Absolute values ​​are expressed in. Absolute and relative values ​​in statistics

Relative values ​​of dynamics characterize the change in the phenomenon under study in time, reveal the direction of development, measure the intensity of development. Relative values ​​are calculated
in the form of growth rates and other indicators of dynamics.

Example. The sale of cotton fabrics by the section of the department store in January amounted to 3956 thousand rubles, in February - 4200 thousand rubles, in March - 4700 thousand rubles.

Rates of growth:

basic(base - sales level in January)

KF/I = 4200: 3950 ´ 100% = 106.3%;

KM/I= 4700: 3950 ´ 100% = 118.9%;

chain

KF/I = 4200: 3950 ´ 100% = 106.3%;

KM/F= 4700: 4200 ´ 100% = 111.9%;

Relative values
comparison of coordination and intensity

Relative comparison values characterize the quantitative ratio of the same-name indicators related to various objects of statistical observation.

Example. According to the All-Union Population Census of 1989, the population of Moscow was 8967 thousand, and the population of Leningrad (now St. Petersburg) was 5020 thousand people.

Let us calculate the relative value of the comparison, taking the number of residents of St. Petersburg as the basis for comparison: Therefore, the population of Moscow is 1.79 times greater than that of St. Petersburg.

You can use relative comparison values ​​to compare the price level for the same product sold through state stores and in the market. In this case, as a rule, the state price is taken as the basis for comparison.

Relative values ​​of coordination are one of the types of indicators of comparison. They are used to characterize the relationship between the individual parts of the statistical population and show how many times the compared part of the population is greater or less than the part that is taken as the basis, or base of comparison, that is, in essence, they characterize the structure of the population under study, and sometimes more expressively, than the relative values ​​of the structure.

Example. At the beginning of the year, the number of specialists with higher education employed in the association " Trading house”, amounted to 53 people,
and the number of specialists with secondary specialized education -
106 people. Taking as the base of comparison the number of specialists with higher education, we calculate the relative value of coordination:

that is, there is one specialist with higher education for every two specialists with secondary specialized education.

Relative intensity values show how widespread the phenomenon under study is in a particular environment. They characterize the ratio of oppositely named, but interconnected absolute values.

Unlike other types of relative values, relative intensity values ​​are always expressed by named values.

The relative intensity values ​​are calculated by dividing the absolute value of the phenomenon under study by the absolute value characterizing the volume of the medium in which the phenomenon develops or spreads. The relative value shows how many units of one population account for a unit of another population.

An example of relative intensity values ​​is the indicator characterizing the number of stores per 10,000 population.
It is obtained by dividing the number of stores in a region by the population of the region and multiplying by 10,000.

The effectiveness of the use of statistical indicators largely depends on compliance with a number of requirements and, above all, the need to take into account the specifics and conditions for the development of social phenomena and processes,
as well as the complex application of absolute and relative values
in a statistical study. This provides the most complete reflection of the studied reality.

One of the conditions for the correct use of statistical indicators is the study of absolute and relative values ​​in their unity. If this condition is not met, you can come to the wrong conclusion. Only the complex application of absolute and relative values ​​gives a comprehensive description of the phenomenon under study.

Average values

Market research based on indicators of the ratio of elements (relative values) is not able to fully satisfy the requirements for the speed of decision-making that market reality imposes on the leader (manager). To create a holistic view of what is happening economic processes and tendencies of their development use average values. They provide a recreation of common features that can be used as the basis for calculation. At the same time, even qualitative characteristics are sometimes calculated on the basis of knowledge of the average values ​​of the required qualities of the result being created. Consider the average values ​​within the framework of statistics.

average value- an abstract value, because it characterizes the value of an abstract unit, and therefore, it is abstracted from the structure of the population.

The average is abstracted from the diversity of the feature in individual objects. But the fact that the average is an abstraction does not deprive it of scientific research. Abstraction is a necessary stage of any scientific research. In the average, as in any abstraction, the dialectical unity of the individual and the general is realized.

The use of averages should proceed from a dialectical understanding of the categories of the general and the individual, the mass and the individual.

The average reflects the general that is formed in each individual, single object. Due to this, the average becomes of great importance for revealing the patterns inherent in mass social phenomena and not noticeable in single phenomena.

The deviation of the individual from the general is a manifestation of the development process. In individual isolated cases, elements of a new, advanced one can be laid. In this case, it is concrete facts, taken against the background of average values, that characterize the process of development. Therefore, the average reflects the characteristic, typical, real level of the studied phenomena. The characteristics of these levels and their changes in time and space is one of the main problems of averages. So, through the averages, for example, the pattern of changes in the productivity of workers, characteristic of enterprises at a certain stage of economic development, is manifested; the change in the well-being of the population is reflected in the average wages, family incomes
in general and for individual social groups, the level of consumption of products, goods and services.

Types of averages and methods for their calculation

In the practice of statistical processing of material, various problems arise, there are features of the phenomena under study, and therefore different averages are required to solve them. Mathematical statistics derive various means from power mean formulas:

at - arithmetic mean;

at - average harmonic;

at - root mean square.

However, the question of what kind of average should be applied
in a particular case, it is resolved by a specific analysis of the population under study, is determined by the material content of the phenomenon under study, and also based on the principle of meaningfulness of the results when summing up or when weighing. Only then is the average applicable correctly when values ​​are obtained that make real economic sense.

Let us introduce the following notions and notation: the criterion by which the average is found is called average sign and denoted x; the value of the averaged attribute for each unit of the population is called its individual meaning, or options, and denoted as frequency - this is the frequency of individual values ​​of the feature, denoted by the letter f.

Arithmetic mean- the most common type of medium. It is calculated in those cases when the volume of the averaged attribute is formed as the sum of its values ​​for individual units of the studied statistical population.

Depending on the nature of the initial data, the arithmetic mean is determined as follows.

1. Suppose that you want to calculate the average tenure of ten employees commercial enterprise, and each of them worked here
6, 5, 4, 3, 3, 4, 5, 4, 5, 4, that is, given a series of single values ​​of the attribute, then
calculated as

that is, it is calculated as an arithmetic mean (unweighted) by dividing the number of summary features by the number of readings:

It is often necessary to calculate the average value of a feature over a distribution series when the same feature value occurs several times. By combining the data by the value of the attribute (that is, by grouping)
and counting the number of cases of repetition of each of them, we get the following variation series (Table 2.1.). Then the average is:

that is, it is calculated as weighted arithmetic mean

Table 2.1.

A number of distribution of employees at a trading enterprise by length of service

Duration of work experience (options)	Number of employees of a trade enterprise (frequency)	Man-years worked	Share of employees to the total number of employees, % (frequent)

Therefore, to calculate the weighted arithmetic mean, the following sequential operations are performed: multiplying each variant by its frequency, summing the resulting products, dividing the resulting sum by the sum of the frequencies.

In some cases, the role of frequencies in the calculation of the average is played by some other quantities. For example, when calculating the average yield, the only correct weighting will be by the size of the crop area,
not by the number of sites. The frequencies of individual variants can be expressed not only in absolute values, but also in relative values ​​- frequencies (wi). Replacing in this example the absolute values ​​of the frequencies with the corresponding relative values, we get the same result

The weighted average takes into account different meaning individual options within the population. Therefore, it should be used in all those cases where the variants have different numbers. The use of an unweighted average in these cases is unacceptable, since this inevitably leads to a distortion of statistical indicators. In itself, the question of the weights that must be taken in calculating the average, as can be seen from the examples given, is determined by the initial information.

The arithmetic mean, as it were, distributes equally among the individual objects the total value of the attribute, which in fact varies for each of them. The total length of service worked out by all workers is distributed equally among them.

