Summary and grouping.
On the basis of the data collected can not calculate and draw conclusions for the start of their need to compile and consolidate in a single table. To serve this purpose, and a summary of the grouping.
Summary - a set of sequential steps in synthesis of specific individual facts constituting the aggregate and identify common features and regularities inherent in the studied phenomenon in general.
Simple vodka - count total population of the population.
Sophisticated summary - a set of operations on grouping of individual observations, the results of calculation for each group and for the whole object and presenting the results in the form of statistical tables.
The shape of the processing material is a summary of decentralized, centralized - this summary is conducted at single statistical observation.
Grouping - dismemberment of a plurality of units of the target population into groups according to certain priznakam.Vidy gruppirovok.Intervaly. Types of statistical groupings.
1. typological - the division into classes together, socio-economic types (state-owned enterprises, JSC, LLC, CJSC)
2. Structure - separation together on any single feature. (Age)
3. Analytical group characterizes the relationship between the features one of which is a quotient other productive.
According to the structure:
1. Simple (monothetically)
2. Complex (political)
- MnogomernayaMnogomernye groups
Multidimensional categories used in statistics when the group performed on several grounds. Apply in practice the method of multidimensional classification using computers. The simplest method of multi-dimensional classification is multi-dimensional medium, which is called the mean value of several attributes for one unit together. It is determined from the relative values ??tend relationship of absolute values ??of attributes for the unit to the mean values ??of these attributes.
- Multi-dimensional average of the i-th unit
the number of signs;
is the absolute value of the characteristic x to the i-th unit;
the average value of feature xAbsolyutnye and relative values ??in the statistics.
Results summary and categories should be presented so that they can be used.
There are 3 ways of reporting:
1. The data may be included in the text.
2. The representation in the tables.
3. The graphical method
Be sure, when grouping, use the characteristics that will be held this grouping - grouping characteristics. In order to separate one group from another grouping intervals is used. Dismemberment of collections made by groups of units:
1. According to one feature, ie Easy grouping (monothetically);
2. VO2-m or more attributes, ie complex group (combination, polythetic).
Compared with the simple combination groups have additional analytic properties.
Sign, over which the group formation is called a grouping variable or base groups. It depends on the selection of a particular purpose. For many signs develop sustainable nomenclature groups and subgroups, called classifications. To form groups usually set intervals. In statistics intervals are 2 types:
· Closed - this is when the specified upper and lower limits of the interval. This record suggests that a unit in which characteristic value coincides with the upper boundary of the interval refers to a following group.
· Open - an uncertain border, they are accompanied by the words "up", "above", "about".
Largest grouping variable intervals are divided into:
2. Unequal intervals.
Value equal intervals determined by dividing the difference between the maximum and minimum indication on the number of generators of the groups.
Using equal intervals facilitates the analysis of the materials obtained as a result of the grouping. This allows you to predict what changes will result in an increase or decrease grupirovochnogo trait that underlies groups. Hence - should be resorted to equal intervals.
In the formation of intervals attention should be paid to the marking of boundaries. In allocating slots for discrete intermittent (quantitative) characteristics should denote the borders so that the upper and lower limits of 2 adjacent intervals differed by one (101-200). If the intervals are formed in a continuous basis, ie take any value within certain limits, in this case the border must be indicated so that all groups have been severely restricted by one another. This is achieved by adding to the numerical limits of the intervals guidance about which group should be attributed a particular border.
Statistical Table - a system of rows and columns, which in a certain sequence presents statistical information on the socio-economic phenomena.
Distinguish between the subject and predicate of the table.
Subject is an entity characterized by the number, typically the subject is given in the left part of the table.
Predicate - a system of indicators, by which is characterized by an object.
Statistical table contains 3 types of headers: general, side, top.
The overall title should reflect the contents of the entire table, located above the table in the middle.
1. Be sure to all three types of headers without using abbreviations common unit of measurement can be taken in the header.
2. The table should not be extra lines, vertical layout may be missing.
3. The final line is required. It may be at the beginning and end of the document. If at the beginning of that docum TOTAL (including), if in the end it TOTAL;
4. The digital audio data within a recorded audio graphs accuracy. Bits are written strictly for discharges integer part separated by a comma.
