number of goods sold not in monetary, but physical terms:

Weighs in the index are the prices that are fixed at the basic level.

Indices are associated between themselves:

Example. There are data on implementation in two months (Table 13).

Table 13.

Implementation in the conditional enterprise in two months

Product	August	September	Estimated data
P 0	Q 0	P 1	Q 1.	P 0 Q 0	P 1 Q 1	P 0 Q 1
BUT
B.
IN
å	-	-	-	-

The turnover for this product group in the current period compared to the basic decreased by 100-96.9 \u003d 3.1%

According to this product group, prices in September compared to August decreased by 10.8%.

Savings of 300 monetary units.

The physical amount of product implementation (trade turnover) increased by 8.6%.

Check the correctness of the calculations:

Consolidated indices in medium harmonic form:

Consolidated indices in medium arithmetic form:

Example

Product	Basic period, rub. Q 0 P 0	Changing Piz. Volume in the current period,% i Q * 100% - 100%	Estimated graphs
I Q.	I Q * Q 0 P 0
BUT		-6,4	0,936
B.		-8,2	,918
IN		1,3	1,013
TOTAL:

Decision. .

The physical volume of the implementation of these goods on average decreased by 3.6%.

In the middle arithmetic form, there may also be calculated and the labor productivity index by labor intensiveness, known as the index of this year. Strumina:

where I W. - a consolidated index of labor productivity index;

T 0. and T 1 - time spent on the release of all products in the basic and current periods, respectively;

q 0.and Q 1 -produced all products in the basic and current periods, respectively.

End of work -

This topic belongs to the section:

Statistical analysis in the economy

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Faofanov V.N.
Table of contents preface. 2 Introduction. 4 Section 1. General statistical theory. 15 1.1. The value of statistics, its tasks and organization. 15 diameters 200 heads

The value of statistics, its tasks and organization
For adequate perception of the course of statistics and independent work With literary sources, it is necessary to assimilate the most important concepts and definitions that will operate statistical science.

Statistical observations
Obtaining source information The object of interest is the first and main component of statistical analysis. The quality of the conclusions depends on the "quality" of the source information, and, consequently

Statistical tables
Statistical tables are a means of visual and compact submission of statistical information. When constructing tables, three elements are used: a mandatory part of the table - s

Graphic display
Classification of statistical graphs With all its diversity, statistical graphics are classified for a number of features: a method for constructing, form of graphic form

Absolute and relative statistical indicators
The statistical indicator is a quantitative characteristic of socio-economic phenomena and processes in conditions of qualitative definiteness. Qualitative definition

Average indicators
The average value is the most common form of statistical indicators used in managerial practice and is a generalized quantitative characteristic of a feature in

The main properties of the middle arithmetic
1) The sum of deviations of the sign values \u200b\u200bfrom the middle arithmetic equal to 0.

Decision
Average age Equipment is determined by XSR \u003d σ (xi * fi) / σfi \u003d 1370/100 \u003d 13.7 years. According to Table 1.7, the highest frequency f

Grouping statistical data and analysis of groups
As a result of the first stage statistical research - Statistical observation - receive information about each unit of aggregate. The task of the second stage of a statistical study consists in T

Rows of speakers
Type of series of speakers The main goal of the statistical study of the dynamics of business activities is to identify and measure the patterns of their development in time. This is achieved by

Economic indices and their use in economic and statistical studies
The index is a generalized relative indicator of the comparison of statistical aggregates in time consisting of elements directly not to summation. For example, A.

Quantitative Indicators
As noted above, the need to build indexes of quantitative indicators occurs when the results for individual elements of the complex phenomenon are directly incommensurable. Nine

Indices of quality indicators
The qualitative indicator characterizes the level of the studied performance in the calculation on the quantitative unit and is defined as the ratio of this effective indicator to the associated

Individual indexes
The simplest indexes used in statistical analysis characterizes the change in time or space individual elements aggregate. Indices are expressed either in fractions or in%. Below next

Aggregate index
The aggregate index is a form of a consolidated index used to characterize the change in a complex economic phenomenon. The numerator and denominator of the aggregate index are sums

Chains and basic indexes
To study the dynamics of the phenomenon over a number of periods, it is possible to calculate the chain and basic indexes. Building such a system is possible in two versions: 1. Relative changed