Considering that statistical averages always express the qualitative properties of the studied social processes and phenomena, it is important to choose the right form of the average based on the relationship between phenomena and their features. Average harmonic is the reciprocal of the arithmetic mean. When statistical information does not contain frequencies for individual population options, but is presented as their product, the formula is applied average harmonic weighted.

For example, the calculation of the average price is expressed by the ratio:

When determining the average price, using the unweighted arithmetic average, we get an average that does not reflect the volume of sales, that is, it is unrealistic.

As you can see, the harmonic mean is a converted form of the arithmetic mean. Instead of the harmonic mean, you can always calculate the arithmetic mean, but to do this, you first need to determine the weights of the individual values ​​of the feature.

In the event that the volumes of phenomena, that is, works, are equal for each attribute, the harmonic average (simple) is applied.

Geometric mean is a value calculated as the average of the ratios or as the average in the distribution series, presented as a geometric progression: . This average is convenient to use when attention is paid not to absolute differences, but to the ratios of two numbers. Therefore, the geometric mean is used in the calculation of average annual growth rates.

Properties of averages

Basic properties of averages.

1. From a decrease or increase in the frequencies of each attribute value by a factor of 1, the average value will not change. If all frequencies are divided or multiplied by some number, then the value of the average will not change.
This property makes it possible to replace frequencies with specific weights, called frequencies, and also, when the frequencies of all options are the same, calculate the averages using the simple arithmetic average formula. This property is important when the absolute frequencies are not known, but only the specific weights, that is, the relative values ​​of the population structure, are known.

2. The total multiplier of the individual values ​​of the attribute can be taken out of the sign of the average:

3. The average sum (difference) of two or more quantities is equal to the sum (difference) of their averages:

4. If where is a constant value, then

5. The sum of deviations of the attribute values ​​from the arithmetic mean is zero:

The above properties of the average allow in many cases to simplify its calculations: it is possible to subtract an arbitrary constant value from all values ​​of the attribute, reduce the difference by a common factor,
and then multiply the calculated average by the common factor and add an arbitrary constant value.

Structural averages

To characterize the structure of the population, special indicators are used, which can be called structural averages. These indicators include mode and median.

Fashion the most common variant is called, or the value of the attribute that corresponds to the maximum point of the theoretical distribution curve.

Mode is the most frequently occurring or typical value. Fashion is widely used in commercial practice in the study of consumer demand (when determining the sizes of clothes and shoes that are in great demand), price registration.

In a discrete series, the mode is the variant with the highest frequency. For example, according to the data below, size 37 is in the greatest demand for shoes (Table 2.2.).

In the interval variation series, the mode is approximately considered the central version of the so-called modal interval, that is, the interval that has the highest frequency (frequency). Within the interval, it is necessary to find the value of the attribute, which is the mode.

table 2.2.

Determination of mode by modal interval

Shoe size	Number of pairs purchased

The solution to the problem is to identify the middle of the modal interval as a mode. This decision will only be correct.
in the case of complete symmetry of the distribution, or when the intervals adjacent to the modal intervals differ little from each other in the number of cases. Otherwise, the middle of the modal interval cannot be considered as a mode.

Fashion is always somewhat uncertain, as it depends
on the size of the groups, on the exact position of their boundaries.

Mode is exactly the number that actually occurs most often (is a certain value), and in practice has the widest application (for example, the most common type of buyer).

Median- this is the value that divides the number of the ordered variation series into two equal parts: one part has the values ​​of the variable attribute smaller than the average variant, and the other has large values. The concept of the median is easy to understand from the following example. For a ranked series (that is, built in ascending or descending order of individual values) with an odd number of members, the median is the option located in the center of the series.

In the interval variational series, the order of finding the median is as follows: we arrange the individual values ​​of the attribute by rank; determine the accumulated frequencies for this ranked series;
according to the accumulated frequencies, we find the median interval.

The concept of statistical time series

Commercial activity in the market of goods and services is developing
in time. The study of the resulting changes is one of the necessary conditions knowledge of the laws of their dynamics. The dynamism of socio-economic phenomena is the result of the interaction of various causes and conditions. And since their cumulative action occurs in time, then in a statistical study of the dynamics commercial activities time appears as a collective factor of development.

The main purpose of the statistical study of the dynamics of commercial activity is to identify and determine the patterns of its development.
in time. This is achieved through the construction and analysis of statistical time series.

Rows of dynamics called statistical data that reflect the development of the phenomenon under study in time.

There are two main elements in each row of dynamics:

1. time indicator

2. corresponding levels of development of the phenomenon under study

As a time reference in the series of dynamics, either certain dates (moments) of time, or separate periods (years, quarters, months, days) are used.

Row levels dynamics reflect a quantitative assessment (measure) of the development of the studied phenomenon in time. They can be expressed as absolute, relative or average values.

Types of time series

Depending on the nature of the phenomenon under study, the levels of the series of dynamics can refer either to certain dates (moments) in time, or to individual periods. In accordance with this, the series of dynamics are divided into moment and interval.

moment series dynamics reflect the state of the studied phenomena at certain dates (points) in time.

An example of a moment series of dynamics is the following information on the payroll number of store employees in 1998:

Number of employees, people

A feature of the moment series of dynamics is that its levels can include the same units of the studied population. So, the main part of the store staff, which is payroll as of January 1, 1999, which continues to work during this year, is displayed in the levels of subsequent periods. Therefore, when summing the levels of the moment series of dynamics, a repeated calculation may occur.

By means of moment series, dynamics in trade is studied inventory, the state of personnel, the amount of equipment and other indicators that reflect the state of the phenomena under study at certain dates (points) in time.

interval series dynamics reflect the results of the development (functioning) of the phenomena under study for separate periods (intervals) of time.

An example of an interval series of dynamics is data on the retail turnover of a store in 1994–98. (expressed on the same scale):

The volume of retail trade turnover, thousand rubles.

A feature of the interval series of dynamics is that each of its levels is made up of data for shorter intervals (sub-periods) of time. For example, summing up the turnover for the first three months of the year, they get its volume for the first quarter, and the sum of the turnover of four quarters gives the volume of trade for the year, etc.

The property of summing levels for successive time intervals makes it possible to obtain series of dynamics of more enlarged periods.

By means of interval series of dynamics in trade, we study the change in the time of receipt and sale of goods, the amount of distribution costs and other indicators that reflect the results of the functioning (development) of the phenomena under study for certain periods.

Statistical display of the development of the phenomenon under study in time can be represented by series of dynamics with progressive results.
Their use is due to the need to display the results of the development of the studied indicators not only for a given reporting period,
but also taking into account previous periods. When compiling such series, successive summation of adjacent levels is performed. This achieves a summary generalization of the result of the development of the indicator under study from the beginning of the reporting period (month, quarter, year, etc.).

Dynamic series with progressive results are built when determining the total volume of retail trade turnover. Thus, the volume of sales of goods in a store is determined every month by summarizing commodity-money reports for individual operating periods (five days, weeks, decades, etc.).

As an example, let's use the following data on the progress of the sale of goods in a store for October 1997 (Table 2.3.).

Table 2.3.

Five days	Retail sale of goods, thousand rubles
for five days	from the beginning of the month
Fourth

Data gr. 3 tab. 2.3. display the results of sales of goods summarized from the beginning of the month for certain periods of the monthly cycle of the store.

With the help of time series, the study of the patterns of development of socio-economic phenomena is carried out in the following main areas:

Characterization of the levels of development of the studied phenomena in time;

Measurement of the dynamics of the studied phenomena through a system of statistical indicators;

Identification and quantitative assessment of the main development trend (trend);

Study of periodic oscillations;

Extrapolation and forecasting.

Comparability in time series

The main condition for obtaining correct conclusions in the analysis of time series is the comparability of its elements.