5. in the table should not be empty cell if data is missing, write "Nil" or "..." if the data are zero, "-". If the value is not zero but the first significant digit appears after the specified accuracy 0,01®0,0 - if adopted by the nearest tenth.
6. If the table a lot of the graph, the graph to be designated by capital letters, and graphs predicate figures.
7. If the table is based on data borrowed, something under the table indicates the source of the data, if necessary, the table may be accompanied by notes.
Statistical graphics - Symbols of numerical values ??and their relations by means of lines, geometric shapes, patterns.
1. clearly, visibility, expressive.
2. immediately visible limits of change indicator, the relative rate of change and variability
1 comprises less than the amount of data in the table.
2. The chart shows the rounded data, the overall situation, but not the details.
- The bar
Statistical indicator - general characteristic of a set of properties.
The structure of the statistic (attributes):
1. Indicators of the properties of concrete objects
2. Statistical indicators
- Indicators of variation
- Indicators of communication features
- Indicators of the structure and distribution of
- Indicators of dynamics
- Indicators vibrations
- Accuracy and reliability of sample estimates
- Accuracy and reliability of forecasts
1. Absolute - the total number of units or total property of the object. This is the amount of primary characteristics measured in pcs., Kg m $, etc.
2. The relative indicator - obtained by comparing the absolute and relative performance in space, in time or in the comparison of the different properties of the object being studied.
Relative index is obtained by comparing 1goporyadka 2habsolyutnyh indicators. Relative index 2goporyadka obtained by comparing the relative performance 1goporyadka etc.
Relative index 3goporyadka and above are very redko.Suschnost absolute values.
Absolute statistical indicators - indicators expressing dimensions of specific social phenomena (cost, weight, volume, area, etc.). The absolute values ??are always named number (m2,10 thousand. Rub.). Very important question of choosing the units in each case. It depends on the properties of the feature, its nature and objectives of the study. All variety of units in the statistics is reduced to three types:
Physical indicators used to characterize the scope, size, measure the length, weight, etc. In some cases, conditional physical indicators, when the kind of the same value in use is taken as a unit, and the other was converted to that unit.
Cost parameters are given to characterize the processes or phenomena in terms of value.
The employment figures used to determine the cost of labor for the production of specific products.
All absolute statistical values ??are divided:
· Individual - indicators that express the size of quantitative traits in individual units of the target population (the number of employees in the firm). These data are obtained by statistical formulas and recorded observations, and it is used for the final (overall) performance.
· Summary (general summary) express the dimensions, the value of a trait in all units of the population (the number of workers Shah will give a total number of employees in the country). These data are used for grouping indicators for reports and for analiza.Statisticheskie relative values
Absolute values ??themselves do not provide sufficient characteristics evaluation conditions. Therefore, in the statistics, along with the absolute values ??are relative, which are indicators that characterize the quantitative relationships inherent in a particular economic phenomena (the proportion of urban and rural population in the total population). A distinctive feature of the relative values ??is that they are usually expressed in abstract form ratio, either individually or summary of the absolute values. By the relative values ??in the statistics include some concrete numbers (meat consumption per capita). This kind of relative values ??indicate how many units of one set per unit of another.
In calculating the relative magnitudes are compared one or more indicators to the base or base (the base value). A specific feature is that they allow you to escape from the specific differences of absolute values, which makes it possible to compare these phenomena, the absolute values ??are not sopostavimy.Formy and types of relative values.
In terms of what is to compare what the ratio should be obtained by using several kinds of statistics in the relative quantities:
1. The relative values ??of the scheduled tasks - such quantities that express the relationship between the actual results and those that are planned (usually expressed as a percentage). These values ??characterize the progress and result.
2. The relative magnitude of the structure. The value of the structure is very important in statistics and is the ratio of part and whole. When calculating the magnitude of the base structure is taken as the aggregate sum total (overall dimensions), and is taken as reference values ??of the quantities of individual groups or individual parts (expressed in percentages or ratios). Therefore, the statistics usually called attitude to the whole or part of the shares, or specific gravity. The relative magnitudes of the structure allow to find out not only the structure of the target population, but also structural changes, ie change in its composition, structure, trend, trend, which occurred over a period of time. For this purpose, usually analyzed and calculated structure parameters over several periods.