Use of indexes in economic analysis
Aggregate indices are used to characterize the change in the level of complex public phenomena. They can be applied for analytical purposes to assess the impact on the volume of the change in factor

Calculations of missing indexes using index systems
Many economic indices are closely related to each other and form index systems. Thus, the price index is associated with the index of the physical volume of turnover or physical volume of products, forming

The sample should provide the ability to distribute the findings obtained on the basis of its analysis at the minimum time and means
Conducting a study of social and economic phenomena by the selective method is made up of a number of consecutive stages: 1) the rationale (in accordance with the objectives of the study) exercof

Errors sampling
Error sampling is an objectively emerging discrepancy between the characteristics of the sample and the general population. It depends on a number of factors: the degree of variation of the studied sign

Small sample
When monitoring the quality of goods in economic studies, the experiment can be carried out on the basis of a small sample. Under a small sample means unpaid statistical

Ways to distribute sampling characteristics on the general set
The selective method is most often used to obtain the characteristics of the general population according to the corresponding sample indicators. Depending on the research objectives, this is carried out or straight

Statistical connections
Exploring the relationships in the market of goods and services - the most important function of employees of commercial services: managers, merchants, economists. Study of the mechanism of market connections, the interaction of demand and

Statistical methods in economic modeling
The main element of economic research is the analysis and construction of the relationships of economic variables. The study of such relationships is complicated by the fact that they are especially in Macroeconomic

Statistical data and stochastic model. Econometric model
The introduction of a random component into an economic model leads to the fact that the relationship of the rest of its variables ceases to be strictly deterministic and becomes stochastic, which is observed

Preparation of statistical data and using them in the model
When preparing statistical data to work with the economic model, two problems arise. First, there may be no data necessary for the model. Secondly (if all the data is), you need

Processing of statistical data and analysis of random discrete data
The procedure for processing discrete sample data can be illustrated on specific example. Suppose we analyze the volume of computers in the supermarket in 10 working days (see Table

Statistical distributions and their main characteristics
Types of distributions distinguish discrete and continuous probabilistic distributions. The discrete distribution is characterized by the fact that it is concentrated in the final or counting number T

Relationships between economic variables. Correlation and its statistical study
Various economic indicators both on micro and on the macro level are not independent, but are interconnected; For example, the price of any product and the amount of demand for this product, the volume of

Probabilistic ratios: joint frequency (probability), conditional frequency (probability), statistical independence of random variables
Under the joint frequency V (x, y) of two random variables x and y, we understand the relative frequency of the event consisting in the fact that the values \u200b\u200bof X and Y are accepted at the same time

Evaluation of parameters and verification of the hypotheses about the correlation of random variables
Next, the next question arises in the correlation coefficient analysis. If it is zero for the general aggregate, it does not mean that it will accurately be zero for sampling. On the contrary,

Collection and analysis of data on the status and prospects of the labor market
The purpose of this work is to secure the statistics obtained at the course of theoretical knowledge, the acquisition of technical skills of collecting, tool processing and analyzing statistics

Collect statistical information on current states of labor market
The collection of statistical information on the current states of the labor market is carried out in accordance with the selected student specialty (terminologically on the site www.job.ru - director, head, auditor

Certification and exam questions
1. Examples of using statistical analysis methods in applied management practices. 2. Signs, statistical data and indicators, statistical patterns. 3. Stat.

Unlike individual, consolidated indices allow us to summarize indicators on several types of goods, several types of products, on securities of several issuers, etc. The initial is the aggregate form of the consolidated index. Consolidated indices can also be calculated in the middle arithmetic and medium harmonic forms. Special importance are consolidated indices in stock exchange statistics, where they are given the role of the status indicators and market dynamics valuable papers (stock indexes).

When constructing consolidated indices, two methods are most common. The first is that for the current and base period, the phenomenon is determined throughout the totality, and then the ratio of the reporting value to the basic. As a result, it is possible to obtain a change in the entire totality of the analyzed indicators - the cost of products produced, turnover, costs, supply costs, etc. In addition, it is possible to determine due to which element and in what step-pi these changes occurred. Such indexes are called aggregate.

The essence of another method for constructing a consolidated index is that, knowing individual indices characterizing changes in individual elements of a complex phenomenon, the average change in all its elements is determined. Such indexes are called average. Middle Index represents only another reception of solving the same task. For its magnitude, he must give the same result as an aggregate.