Time series are formed as a result of summaries and processing of periodic observation materials. Repeating in time (according to reporting periods) values ​​of the same indicators in the course of a statistical summary are systematized in chronological order.

At the same time, each series of dynamics covers separate isolated periods in which changes can occur, leading to incompatibility of reporting data with data from other periods. Therefore, to analyze a series of dynamics, it is necessary to bring all its constituent elements to a comparable form. To do this, in accordance with the objectives of the study, the reasons for the incompatibility of the analyzed information are established, and appropriate processing is applied, which makes it possible to compare the levels of a series of dynamics.

The incompatibility in the series of dynamics is caused by various reasons. These can be different sizes of time readings, heterogeneity of the composition of the studied populations over time, changes in the method of primary accounting and generalization background information, differences in units of measurement, prices, etc. used in certain periods.

So, when studying the dynamics of trade turnover for intra-annual periods, incompatibility arises when the length of time indications (months, quarters, half-years) is not the same.

The requirements for improving the accuracy of economic and statistical analysis make the initial data incomparable due to the unequal duration of the so-called leap year (366 days) and the usual year (365 days). This has to be taken into account in modern conditions development of trade, when one day on average accounts for more than 1200 million rubles. retail trade.

To analyze the intensity of trade development, volumetric data for periods of different lengths are recalculated (taking into account actual working hours) into average daily indicators. This eliminates the incompatibility of the levels of the time series and protects against errors in the conclusions.

As an illustration, we present data on retail trade duty grocery stores in the city by quarters in 1998 (Table 2.4.).

Table 2.4.

Index
Volume of retail trade turnover, million rubles
Average daily turnover, thousand rubles

From the data in Table. 2.4 shows that for the III quarter are characterized by the largest volume of trade and at the same time the lowest intensity.

In the absence of information on the actual operating time, normal operating hours are used to obtain comparable average daily indicators. The latter is different depending on the functions performed by trade and the contingent served.

For retail The following main options are available:

a) enterprises operating without interruption on holidays and weekends (for example, on-duty grocery and bakery shops, restaurants, cafes). Their working time fund corresponds to the calendar;

b) enterprises that do not work on holidays (for example, city markets). Their working time fund is less than the calendar one by the number of annual holidays;

c) enterprises that do not work on holidays and public holidays (for example, city department stores, enterprises Catering in factories, institutions, etc.). The size of their working time fund depends on the placement of holidays in each calendar year.
and days off;

d) enterprises operating in certain periods (seasons) of the year (for example, city vegetable markets, trade in places of mass summer recreation, etc.).

Incompatibility in the series of dynamics may occur due to the administrative-territorial changes that took place in the reporting period.

Example. In 1996, there was an enlargement of the serviced trade organization region, the results of which are reflected in the following changes in the volume of trade (million rubles):

Year
Trade turnover
within the former borders
Within the new frontiers

To bring this information to a comparable form, the so-called closing of the dynamics series is performed. At the same time, for 1996, the ratio of the two levels is determined: 630/450 = 1.4. multiplying
For this coefficient, the volume of trade in 1995 (432 × 1.4 = 604.8 million rubles), it is possible to construct a series of dynamics of comparable levels within the new borders of the region (million rubles):

Application of various statistical information
in the dynamics

The problem of comparability in the series of dynamics arises in connection with the use in statistical information of various economic importance money meters. Thus, for the monetary value of the volume of supply (wholesale) of goods, wholesale prices of industry are used, and for the assessment of the volume of sale of goods to the population, retail prices are used. The types of retail prices include cooperative and contract prices, market prices, purchase and delivery prices for agricultural products, etc.

Since price levels change over time, the prices of the corresponding periods are used to value the turnover.
But for studying the dynamics of the physical volume of the sale of goods, the monetary value of the turnover in the prices of the corresponding periods is not suitable.
The volume of trade is influenced not only by the factor of the sold mass of commodities, but also by the factor of price changes. To eliminate the influence of price changes, the turnover is recalculated into constant (basic) prices. As a result, we obtain series of dynamics of the volume of trade in comparable prices.

Statistical indicators
dynamics of social - economic phenomena

For quantification dynamics of socio-economic phenomena, statistical indicators are used: absolute growth, growth and growth rates, growth rates, etc.

Comparison of its levels is the basis for calculating the indicators of the time series. Depending on the comparison method used, the dynamics indicators can be calculated on a constant and variable bases of comparison.

The most important statistical indicator of dynamics is absolutegrowth, which is determined in the difference comparison of two levels of a series of dynamics in units of measurement of the initial information.

Base absolute growth Δ yb calculated as the difference between the compared level yi and the level taken as a constant base of comparison y0i:

Chain absolute growth Δ yts- the difference between the compared level and the level that precedes it yi-1:

Absolute growth may also have a negative sign, showing how much the level of the indicator of the period under study is lower than the base one.

There is a connection between basic and chain absolute increments: the sum of chain absolute increments is equal to the basic absolute increment of the last period of the dynamics series Δ ybn:

A common statistic of progress is growth rate. It characterizes the ratio of two levels of the series and can be expressed as a coefficient or as a percentage.

Base growth rate Tpb are calculated by dividing the compared level y0i:

Chain growth rates mall calculated by dividing the compared level by the previous level yi-1:

If the growth rate is greater than one (or 100%), then this indicates an increase in the studied level compared to the baseline. A growth rate equal to one (or 100%) shows that the level of the study period
unchanged from baseline. A growth rate less than one (or 100%) indicates a decrease in the level of the study period compared to the base one. The growth rate is always positive.

Growth rates and growth rates

Growth rates characterize the absolute increase in relative terms. The growth rate calculated as a percentage shows how many percent the studied level has changed compared to the level taken as the comparison base.

Base growth rate Tb is calculated by dividing the compared basic absolute growth Δ ybi to the level taken as a constant base of comparison y0i:

Chain growth rate Tnц is the ratio of the compared chain absolute growth to the previous level yi-1:

There is a relationship between the indicators of the growth rate and the growth rate:

(when expressing the growth rate as a percentage),

(when expressing the growth rate in coefficients).

If the levels of the dynamics series are decreasing, then the corresponding indicators of the growth rate will be with a minus sign, since they characterize the relative decrease in the growth of the level of the dynamics series.

An important statistical indicator of the dynamics of socio-economic processes is build-up rate, which, in the conditions of intensification of the economy, measures the growth of economic potential over time.

The growth rates are calculated Tn division of chain absolute increments Δ ytsi to the level taken as a constant base of comparison y0i:

It follows from the transformations in formula (2.10) that growth rates can be directly determined from the basic growth rates:

(2.11)

Formula (2.11) is convenient for practice, since statistical information on the dynamics of socio-economic phenomena is published most often in the form of basic time series.

Analysis of fulfillment of contractual obligations

We have already said that the market activity is based on the purchase and sale transaction. Before the goods begin their movement from the seller
to the buyer, both of them are connected by a word, by the obligation of one - to sell the goods and the obligation of the other - to buy this goods.

The inviolability of the contract, the contract is protected by the entire force of the laws of a legal society. Our domestic economy is still on the way to understanding this thesis, but the task of assessing
and performance analysis contractual relations both individual firms and the economy as a whole.

A contract (agreement) is a document that defines the rights and obligations of the parties that have entered into a sale and purchase relationship. At the same time, the contract can be considered as a source of information, since it fixes the quantity and assortment of goods intended for sale, it provides qualitative characteristics of the goods, stipulates its price and, accordingly, total cost the whole party. In addition, the contract defines the terms and conditions for the delivery of goods. All this makes it possible to compare the actual results of the delivery with contractual obligations and draw a conclusion about the conscientious or, conversely, unfair, incomplete fulfillment of its conditions and requirements.