3. The relative magnitudes of coordination - the ratio of parts of the whole together. When calculating the one of the components of this aggregate is taken as the basis for comparison and are related to all other parts of it. With their help determine how many units of this part together accounted for another part, adopted as a base of comparison.
4. Relative values ??of the dynamics express the degree of change phenomena in time, ie they measure the speed (tempo) development. The relative value of speakers is the ratio of the value (level) of the index for the period (month, quarter, year) to its level in the previous period. Therefore, for the calculation of the relative magnitudes of the dynamics necessary to have data for several periods.
In statistics, there are two types of calculation of the relative magnitudes of the dynamics:
· Chain calculations - when the relative values ??of the dynamics is determined by a variable base of comparison. Show how to quickly change the value of the index for the year or any other time unit.
· Basic calculations - when the relative values ??of the dynamics are calculated at constant base of comparison. Characterize the change in the number of gradually increasing periods.
Often, when calculating the relative values ??of the dynamics of the question of choosing a basis for comparison. Usually, when describing the dynamics of the long periods of time as a base take a period of great importance in the economy. Also often used as a base member of the first series of speakers.
5. The relative magnitudes of the comparison is a ratio similar quantities relating to the different objects (the population of the city of Tver and Torzhok). Especially it is widely used in international comparisons, and for the calculation is used as absolute values ??and relative.
6. The relative magnitudes of intensity - indicators characterizing the spread, the development of a phenomenon in a particular environment. They measure the degree or intensity of the spread of performance or events. Most often they are of opposite parity, but related phenomena, where the numerator - the value of the phenomenon, and the denominator - the volume of the environment in which the development of the phenomenon. Most often they are calculated for 100 or 1000 edinits.Srednie value. (Indicators). The essence of statistical averages.
The most common form of statistical indicators is the average value.
The most important property is the medium that it reflects something in common, that is inherent in each unit of the target population, although the value of feature separate population units may fluctuate in one direction or another.
Typical middle is directly related to the homogeneity of the studied population. In the case of a homogeneous aggregate must be a breakdown of its qualitatively homogeneous group and calculate the average for each for each of the homogeneous groups.
You can determine the average over the initial ratio of the mean (ISS), its logical formula.
On the form in which the data for the calculation of the average, it will depend on how the ISS.
types of averages
1. The arithmetic mean
2. The harmonic mean
3. Average quadratic, cubic
4. The geometric mean
Rule mazherantnosti srednih.Sposoby calculating statistical averages
Other types of medium
Among the simple view of the weighted average of the average
Simple and weighted average.
From the above formulas, the arithmetic mean and the mean of the harmonic, it follows that the average value does not depend only on the size of averaged feature x, but to a greater extent in the values ??of f and W. In this case, obviously, when well-defined specific values ??of x (x1 , x2, ..., xn) the average value will be greater, the greater the share of the sum of the values ??have a number of options for those who have the largest size.
On average value will not affect the values ??of f and W is the case if they were the same for all variants averaged characteristic x: f1 = f2 = ... = fni W1 = W2 = ... = Wn.
If such a condition exists, then to calculate the arithmetic mean formula is used:
1, where n is the number of options is averaged characteristic x.
2. For the harmonic mean:
Mean calculated using formulas ¹1, 2, 3, i.e. f and containing W, called weighted and the values ??f W called weights and average calculation process and, in turn, is called weighting. If payment is made by the formulas ¹4, 5, medium, defined in this way are called simple or unweighted.
When calculating the average is most often used formula weighted average. Formula number 4, 5 are used in cases where the options are averaged feature is not repeated or not made their grouping. This distinction on the simple average and weighted very important in the economy, then use that instead of just a simple weighted average can lead to erroneous results and conclusions.
Variation in the ranks of the distribution.
Conducting analysis of variance begins with the construction of a number of variations - ordered distribution of population units by increasing or decreasing the grounds and counting the respective frequencies.
Series of distribution:
1. Ranked variational series - a list of individual units. together in ascending order of decreasing feature ranked
2. Discrete variational series - table consisting of 2hstrok - plastic tag values ??vary and the number of units with a given trait.