Consider the construction of aggregate indices on the example of the table. 9.2, where data is presented in two periods. The aggregate index is the ratio of two values, each of which is the amount of the works of two elements that make up the index. For example, trade turnover p products in the current period will be:

Similarly, for the base period, the turnover is:

If you compare the turnover in the current period with its value in the basic period, we get complete Index Turnover:

Calculate the process of turnover in three products in two months (Table 9.2):

The value of the index allows us to conclude that the turnover according to this product group in April compared with the March increased by 50.3% (150.3 - 100.0). In absolute values, the total change in turnover was 83 thousand rubles. (248-165).

It should be noted that the units of measurement of goods when calculating this and subsequent indexes do not have any values. So, some of the goods can be measured in kilograms, the other part is in pieces, the third is in meters.

According to the theory of the index method, there are two types of index analysis: synthetic and analytical. Synthetic analysis allows you to estimate the average change in the level of the indexed indicator, and analytical it makes it possible to estimate the effect of indexed value for a general change in the index.

The magnitude of the turnover index is formed under the influence of two factors: it affects it both a change in prices for goods and changes in their implementation. Such indexes of "efficient" indicators (cost, total production costs, etc.) give a characteristic of the change in the indicator on average, and their interpretation is "synthetic".

In order to estimate the effect of changes on the total index value of only one of the two elements, the second element must be left unchanged, i.e. Fix it on the same level. In this case, the aggregate index is the ratio of the work of two elements, one of which changes (indexed value), and the other is fixed (index weight). The indexed value becomes the influence of which on the change in the general index is studied, for example, in the price index - is a zepa; In the index of physical volume is the volume of products. One of the issues arising from the construction of an aggregate index is the question of the period of fixing the weight of the index.

When building indexes of quality indicators (such as price, cost), quantitative indicators are used as weights (for example, the volume of products), fixed at the level of the reporting period.

In this way, a consolidated price index (Methyl Paasheas) is obtained:

For the example under consideration (see Table 9.2) we get:

Thus, according to this product group, prices in April compared with March increased by 5.5%.

Consider the consolidated price index in more detail. The numerator of this index contains the actual turnover of the current period. The denominator is a conditional magnitude showing how the turnover would be in the current period, subject to the preservation of prices at the basic level. Therefore, the ratio of these two categories and reflects the impact of changes on the turnover of only one element - the price.

The numerator and denominator of the consolidated price index can be interpreted otherwise. The numerator is a sum of money actually paid by buyers for goods in the current period. The denominator shows how much buyers would pay for the same goods if prices have not changed. The difference in the numerator and the denominator will reflect the amount of savings (if the sign "-") or overrun (sign "+") buyers from price changes, thousand rubles:

The result obtained can be interpreted and as the magnitude to which the turnover has changed due to the increase in the circuit.

When building this index, the price acts as an indexed value, and the number of goods sold is weight. It should be noted that in statistical practice is also used consolidated price index, built according to the method of Laspeyres, when weights are fixed at the base level, not the current period:

According to Table. 9.2 This index will be:

Depending on the objectives of the study and the available information uses one or another index. Pasheas price index is usually less than Laspeyres index.

When constructing indices of quantitative indicators (for example, product volume), qualitative indicators are used as weights, such as the price, the cost, fixed at the base period level. Such an index in the index system under consideration is the consolidated index of the physical volume of sales (or production) of products. It characterizes the change in the number of goods sold not in cash, but in physical units Measurements. Weighs in this case are the prices that are recorded at the baseline level:

The physical sales volume on average increased by 42.4% (142.4 - 100.0). In absolute value, this is the difference between the numerator and the denominator, equal to 70 thousand rubles, i.e. In this amount, the turnover increased by increasing sales.

There is a multiplicative relationship between the calculated indices:

Check this relationship according to Table. 9.2:

1,055-1,424 = 1,503.

In absolute values, the relationship of indexes is as follows:

This relationship is called additive. According to Table. 9.2 Relationship Looks like this: 83 \u003d 13 + 70 (thousand rubles) Thus, the general change in the cost of turnover is made up of turnover due to sales and price increase.

We reviewed the use of the index method in the analysis of turnover. However, the same index system can be used to analyze the results of industrial activities of the industry or individual enterprises producing heterogeneous products. Then the above indexes are respectively called:

1R1 / - product value index;
1r. - wholesale price index;
1d - index of physical volume of products. The relationship between these indices remains the same:

Another area of \u200b\u200bapplication of indexes is an analysis of costs for production and cost.