Basic methods for estimating contractual obligations

The first thing with which the analysis of contractual obligations begins is the assessment of the fulfillment of the contract (agreement, application) in terms of the scope of supply. In this case, the actual volume of delivery is compared with the contractual value, and if a discrepancy is found, then the relative and absolute sizes of the underdelivery are determined. A delivery that exceeds the amount established by the contract and is not subject to mutual agreement is just as unprofitable for the buyer as an underdelivery. It is necessary to exclude from the practice of statistics and its lexicon the term characteristic of a planned economy: “overfulfillment of the plan”. For market relations feature there must be scrupulous observance of the agreements, including
in terms of supply. "Superfluous" goods will slow down the turnover, cause unjustified costs and may settle in the commodity distribution system. The assessment of the level of fulfillment of the agreement (contract) for the supply of goods, sufficiently homogeneous, narrowly assortment, measured in physical terms, is characterized by the following formulas:

a) level (degree) of fulfillment of contractual obligations:

b) the absolute size of the deviation of the delivery from the terms of the contract (underdelivery or excess delivery):

where and - the amount of delivered i-th goods, respectively, under the contract and in fact.

If the calculation of this indicator is carried out in natural units, then the comparability of the numerator and denominator of the indicator of fulfillment of contractual conditions is automatically ensured. When is the calculation
in cost units (and this is inevitable in the analysis of a wide range and heterogeneous products), then the principle of ensuring comparability of prices in the numerator and denominator of the deviation level indicator should be strictly observed. If, under the terms of the contract, the delivery was taken into account
in current, changed prices, then the formulas for indicators of the relative level (index, Idog) and absolute size (growth, Δ great dane), compliance of the delivery with contractual conditions will take the following form:

where and are prices i th goods, respectively, under the contract and actual; m- number i-x goods.

Determination of compliance with the scope of supply

Deviation from the amount of delivery stipulated by the contract may be due to both a quantitative factor and a value one.
In order to determine the actual compliance of the volume (quantity factor) of the supply with the terms of the contract, it is necessary to recalculate the actual supply in the prices of the period when the contract was concluded. The level (degree) of fulfillment of contractual obligations is determined in this case by the following index formula:

Absolute deviation in comparable prices:

Another index indicator of the level of fulfillment of the contract will reflect the influence of the value factor on the level of deviation of the delivery from the contractual terms. This indicator is calculated using the Paasche price index formula:

The absolute deviation of the supply cost due to the value factor is the difference between the numerator and denominator of the previous deviation index:

You can use index link formulas to control and reflect the role of each of the factors in the level and absolute deviation of the actual cost of delivery from the terms of the contract:

Deviations by assortment items

In the process of analyzing the fulfillment of contractual conditions, it can be found that the full compliance of the scope of supply with the indicator of the contract
does not exclude deviations in various positions of the assortment.

Various methods can be used to identify and characterize the assortment deviations of the supply from the terms of the contract (agreement). The first method can be considered the determination of absolute linear deviations of delivery from the terms of the contract for each assortment position. It is advisable to attribute the amount thus received to the entire amount of the supply provided for by the contract. Thus, it is possible to obtain both absolute and relative values ​​(that is, the size and degree) of violation of contractual conditions for the assortment. The following formula is used:

where and - supply j th assortment type of goods, respectively, under the contract and in fact;

k- the number of assortment types of goods.

If assortment items are taken into account in value units, then when calculating deviations, it is necessary to first ensure price comparability. The second method can be to determine the degree of structural differences (that is, it is established to what extent the shares of individual assortment items in the total volume of goods supply coincide or diverge). For this purpose, the average linear deviation of the actual relative indicators of the assortment structure of the supply from those stipulated by the contract is calculated:

where and , - specific gravity (share) j-th assortment type of goods in the total volume of its supply, respectively, under the contract and in fact:

k- number j- x range of products.

The third method allows you to identify the process of influence of assortment shifts in delivery on the indicator of deviation of the actual cost of delivery from the contractual one. For this purpose, the index of the influence of structural changes is used:

where is the price j-th assortment type of goods under the contract;

and - quantity j-th assortment type of goods, respectively, provided for by the contract and actually delivered;

k- number j- x assortment types of goods.

You can use a simplified method for calculating this index, replacing the absolute weights with relative ones, as a percentage of the total:

and the index d, replacing the index q, will be:

The index of assortment shifts will take the following form:

The absolute deviation of the supply due to assortment differences is calculated according to the following formula:

Change in delivery cost

The change in the cost of delivery compared to the terms of the contract due to the quantitative factor includes both the actual deviation of the quantity of goods and its assortment shifts, that is, an amendment is required for a change in the quantity of goods:

The total absolute deviation of the actual delivery from the contractual one will be expressed by the following additive model:

Δdog = Δdog( Iq) + Δdog( ass. page) + Δdog( R)

The overall relative deviation of the actual delivery from the contractual one will be expressed by the following multiplicative index model:

Idog = Idog( q) Idog( ass. page) Idog( R).

Statistical study of elasticity

Elasticity of supply and demand - a phenomenon specifically market, due to the manifestation of the law of the market. The essence of the elasticity of demand lies in its extreme flexibility and variability, depending on the influence of various socio-economic factors, primarily such as price and money income. A product offer has a similar property, which, under market conditions, is sensitive to price changes.

Economists drew attention to the phenomenon of sensitivity (sometimes they say - sensitivity) of supply and demand from the influence of external factors at the beginning of the 19th century. The French economist O. Cournot suggested that in a certain sense, demand is a function of price. This idea was subsequently developed by the English researcher A. Marshall, who expressed it in the form of a formula

D = f(p),

where D- demand; a R- price.

However, the researchers immediately noticed that the demand for each product depends not only on the price of this product, but on the prices of other goods. In the 80s of the last century, the Swiss economist L. Walras, a representative of the so-called Lausanne school, based on the primary Cournot equation, proposed his own version of the elasticity of demand, expressing it by the formula

dx = f(px, p1, p2, p3, …, pn),

where dx- product demand X;

Rx - the price of the product X;

p1 …pn- prices of other goods.

It should be noted that the theory of cross elasticity is based on this idea, which will be discussed below. The views of Cournot - Marshall were subsequently developed by other researchers (in particular, V. Pareto, E. Slutsky, D. Hicks, etc.), who introduced the concept of elasticity income factor. The well-known creator of the theory of "economics" P. Samuelson considers the dependence of the elasticity of demand on prices as the degree of reaction of the purchased quantity of goods to fluctuations in market prices.

Elasticity of supply and demand - it is their response to changing socio-economic conditions in the market.

The measure of elasticity was determined by statistical science, expressing it as a quantitative indicator - coefficient of elasticity.

The coefficient of elasticity is the percentage change in one (resulting) attribute with an increase of another (factorial) attribute by one percent.

A. Marshall derived the formula empirical coefficient of elasticity in the form of the following relationship:

where ∆ y- increase in demand (the sign "delta" is usually denoted

increments);

Δ X - increase in factor trait;

y - basic indicator of demand;

X - the base value of the factor attribute.

Sometimes this formula is shown as a product of ratios, sometimes as a percentage change:

Elasticity coefficient values

At E<1 manifested phenomenon infraelasticity, the product is considered low-elastic or inelastic; at E>1 there is a phenomenon ultra-elasticity, the product is elastic or highly elastic. At E=1 the product is weakly elastic (the so-called unitary demand), in this case, as a rule, price reduction does not lead to a commercial effect (increase in cash receipts). A positive value of the elasticity coefficient means that with an increase in the factor attribute, demand grows, that is, the relationship is direct (usually such a dependence manifests itself on income); a negative value - that with an increase in the factor sign, demand decreases, that is, the relationship is inverse, such a dependence of demand is characteristic when prices are affected (Fig. 2.1.). You just need to keep in mind that there are goods that react differently to changes in prices and income. For example, an increase in income leads to a decrease in demand for goods of low consumer value.