3. Interval variational series constructed in the following cases:
- A sign takes discrete values, but their number is too large
- Attribute accepts any value within a certain range
When constructing an ordered series of interval must select the optimal number of groups, the most common way the formula Sturgess
k = 1 + 3.32lgn
k - the number of intervals
n - amount of aggregate
In the calculations almost always receive fractional values, rounding up to produce an integer.
The length of the interval - l
Types of slots
1. The lower limit of the subsequent interval repeats the upper limit of the subsequent interval
2. individual boundaries in the interval includes upper and lower bounds
3. Open the interval, the interval from one boundary
In the case of an open interval l shall be equal to the length of the interval adjacent to it, or on the basis of logical considerations.
In the calculations for a number of variations of interval for xiprinimaetsya middle of the interval.
The intervals may be equal or not. In the study of variational series provides substantial assistance graphic image.
Discrete variational series is represented by a polygon. (Fiot xi)
Interval variation series is represented by a histogram. . (Fiot xi)
Cumulative frequency - each subsequent frequency is added to the next.
Cumulates - the distribution of 'less than'
Ogives - distribution 'more chem'Moda and median.
In some cases the statistics to determine typical characteristics, particularly for certain feature size, fashion and used medianu.Moda
Fashion is usually used when the average size is difficult to calculate the feature. In statistics mode is defined to feature most frequently encountered in the population.
- Initial boundary modal characteristic, ie, feature, which has the highest number in this distribution,
- The value of the modal interval
- The frequency interval preceding the modal,
- The frequency interval following the modalnym.Mediana
Median variant called dividing the number of ordered variational series, ie, built in ascending or descending order varying trait into two equal parts. For an even number of should be the average of the two options that are in the middle of the range of variation variation ryada.Pokazateli
All of the features mentioned in the statistics, are subject to fluctuations. The simplest indicator of this is any indication koleblimosti swing variations. In general it is the difference between the largest and the smallest value characteristic.
The scale of variation depends on two characteristic values ??that the economy is inaccurate opredeleniya.Srednee linear deviation
Measure of the average linear deviation is considered deviations from the average value taken without algebraic sign. Calculated so that the mean deviation is called the mean linear deviation.
In practice, it should be borne in mind that the amount of linear deviation variation various rows can be compared only if these series are characterized by approximately the same medium. And since it happens in practice is not always something to match koleblimosti calculated relative performance koleblimosti, ie include linear deviation to the arithmetic mean.
Using the notation previously adopted varying characteristic, and average weight, you can calculate the average order linear deviation written as a formula
But if the characteristic variations in the distribution is not repeated, the average linear deviation calculated by the following formula:
Variance and standard deviation
The average of the deviations from the mean can be retrieved if the first all deviations squared, then find the arithmetic mean of the squares, and then from the resulting value of the square root. Thus obtained figure is the average deviation (). The arithmetic mean of the squared deviations is called the variance ().
- The mean square deviation, weighted;
- The mean square deviation nevzveshennyy.Koeffitsient variation.
Very often, to compare the degree of koleblimosti, especially various variational series, calculate the coefficient of variation. To calculate it, it is necessary to include the standard deviation to the arithmetic mean, and the result is expressed as a percentage.
- Residual variance for group j
- The sum of the frequencies for the j group
n - the total amount chastotRyady dynamics. Classification and the concept of time series.
To better characterize the economic situation and the processes used time series. They provide a more precise, a visual representation of the phenomenon and the aggregate.
Near dynamics is a series of statistical data characterizing the phenomenon of change over time. Each value in the series is called the level, figures, forming a number of speakers, can characterize the magnitude of the phenomenon being studied in two ways:
1. for a certain period of time;
2. The condition for a certain time.
In this regard, the statistics are distinguished:
1. The interval time series - these series, which consist of a quantitative indicator values ??for some period of time;
2. Snapshots series - a number that characterizes the size of an index as of a certain date.
Levels of a number of speakers can be expressed as the absolute size of the phenomenon and the relative. Distinguish
1. The time series of absolute values ??- such series, whose members express the absolute values ??of the studied parameter for several successive moments;
2. The time series of relative values ??- such series, whose members express the relative sizes of the phenomenon under study for a number of intervals.