An individual cost index characterizes the change in the cost of a separate type of product in the current period compared to the basic. To determine the general change in the cost of the cost of several types of products manufactured by the enterprise, is calculated consolidated cost index.At the same time, the cost "is weighed" by the volume of production of individual types of products:

The methodology for constructing this index is similar to the methodology for constructing the price index. The index numerator reflects the cost of production of the current period, and the denominator is the conditional value of costs while maintaining the cost at the base level. The difference in the number and denominator shows the amount of economy (recalculation) of the enterprise from the cost of cost:

Complement index of physical volume of products,"Weighted" at cost, has the following form:

The interaction of factors for changing costs and sales volumes is reflected in the meaning consolidated production cost index:

All three indexes are also interconnected by each other:

In practice, as a rule, the calculation of indexes is carried out in more than the bottom of the period. Indices allow to obtain a consolidated assessment of the processes under study constantly, month after month, year after year. To achieve comparability, they are calculated by a single methodology. Such a methodology or scheme for calculating indexes in several consecutive time periods is called the index system.

Depending on the information base and research objectives, the index system can be built in different ways. Consider some options for its construction on the example of a consolidated price index, calculated for p periods.

If we compare the prices of each period with the prices of the preceding period, then the received index system will include chain indices that reflect the change in prices for each of the periods of the time interval under consideration. At the same time, as weights, it is possible to use the volume of implementation of each specific period or the constant volumes of any period adopted as a basic one. Then the index system will include indices chain or basic, with variable or with constant weights.

Chain price indexes with variables they have the following form:

Chain price indices with permanent weightscalculate according to the following formulas:

Note that use permanent weights More preferably, since the indices calculated in this way, i.e. They can be sequentially multiplying and obtaining the value of the indicator for a longer period. Thus, having price indexes for three consecutive months, it is possible to obtain a consolidated assessment of the change in price as a whole for the quarter. Indices with variable weights do not have such an opportunity.

If we compare the prices of each period with the prices of any base period (usually the initial), then the received index system will include basic indexes that reflect the change in the prices of the accumulated outcome, i.e. Since the beginning of the time interval under consideration. For example, a change in prices in January, but compared to December of the previous year, in February - compared with the same decabre, etc. At the same time, as weights, the volume of the implementation of each particular period or constant volumes of the period adopted as a basic can also be used.

With general indices, as noted above, most often and is characterized by changing economic phenomena and processes.

In contrast to individual indexes, their construction and calculus is more difficult, the theory of indices is engaged.

By calculation methodology, general indices are divided into:

aggregate, from Latin Aggrego - I attach;
medium of individual.

The main form of economic indices in domestic practice is aggregate. They consist of 2 parts:

Indexed value (the nature of which is determined).
Summarizer (weight) with which the indexed value is included in the overall result.

The monogram (weight) is introduced into the index in order to overcome the incomprehensibility of individual elements of the studied phenomenon. Those. Using weights, sets (aggregates) of indexed indicators are summed up. The monogram (weight) is economically closely related to the indexed value and leads elements of a complex phenomenon to comparable mind. For this weight, they are taken the same in the numerator and index denominator.

Aggregate price index

Consider the basic principles and methods for calculating aggregate indices and.

If the price is the price as an indexed value, i.e. We need to determine the total price change on the various goods, then to overcome the price incommability follows:
- Enter the monogram meter to the index (weight) in the form of the number of goods sold (or produced).

Then the product of prices for the number of relevant goods will give the value of these goods. And the cost of various products can already be summarized.

Consequently, in price indices, the number of goods are in price indexes (weight). Moreover, these quantities should be the same for the current and for the base period so that the index reflects only the change in the price level.

Thus, the overall change in prices for various products can be determined by calculating the aggregate price index entering it as weight the same value: the number of goods sold for the current or base period.

Adhering to the above designations and adopting the number of goods sold over the current period as a weight, the formula of the aggregate price index can be represented as:

where P1 and P0 are the price of the unit of goods sold in the current and basic period, respectively;
Q1 - the number of goods sold in the current period.

If the data on the number of goods sold in the basic period as weights as weights, the formula of the aggregate price index will have the following form:

Aggregate price indexes obtained on these 2nd formulas - with current and basic weights are not identical. They have a different economic content.