Rice. 2.1. The inverse dependence of demand on price changes, expressed by hyperbole.

In practical calculations, the elasticity coefficient can be calculated in dynamics and statics, that is, it reflects either a change in demand over time, or in comparison with some other unit of the population (for example, the demand of different consumer groups, different regions, etc.). In the first case, the formula is transformed as follows:

where y0 and y1 - demand, respectively, of the base and current periods;

x0 and x1- factor sign, respectively, of the base and current periods.

In statics (usually according to grouping data), this formula looks like this (for each i- th group):

where atn - demand in the characterized n-th group;

yn-1 - demand in the previous group;

- average level of demand;

xn,xn-1, - factor signs, respectively, in n-th group,
in the previous n-1 th group and the average for all groups.

Another calculation option is also used, when not averages, but indicators of the previous group are used as the base value in relation:

The general coefficient of elasticity for all groups is calculated as the arithmetic weighted average of the group coefficients. Frequencies or frequencies for each group can be used as weights:

where - average coefficient of elasticity;

Ei- group coefficient of elasticity;

Wi- weight of each i-th group;

t - number of groups (without the first).

Features of calculating the coefficient of elasticity

Manifestations of the elasticity of supply and demand have a number of features. If the demand in the consumer market reacts almost instantly to changes in prices and income, and the nature of these changes is stochastic, manifests itself as an average or trend, then the demand for wholesale market often reacts with a certain lag, since it is to some extent determined by the directed activity of wholesalers based on one or another marketing strategy using various methods to stimulate demand. The same can be said about the supply, the elasticity of which is manifested in the organized forms of contractual (contractual) relations between suppliers and wholesale buyers. Here, an essential element of elasticity is the time during which the wholesaler adjusts to price changes. Of course, the response time to price changes depends on a number of conditions,
in particular from the development of information systems.

The vector of influence of prices on demand is inversely related
to the income impact vector. However, there are several exceptions to this rule. Firstly, elasticity is affected by the degree of utility of the product (that is, its place in the hierarchy of needs). The more important a commodity is to consumption, the less elastic it is usually. However, there is a phenomenon called Giffen paradox: the more expensive the bread, the more it is bought. Rising prices reduce demand primarily for high-quality, but expensive goods that do not appear on the scale of needs
in the first places. In conditions of rising prices, they are bought less than the requirements of elasticity dictate, and instead they buy essential goods. This means that one commodity in demand is being replaced by another. Substitutability effect is manifested in the fact that a decrease in price makes it more
and price increases - less competitive. This leads to
in the first case, it crowds out another commodity (becomes its substitute, substitute), and in the second - itself is replaced by a cheaper product. Thus, after the liberalization of prices at the beginning of 1992 and subsequent galloping inflation, the share of non-food products in the retail trade turnover of Russia decreased sharply, being squeezed out in the structure of demand by foodstuffs.

On the other hand, the effect of the so-called the Vebelen paradox. It consists in the fact that luxury goods are bought not so much for their consumer properties, but for their social value,
in particular, prestige, fashion, etc. Not without reason in the hierarchy of needs of the well-known American economist and sociologist A. Maslow, the need for self-affirmation and self-expression is at the top of the pyramid of needs proposed by him in the theory of motivation. This is also confirmed by domestic practice. We should agree with the opinion of the well-known economist R. Baduen, who pointed out that the Giffen effect is generated by poverty, and the Vebelen effect is generated by wealth.

A variant of calculating the coefficient of elasticity of demand is proposed, which to some extent allows to smooth out the contradiction, which is increasing
during a period of inflation, when the decline in demand caused by rising prices is to some extent offset by an increase in income. It is clear that in order to regulate demand, it is necessary to evaluate the role of each factor and both inextricably linked factors together. A multivariate regression model cannot be used because the price and income factors are collinear under these conditions. The use of combined grouping is not entirely correct.
Firstly, the time factor cannot be completely eliminated, and therefore, fixing the invariance of the price.

Secondly, the factor of prices for the purchase of goods of different quality will appear in the average group price.

In terms of inflation, it seems more reliable to model the elasticity of demand from the relative price level, expressed in terms of average income:

where D- demand;

R - price;

R- average consumer income.

The elasticity of the structure of demand, the displacement of one product by another under the influence of price factor are called cross elasticity. There are various methods for its detection. The most common is the following empirical coefficient of cross elasticity:

where Eh, u - coefficient of cross elasticity of demand;

Δ qx - increase in demand for a product X;

Δ qy- increase in demand for a product y;

Ry - the price of the product at;

Rx- the price of the product X.

Calculation of elasticity taking into account paired and multifactorial regression equations

The empirical coefficient of elasticity, for all its outward simplicity and accessibility, has one significant drawback: it is conditionally believed that all changes in demand are due to changes in one factor attribute, although in practice many factors simultaneously affect demand. In addition, the relationship between demand and other market factors, as a rule, is not functional, but probabilistic - correlational. The calculation of elasticity indicators should be closely related to modeling relationships using paired and multifactorial regression equations.
In this case, the formula empirical Marshall elasticity coefficient converted to formula theoretical Allen elasticity coefficient-Bowley. Mathematically, this is justified as follows: when studying the connection of mass data, the elasticity coefficient takes the form:

and since i.e. the first derivative at on x(y'); then the theoretical coefficient of elasticity takes the form:

where yx - the aligned value of the resulting attribute, that is, the expression of the dependence:

y = f(x);

y'- the first derivative of the corresponding function.

This formula allows you to determine the elasticity for each point of the curve, its economic interpretation, in particular, is to characterize the elasticity of demand for individual contingents (groups) of consumers. If we take the average values ​​of the effective and factor signs, then the average elasticity will be determined. At the same time, in practice, they usually replace the average value of the equalized resultant feature with the average value of the empirical value of the resultant feature Parabola of the 2nd order

nth order parabola

b1 +2b2x + …+nbnxn-1

Hyperbola

Semilogarithmic

b/x ln 10

Demonstration

ab2 ln b

Logistics

kabe-bx/(1+ae‑bx)2

Power

It should be added that the first derivative itself is also amenable to economic interpretation: it reflects the change in the effective attribute, but not as a percentage, but in named numbers under the influence of an increase in the factor sign, also in named numbers by one unit. Consider an example of calculating the theoretical coefficient of elasticity.

Having built a system of normal equations (the indicator of the number of families was used as weights), we obtained the following linear regression equation:

Hence, the coefficient of elasticity is equal to:

that is, the phenomenon of ultra-elasticity was revealed: demand increases
by 1.3% for a 1% increase in revenue. The first derivative of the linear regression equation is equal to the regression coefficient. Consequently, an increase in income by 1 thousand rubles. caused an increase in demand by 306 rubles.

Calculation of Net Elasticity Coefficients

In practice, consumer demand is simultaneously influenced by a complex of factors, each of which determines a certain elasticity of demand. In this regard, it is necessary to calculate "pure" elasticity coefficients, freed from the influence of other factors. For this purpose, a multifactorial regression equation is constructed, often of a linear form:

where bi- regression coefficients;

xi - factors.

Theoretical "pure" elasticity coefficients are calculated using the following formula:

However, the dependence of demand, as a rule, is non-linear. It is quite difficult to use many non-linear multivariate functions or mixed models. But from the linear form of the regression equation it is relatively easy to come to a power function, proving that the law of demand with constant elasticity can be represented by an equation like

then a multiplicative power multifactorial model can be constructed:

The elasticity coefficient in this case is equal to the regression coefficient:

Ei= bi.

The price elasticity of demand can be determined not only according to statistical records, but also on the basis of consumer surveys. Each individual consumer is not always able to answer how much he will buy a product at a price exactly equal to R, but the question may be clear to him, how much he will buy goods at a price lower R. If consumers are offered a range of prices, they will naturally choose the lowest. If the proposed prices are called the maximum permissible, then the opinions of buyers will be divided. The division of opinion will obey the law of demand.

There are several ways to detect customer reaction
on the proposed price level, which reflects the elasticity of demand:

1. A group of experts is asked about the quantity of goods purchased at a price not exceeding R, the question is repeated for different levels of the marginal price (Delphi method), the result reflects the demand corresponding to each price;

2. a certain number of consumers are interviewed (sample panel), each respondent names the marginal price at which
he is ready to buy a unit of goods (a number of levels can be prepared in advance, then the respondent indicates the corresponding level), as a result, a series of distribution of consumers by price level is compiled (frequency - the number of people who named the same price);

3. differs from the second one in that the respondent indicates not only the purchase price of one unit of the product, but also the prices at which he would purchase two or more units of this product. For each distribution obtained, a regression model is built and the elasticity coefficient is calculated.

SELF-CHECK QUESTIONS

1. What is absolute and relative value?

2. What methods of calculating averages in statistics do you know?

3. Give a definition of statistical time series.

4. What do the levels of dynamics series, moment and interval series display?

5. What statistical indicators of the dynamics of socio-economic phenomena do you know?

General Theory of Statistics: Statistical Methodology in the Study of Commercial Activities: Textbook / Ed. , . - M.: Finance and statistics, 1995. S. 77-79.

General Theory of Statistics: Statistical Methodology in the Study of Commercial Activities: Textbook / Ed. , . - M.: Finance and statistics, 1995. S. 79-84.

General Theory of Statistics: Statistical Methodology in the Study of Commercial Activities: Textbook / Ed. , . - M.: Finance and statistics, 1995. S. 88-99.

General Theory of Statistics: Statistical Methodology in the Study of Commercial Activities: Textbook / Ed. , . - M.: Finance and statistics, 1995. S. 155-160.

General Theory of Statistics: Statistical Methodology in the Study of Commercial Activities: Textbook / Ed. , . - M.: Finance and statistics, 1995. S. 161-165.

i statistics, 1995, pp. 233-240.

Statistics of the market of goods and services: Textbook / Ed. - M.: Finance
i statistics, 1995, pp. 78-88.

Types of absolute values, their meaning

Types of relative values, methods of their calculation and forms of expression

Essence and meaning of average values. Mean power quantities

Average structural values

1. Types of absolute values, their meaning

As a result of statistical observation and summaries, generalizing indicators are obtained that reflect the quantitative side of the phenomena.

All indicators used in statistical practice according to the form of expression classified into absolute, relative and average.

The initial form of expression of statistical indicators are absolute values. Absolute values ​​characterize the absolute dimensions of the studied phenomena, and also give an idea of ​​the volumes of the aggregates.

Absolute value- an indicator that reflects the size of social phenomena and processes in specific conditions of place and time. It characterizes the social life of the population and the country's economy as a whole (gross domestic product (GDP), national income, industrial production, population, etc.).

In practice, there are two types of absolute values: individual and total.

Individual values show the dimensions of the attribute of individual units of the population (for example, the weight of one person, the amount of wages individual worker, the amount of the deposit in a particular bank).

Total values characterize the final value of the attribute for a certain set of subjects covered by statistical observation (for example, the size of the wage fund, the total amount of deposits in banks).

Absolute statistics- always named numbers, i.e. have units of measure.

Absolute values ​​are expressed:

in natural units(kilograms, grams, centners, units, pieces, etc.), which are used in the case of characterizing the size of one phenomenon (for example, the volume of milk sales);

in conditionally natural units(feed units, standard fuel units, etc.), which are used to characterize the size of homogeneous phenomena (for example, the volume of feed in feed units);

in value units(rubles, dollars, euros, etc.) used in determining the size of heterogeneous phenomena (for example, the cost of buying a variety of food products);

in labor units(man-hours, man-days, etc.), which express the size of the cost of working time.

1. Types of relative values, methods of their calculation and forms of expression

Absolute values ​​do not always fully characterize phenomena. In order to correctly evaluate one or another absolute indicator, it is necessary to compare it with a plan or indicator relating to another period. For this, relative values ​​are used.

Relative value- the result of dividing one absolute indicator by another, expressing the ratio between the quantitative characteristics of socio-economic phenomena and processes. According to the relative value, one can judge how much the compared indicator is more than the baseline or what proportion it is of the baseline.

When calculating relative values, the absolute indicator in the numerator is called compared (current), and located in the denominator - base of comparison. AT depending on the base of comparison, the resulting relative indicator can be in the form of an expression or be a named value.

There are the following forms of expression relative values:

coefficient , if the comparison base is taken as 1;

percent, if the comparison base is taken as 100;

ppm if the comparison base is taken as 1000;

decimille if the comparison base is taken as 10,000.

If the relative value is obtained by dividing opposite indicators, then it will be expressed using units of measurement which reflect the ratio of the compared and basic indicators.

OVPV - the relative value of the planned target;

OVVP - the relative value of the implementation of the plan;

ATS - the relative value of the dynamics;

OVS - the relative value of the structure;

OVK - the relative value of coordination;

OVSR - relative value of comparison;

JVI - relative intensity value;

OVWER - the relative value of the level of economic development.

Relative value of the planned target (OVPZ) represents the ratio of the value of the indicator set for the planned period to its actual value achieved per the previous period or for any other period taken as the basis for comparison.

Where - the level planned for the upcoming period.

The level of the indicator achieved in the past (previous, base) period.

OVPV characterizes the growth or reduction of the phenomenon under study in the planning period compared to the level achieved in the previous period.

The relative value of the implementation of the plan (RTI) is the result of comparing the actual level of the indicator with its planned level.

,

where , - the level of the indicator achieved in the reporting period.

OVVP characterizes the growth or reduction of the studied phenomenon, actually achieved in the reporting period, compared with the plan.

Relative value of dynamics (RTS) is calculated as the ratio of the current indicator to the previous or basic one, i.e. characterizes the change of certain phenomena in time.

.

ATS is called the growth rate, expressed in coefficients or percentages.

The last three quantities are interconnected as follows:

ATS \u003d OVPV x OVVP

This relationship is manifested only if the relative values ​​are expressed in coefficients.

ATS is calculated in a chain or basic way. At chain method of calculation each subsequent reporting level is compared with the previous level, with basic calculation method- with the first level taken as the base of comparison.

If the level of each subsequent period (Y n) is compared with the level of the previous period (Y n -1), then ATS is calculated chain way .

If the level of each subsequent period (Y n) is compared with the level taken as the comparison base (Y 0), then the ATS is determined basic way .

Relative Structure Value (RVS) shows the share of a part of the population in its total volume:

,

where fi – the number of units of a part of the population,

∑ fi - overall volume aggregates.

OVS expressed in coefficients or percentages and is used to characterize the structure of the phenomenon.

Relative Coordination Value (RVR) characterizes the ratio of individual parts of the whole. In this case, the part that has the largest share or is a priority from an economic, social or other point of view is selected as the basis for comparison.

,

where fi- number of units i- parts of the population;

fj- number of units j- parts of the collection.

The relative values ​​of coordination show how many times one part of the population is larger than the other, or how many units of one part account for 1,10,100,1000,10000 units of the other part.

Relative comparison value (RVR) represents the ratio of absolute indicators of the same name characterizing different objects (enterprises, regions, countries, etc.), but corresponding to the same period or point in time.