Index Paashe It characterizes the change in the price of the current period, compared with the basic, the goods implemented in the current period.

sellers benefit from prices and lose buyers;
from their decline - on the contrary, buyers won and lose sellers.

Index Laspeyres Shows how much prices have changed in the current period compared to the basic, on goods that were implemented in the base period.

Those. It allows you to calculate a conditional economic effect, conditional savings or consumption of funds. Therefore, when calculating the price index is used, as a rule, the 1st formula of the index with the weights of the current period, because the economist is not interested in the conditional savings or overrun, but the actual economic effect on price changes.

Aggregate index of physical volume

If the indexed value is the quantities (volumes) of sold or produced goods, so that they can be summed according to various goods - it is necessary to enter the amount of the co-measurater in the form of prices for products, i.e. Measure quantities at prices.

The amount of quantities on the price will give the cost (or turnover for sale), i.e. The values \u200b\u200bthat can be summarized.
Consequently, in the indices of the physical volume of products, prices are weights. These weights must be taken the same (unchanged) for the current and basic periods. In this case, the indices will only decide the change in the volumes of produced or sold goods.

Thus, in the price index, and in the index of the physical volume of turnover with the help of comparaders, we turn to the value of the products sold (produced).

When building and calculating the index of the physical volume of turnover, the question arises: what are the prices to take as a co-measurater (weight)? Prices of the basic, or price of the current period?

In order for the aggregate index to characterize only the change in the physical volume and did not reflect the changes in prices, as weights it is necessary to take regular prices for both the basic and current periods.

Then the formula of the aggregate index of the physical volume of products can be represented as follows:

The choice of the weighing period of indexes is explained by the fact that high-quality indexed indicators do not require compulsion and their factors are only weights, and quantitative - require composure and their factors are comparable.

The index numerator is the cost of production of the current period in basic prices, the denominator is the cost of products of the base period in the prices of the base period. The difference between the numerator and the denominator (σQ1p0 - σq0p0) characterizes absolute change in the physical volume of products in the current period.

Prices of different goods implemented in retail trade are unlawful, but from an economic point of view, it is permissible to summarize their trade turnover. If you compare the turnover in the current period with its value in the base period, then we will get a consolidated turnover index:

Example 1. There are the following data on the implementation of vegetable products in the city market:

Calculate the process of turnover for example 1:

We obtain that the trade turnover as a whole under the product group under consideration in the current period compared with the basic decreased by 0.9% (100-99.1).

The value of this index affects both the change in prices for goods and the change in the volume of their implementation. In order to estimate the change in price only (indexed value), the number of goods sold (index weights) is required at a constant level. In the study of the dynamics of such qualitative indicators as the price, the cost, labor productivity, the quantitative indicator is usually fixed at the level of the current level. In this way, a consolidated price index is obtained:

The numerator of this index contains the actual turnover of the current period. The denominator is a conditional magnitude showing how the turnover would be in the current period, subject to the preservation of prices at the basic level. Therefore, the ratio of these two categories and reflects the change in prices. Changing the amount of product implemented does not affect the index value.

Calculate the consolidated price index for Example 1:

Consequently, according to this product group, prices in October compared with August decreased by 31.7%.

The numerator and denominator of the consolidated price index can be interpreted from the point of view of consumers. The numerator is the amount of money actually paid by buyers for goods purchased in the current period. The denominator shows how much buyers would pay for the same goods if prices have not changed. The difference in the number and denominator will reflect the amount of savings (if the sign "-") or overrun (if the sign "+") buyers from price changes:

The third index in this index system is the consolidated index of the physical volume of implementation. It characterizes the change in the number of goods sold not in cash, but in physical units of measurement:

Weighs in this index are the prices that are recorded at the base level.

The index of the physical volume of implementation in Example 1 will be:

The physical scope of implementation in October compared with August increased 1.45 times, or 51,500 rubles. (165 500 - 114,000).

There is the following relationship between the calculated indexes:

IP. × IQ. = IPQ..

Using the relationship of indexes, check the correctness of the calculations in Example 1:

IPQ.= IP. × IQ. \u003d 0.683 × 1,452 \u003d 0.991, or 99.1%.

Therefore, the decrease in trade (by 0.9%) is due to the growth of the volume of products sold (by 45.2%) and lower prices (by 68.3%), which in absolute terms amounted to -1000 rubles. (-52 500 + 51 500).