The form of expression OVSR can be taken in coefficients or percentages.

Relative intensity value (RVI) shows the degree of distribution of the phenomenon in its inherent environment and is the result of a comparison of opposite, but in a certain way interconnected absolute values ​​(population density, labor productivity, unit cost of production, etc.). Calculated per 100, 1000, etc. units of the studied population.

A special case of the relative intensity value is relative value of the level of economic development (ERWER), which represents the volume of production of any commodity per capita. This value has a unit of measurement (kilograms, centners, tons, etc. per capita).

The concept of absolute and relative values

Absolute and relative values, reflecting the corresponding characteristics, cannot exist without each other.

Absolute values ​​in economic analysis

Definition 1

The absolute value expresses the quantitative dimensions of a certain phenomenon without its relationship with others, without assessing the ongoing changes and deviations. The absolute value characterizes the volume and level of the process (phenomena), being always named numbers.

Absolute values ​​have a dimension, that is, a unit of measurement.

Classification of absolute values:

• natural,
• labor,
• money, etc.

Average and relative values

The ratio of several absolute values ​​is expressed using average and relative values.

Remark 2

To determine the relative values, it is necessary to divide one indicator by another, which is taken as the base one.

The following indicators can be the base value:

• plan data,
• Factual data,
• Information from previous years
• Indicators of other enterprises, etc.

Relative comparison values ​​can be expressed as a percentage (based on the base, which is taken as 100) or as coefficients (in this case, the base is one).

Classification of absolute values

Absolute values ​​can be of two types:

• Individual absolute values ​​characterizing the size of a feature of a particular unit. Examples of such values ​​can be the size of employees' wages or a bank deposit. These dimensions are determined directly in the process of observation, while they are recorded in the primary accounting documentation.
• The total absolute values ​​reflecting the final indicator of the attribute in the totality of objects. This size acts as the sum of the number of units (population size) or the volume of varying characteristics.

Classification of relative values

The main condition for calculating relative values ​​is the comparability of units and the existence of a real connection between the phenomena under study. The value with which the comparison is made, which is in the denominator in a fraction, acts as the base or base of the ratio. In accordance with her choice, the result can be expressed in various fractions of a unit, then a network of tenths, hundredths (percent), thousandths (a tenth of a percent, ppm), ten thousandths (a hundredth of a percent of a decimille).

The units that are matched can be both of the same name and of the opposite name. If the units are of different names, then their name is formed depending on the units used (c/ha, rubles/person, etc.).

AT economic analysis Several types of relative values ​​are used:

1. speakers,
2. The relative value of the structure, characterizing the share of certain parts of the studied population in its total volume;
3. The value of the planned target, expressing the ratio of planned indicators for the future to the actual prevailing values ​​for the current period;
4. intensity,
5. Comparisons
6. coordination,
7. Degrees of economic development.

The calculation of relative values ​​is carried out by determining the ratio of the number in a certain part to their total number (or volumes). These units are expressed as a percentage or as a simple multiple. For example, the calculation of the proportion of the urban population.

Statistics studies the quantitative side of mass phenomena and processes with the help of statistical values, which are divided into absolute and relative values.

Absolute values ​​characterize sizes in specific conditions of time and place. They characterize the entire population.

Units of measurement of absolute values:

1) natural, reflecting the natural properties of the phenomenon, is a physical measure of weight, length, etc. The main disadvantage of natural units of measurement is that it is impossible to sum up various natural absolute values;

2) conditionally natural(used for the purpose of summing consumer products of different shapes);

3) combined. They are obtained by multiplying or dividing two natural units of measurement;

4) value (cash). Eliminate the shortcomings of the previous units of measurement, allow you to evaluate heterogeneous products.

However, absolute values ​​do not provide a comprehensive description of the phenomena and processes under study and are not always suitable for comparison. This necessitates the use of relative values, which are used in comparisons, comparisons and play the role of a ratio measure.

Relative quantities are abstract statistical quantities expressing the quantitative ratio of two quantities.

Types of relative values: 1) relative dynamics- this is the ratio of the actual value of the indicator in the reporting period (y1) to its actual value in the base, previous period (y0):

ATS = Y 1 / Y 0 × 100%.

Relative values ​​of the dynamics characterize the change of the phenomenon in time. In statistics, these indicators are called growth rates; 2) relative values ​​of plan fulfillment- this is the ratio of the actual value of the indicator (y1) to its planned value (upl) of the same period:

OVVP = Y 1 / Y pl × 100%.

This relative value shows the degree of implementation of the plan as a percentage; 3) the relative value of the execution of the planned target- this is the ratio of the planned value of the indicator (sIL) to the actually achieved value in the previous period, i.e. in the base (y0):

OVPZ = Y pl / Y 0 × 100%.

Shows by how many percent the planned target is higher (lower) than actually achieved in the base period. This value is called the planned growth rate;

4) relative size of the structure- shows the composition of the phenomenon, expressed in the form of a share or specific gravity. The share (d) is the ratio of the part to the whole, i.e. the ratio of the constituent parts of the aggregate to its total volume. Specific gravity is a share expressed as a percentage. Relative values ​​of the structure are used in statistics to characterize structural shifts;

5) relative amount of coordination- shows the ratio of the parts of the whole, i.e. the ratio of successively all parts to one of them, taken as the base. The smallest value is taken as the base. The relative value of coordination shows how many units of a given part of the whole fall on its other part, taken as the basis of comparison;

6) relative intensity value is the ratio of two opposite quantities related to each other. Characterizes the degree of development of a phenomenon in a particular environment;

7) relative comparison value is the ratio of similar quantities characterizing different objects of study for the same period. Shows how many times the numerator is greater (less) than the denominator.

The essence of averages. Types and forms of average values. Variants and frequencies

The method of averages is one of the most important methods in statistics because averages are widely used in analysis, in practice, in establishing patterns, trends, relationships, and for many other purposes. The essence of average values ​​is that they characterize the level of the trait under study by one number. A distinctive feature of averages is that they are general indicators.

average value- this is a generalizing indicator that expresses the typical level (size) of a variable trait per unit of the population (qualitatively homogeneous).

The average value reflects the total that is hidden in each unit of the population. She catches common features, general patterns that manifest themselves by virtue of the law big numbers. Speaking of averages, they mean that they characterize the entire population as a whole, however, along with the average, it is necessary to provide data on individual units of the population.

Problems solved using the method of averages:

1) characteristics of the level of development of the phenomenon under study;

2) comparison of two or more levels of the studied populations;

3) characteristics of changes in the level of the phenomenon in time;

4) identification and characterization of relationships between the studied populations.

P principles for constructing averages:

1) average values ​​can be calculated only for qualitatively homogeneous aggregates;

2) averages should not be abstract, that is, only quantitative indicators. They should give a qualitative-quantitative characteristic of the phenomenon under study. Therefore, in statistics, the average value is not an abstract, abstract number, but a very specific indicator related to some phenomenon, place, time;

3) the choice of the population unit, in relation to which the average value is calculated, must be theoretically justified.

The following main types of averages are distinguished: arithmetic average; average harmonic; root mean square; geometric mean.

For the correct calculation of averages, it is necessary to introduce concepts such as variants and frequencies.

As a result, summaries and groupings get statistical series, i.e., series of digital indicators. According to their content, such rows divided into distribution lines and rows of dynamics .

The distribution series characterize the distribution of population units according to any one attribute, the varieties of which are ordered in a certain way. There are two types of distribution series - attribute and variation series.

Attribute rows are formed as a result of grouping data according to qualitative characteristics (for example, the distribution of the population by sex). There are as many groups in these series as there are variants of a qualitative trait.