We considered the use of aggregate indices in the analysis of turnover of prices and physical sales. When analyzing production results industrial enterprise The cumulative indexes are respectively called product value index, wholesale price index and physical product index.

"Index" translated from Latin - pointer or indicator. In statistics, the index is called the indicator of the relative change in this level of the investigated phenomenon compared to its other levels adopted for the comparison base. As such a base, it can be used or a level for any past period of time (dynamic index), or the level of the same phenomenon on another territory (territorial index). Indexes are an indispensable, research tool in cases where two combination should be compared in time or space, the elements of which cannot be directly summarized.

In general, the index method is aimed at solving the following tasks:

characteristics of the general change in the level of complex socio-economic phenomenon;

analysis of the effect of each of the factors on the change in the indexed value by eliminating the impact of other factors;

analysis of the effect of structural shifts to change the indexed value.

In the future, the following generally accepted indications will be used:

i is an individual index;

I - consolidated index;

q - quantity;

1 - current period;
0 - Basic period.

The simplest indicator used in the index analysis is individual indexwhich characterizes the change in the time of economic quantities belonging to one object:

Price index

where R 1 is the price of goods in the current period;

r 0 - the price of goods in the base period;

The change in the physical mass of the product sold in physical terms is measured by the individual index of the physical volume of implementation:

Changing the cost volume of turnover this product It will affect the value of the individual commodity index. For its calculation, the turnover of the current period (the product of the price on the number of goods sold) is compared with the foregoing of the previous period:

This index can also be obtained as a product of an individual index of the price and individual index of the physical volume of implementation.

Individual indices, in essence, are relative indicators of dynamics or growth rates, and according to data for several periods of time can be calculated in chain or basic forms.

Unlike indexes of individual, consolidated indices allow us to summarize the indicators for several products. The initial form of the consolidated index is an aggregate form.

The aggregate form of the index allows you to find such a general indicator for heterogeneous aggregate in which all its elements can be combined. When analyzing the dynamics of prices, the individual prices of various goods are unlawful to fold, but to summarize the turnover for these goods is quite acceptable. In the current period of such trade turnover pproducts will be:

If we compare the turnover in the current period with its value in the base period, then we get complete Index Turnover:

To illustrate this and subsequent indices, we use the following conditional data (Table 10.1.):

Table 10.1 Prices and sales of three products

Calculate the process of turnover:

The calculated index value allows you to conclude that the turnover in general on this product group in the current period compared to the basic increased by 8.9% / 108.9% - 100.0% /. It should be noted that the size of the product group, the units of measurement of goods when calculating this and subsequent indexes do not matter.

The magnitude of the commodity index is formed under the influence of two factors, it affects it as a change in prices for goods and changes in their implementation. In order to evaluate the change in only prices (indexed value), the number of goods sold (index weight) is required at a constant level. In the study of the dynamics of such indicators, as the price and cost, the physical sales volume is usually fixed at the level of the current period. This way is obtained consolidated price index(by the method of PAASH):

For the example under consideration, we get:

Thus, according to this product group, prices in February compared with January increased by 10.7%. When constructing this index, the price acts as an indexed value, and the number of goods sold is as a weight.

Consider the consolidated price index in more detail. The numerator of this index contains the actual turnover of the current period. The denominator is a conditional value showing how the turnover would be in the current period, subject to the maintenance of prices at the basic level. Therefore, the ratio of these two categories and reflects the price change that took place.

The numerator and denominator of the consolidated price index can also be interpreted differently. The numerator is a sum of money actually paid by buyers for goods in the current period. The denominator shows how much buyers would pay for the same goods if prices have not changed. The difference in the numerator and the denominator will reflect the amount of savings (if the sign "-") or overrun ("+") buyers from the price changes:

It should be noted that in statistical practice also uses a consolidated price index, built according to the Laspeyres method, when weights or sales are fixed at the base level, and not the current period:

The third index in the index system under consideration (including the price index calculated by the Pashe method) is complement index of physical sales.It characterizes the change in the number of goods sold is not in cash, but in physical units of measurement. Weighs in this case are the prices that are recorded at the baseline level:

In our case, the index will be:

The physical sales volume (turnover) decreased by 1.6% (98.4% -100.0%). There is the following relationship between the calculated indexes:

Or 1,107-0,984 \u003d 1,089

Based on this relationship with the values \u200b\u200bof two known indexes, you can always determine unknown value Third index.