Variation series- this is an ordered series of values ​​​​of a varying quantitative attribute and the number of units that have a given value of the attribute (for example, the distribution of workers by wages).

In the variation series of distribution, the following elements are distinguished:

1) options(x or x1, x2 ... xn) is a series of numerical values ​​​​of a quantitative attribute (for example, experience, wage, age). Variants can be both absolute and relative values;

2) frequencies(m: m1, m2 ... mn) are numbers showing how many times the corresponding options are repeated (for example, the number of workers). Frequencies are usually denoted by an absolute number; if, according to the condition, the frequencies are expressed as percentages of the total or shares, then they are called relative frequencies (or) frequencies f:

f = m / Σ m .

AT economics statistical disciplines are in priority positions. This is due to various reasons. First of all, within the framework of general economic specialties, statistical research acts as the basis for the development and improvement of analytical methods. In addition, they are an independent direction with its own subject.

Absolute and relative values

These concepts act as key elements in statistical science. They are used to determine the quantitative characteristics, the dynamics of their change. Absolute and relative values ​​reflect different characteristics, but without one, others cannot exist. The former express the quantitative dimensions of this or that phenomenon, regardless of others. It is impossible to assess the ongoing changes and deviations from them. They express the volume and level of a process or phenomenon. Absolute values ​​are always named numbers. They have a dimension or unit of measure. They can be natural, labor, monetary and so on. For example, standard hours, pieces, thousand rubles. and so on. Average and relative values, on the contrary, express the ratio of several exact dimensions. It can be established for several phenomena or for one, but taken in a different volume and in a different period. These elements act as a quotient of statistical numbers, which characterizes their quantitative ratio. To determine the relative values, you need to divide one size by another, taken as the base. The latter may be planned data, actual data from previous years or another enterprise, and so on. Relative can be expressed as a percentage (if the base is taken as 100) or coefficients (if the base is one).

Classification of statistical numbers

Absolute values ​​are presented in two types:

1. Individual. They characterize the size of the trait in specific units. For example, it can be the amount of an employee's salary, a bank deposit, and so on. These dimensions are found directly in the course of statistical observation. They are recorded in the primary accounting documentation.
2. Total. Values ​​of this type reflect the total indicator of the attribute for the totality of objects. These dimensions act as the sum of the number of units (the population size) or the volume of the varying characteristic.

Units

Natural absolute values ​​can be simple. These are, for example, tons, liters, rubles, pieces, kilometers. They can be complex, characterizing a combination of several quantities. For example, statistics use ton-kilometers to establish freight turnover railway transport, kilowatt-hours - to assess the production of electricity and so on. Conditionally natural units are also used in research. For example, the tractor park can be converted into reference machines. Value units are used to characterize a heterogeneous product in terms of money. This form, in particular, is used in assessing the income of the population, gross output. Using value units, extras take into account the dynamics of prices over time, and overcome the disadvantage due to "comparable" or "constant" prices for the same period. Labor values ​​take into account the total cost of work, the complexity of certain operations that make up the technological cycle. They are expressed in etc.

Relative values

The main condition for their calculation is the comparability of units and the existence of a real connection between the phenomena under study. The value with which the comparison is carried out (the denominator in a fraction) acts, as a rule, as the base or base of the ratio. Depending on its choice, the result can be expressed in different fractions of a unit. It can be tenths, hundredths (percent), thousandths (10th part of% - ppm), ten thousandths (hundredth of% - decimille). Comparable units can be either the same or different. In the second case, their names are formed from the units used (c/ha, rub./person, etc.).

Types of relative values

Several types of these units are used in statistics. So, there is a relative value:

1. structures.
2. Planned task.
3. intensity.
4. Speakers.
5. coordination.
6. Comparisons.
7. Degrees of economic development.

The relative value of the task expresses the ratio of what is planned for the upcoming period to what has actually developed for the current period. The plan unit is calculated in the same way. The relative size of the structure is a characteristic of the share of specific parts of the population under study in its total volume. Their calculation is carried out by dividing the number in individual parts by their total number (or volume). These units are expressed as percentages or simple multiples. For example, this is how the proportion of the urban population is calculated.

Dynamics

The relative value reflects in this case the ratio of the level of the object in a particular period to its status in the past tense. In other words, it is characterized by a change in a phenomenon over a period of time. The relative value characterizing the dynamics is called The choice of the base in the calculation is carried out depending on the purpose of the study.

Intensity

The relative value can reflect the degree of development of a phenomenon in a particular environment. In this case, we talk about intensity. Their calculation is carried out by comparing opposite quantities that are related to each other. They are set, as a rule, based on 1000, 100 and so on units of the study population. For example, per 100 hectares of land, per thousand people, and so on. These indicators of relative values ​​are named numbers. For example, this is how population density is calculated. It is expressed as the average number of citizens per square meter. km of territory. The characteristics of the degree of economic development serve as a subtype of such units. These, for example, include such types of relative values ​​as the level of GNP, GDP, VID, and so on. per capita. These characteristics play important role when analyzing the economic situation in the country.

Coordination

The value of relative values ​​can characterize the proportionality of the individual elements of the whole to each other. The calculation is carried out by dividing one part by another. Relative quantities in this case act as a subtype of units of intensity. The difference lies in the fact that they reflect the level of distribution of heterogeneous parts of the same population. The base can be one or another sign, depending on the goal. In this regard, for the same whole, several relative values ​​of coordination can be calculated.

Mapping

Relative comparison values ​​are units that are partial divisions of similar statistical features that act as characteristics for different objects, but refer to the same moment or period. For example, the ratio of the cost of a particular type of product produced by two enterprises, labor productivity for different industries, and so on is calculated.

Economic evaluation

In this study, absolute and relative units are actively used. The former are used to establish the ratio of reserves and expenses with sources of financing and evaluate the enterprise in terms of financial stability. Relative indicators reflect the structure of funds with the state of fixed and working capital. At economic evaluation horizontal analysis is used. The most generalizing absolute value that characterizes the financial stability of the company is the lack or excess of sources of financing costs and reserves. The calculation is made by subtraction. The result is the difference in the size of the sources (minus non-current assets), the means of which stocks are formed, and their number. The key elements in this are the following statistical units:

1. Own current assets.
2. General indicator of planned sources.
3. Long-term borrowed and own funds.

Deterministic factorial research

This analysis is a specific technique for studying the impact of factors whose interaction with the results has a functional character. This study is conducted by creation and evaluation. Relative indicators are widely used in this analysis. In most cases in factor analysis multiplicative models are used. For example, profit can be expressed as the product of the quantity of goods and the unit cost. Part of the analysis in this case is carried out in 2 ways:

1. implies a chain substitution. The change in the result due to the factor is calculated as the product of the deviation of the studied trait by the base of another according to the selected sequence.
2. The relative difference method is used to measure the impact of factors on the increase in the result. It is used when there are previously calculated percentage deviations in the source data.

Time Series

They represent a change in the numerical indicators of social phenomena over time. One of the most important directions in this analysis is the study of the development of events for specific periods. Among them:

Conclusion

Undoubtedly, relative values ​​have a high scientific value. However, in practice they cannot be used in isolation. They are always in relationship with absolute indicators, expressing the ratio of the latter. If this is not taken into account, then it is impossible to accurately characterize the phenomena under study. Using relative values, you need to show what specific absolute units are hidden behind them. Otherwise, you can draw wrong conclusions. Only the complex use of relative and absolute values ​​can act as the most important means of information and analysis in the study of various phenomena occurring in socio-economic life. In general, the transition to the calculation of deviations makes it possible to compare the economic potential and the result of the activities of enterprises that differ significantly in terms of the amount of resources used or other characteristics. Relative values, in addition, can smooth out some processes (force majeure, inflation, and others) that can distort absolute units in financial statements.