Types of dispersion:
1. The total variance - measures the variation of the trait in their entirety under the influence of all factors have caused this variation
Example: consumption of yogurt: the sample of 100 people
2. Intergroup dispersion - characterizes the variation characteristic trait influenced by factors laid the basis for grouping.
- The average for the group
2. Intra-dispersion (residual) characterizes the variation of trait influenced by factors not included in the grouping
x ij - i characteristic value in group j
- Average value of feature j in group
f ij - the frequency of the i-th character in the group j
There is a rule that binds the 3 types of dispersion, it is called the rule of addition of dispersion.
There are a series of calculations of the dynamics of averages - a series whose terms express the average level of the studied parameter for some period of time.
To characterize the dynamic performance of a number of the following applies:
2. The absolute increase,
3. The growth rate,
4. The rate of growth,
5. The average value of a number of speakers pokazateley.Uroven
Source, in the construction of any of the dynamic series, is the level of dynamics, but for the general characteristics for the entire period covered calculated the average number of, ie the average value of the number of aggregates. In the ranks of the dynamics of the average of the levels is called a chronological average. For interval time series with equal intervals of time is as simple arithmetic average, ie the sum of all the levels charged to the number of levels.
The average level provides an overview of the development of the phenomenon and not at some point, but for the whole protsess.Absolyutny growth
To characterize the dynamics of the series use the absolute increase, which is a difference of levels of dynamics. Absolute growth indicators or increases growth performance or increase in the number of over a certain period of time. To determine the size of the increase in the index for the entire period of time covered by a number of speakers, find a common absolute increase, which is equal to the sum of the sequence of calculated absolute increases, and at the same time, it is equal to the difference between the final and initial level.
To characterize the absolute growth for a given time period as a whole, often determine the average absolute increase.
m - number of absolute growth for equal periods.
1. Summary and grouping. Types gruppirovok.Intervaly.
The essence of the absolute values.
Statistical relative values
Mean values. (Indicators). The essence of statistical averages .. Types averages and methods for their calculation.
Simple and weighted average.
Variation in the ranks of the distribution.
Mode and median.
Indicators of variation
Variance and standard deviation. Types of dispersion.
Time series. Classification and the concept of time series.
Growth rate, growth, and their computation.
Since the absolute growth figures on how many units in absolute terms, the level of follow-up period is greater than or less than the preceding, we can not get an answer to the question how many times the level of one period is greater than or less than the other. Therefore, the statistics using the growth rate, ie, ratio of the given period to the level of his previous period. Sometimes it does not use the previous value, and the other taken as the base.
Typically, the growth rate can be expressed as a percentage or as a simple relationship and ratios. The rates, expressed as simple relations is called the growth factor.
To characterize the level of the index over time, along with the growth, use, and other indicators - growth rate, ie, the ratio of the absolute increase to the level adopted for the comparison base. Growth rate and growth rate, calculated on the same basis, called basic, the pace of growth and change, calculated to the variable called chain-based comparison.
With increasing levels of a number of dynamics growth rates are positive values, and with decreasing - negative, depending on the absolute increase, which in the first case there is a plus sign, and the second - minus.
Calculation of chain growth and benchmarking:
Calculation of chain growth and benchmarking:
- Bazisnye.Vychislenie average growth rates and growth
Calculated chain growth and yield characteristics of the aggregate growth from one period to another. But in practice, there are situations when it is necessary for the general characteristics of the process calculate the rate of the index for the entire period, characterized by a number of speakers.
As an indication of the average growth rate is used, which is characterized by the geometric mean of all the chain rates.
- Geometric mean,
- Geometric mean with respect to growth rate, where
- Chain growth rates calculated on the basis of consecutive values.
The number of chain coefficient is always one less than the number of members of the dynamics. Because, etc., then the formula for calculating the average rates:
Interpolation and extrapolation of the series in the dynamics
In statistics, there are cases where a number of speakers lacking data for any period of time or it is necessary to determine the level of future conditions, i.e. leaving the scope of this series.
Interpolation - finding an unknown intermediate member of the series dynamics. The simplest example of interpolation calculation is the following calculation: two members of a number of speakers directly adjacent to the unknown term of the series is the mean value, which is taken as the baseline. Sometimes for greater reliability calculations take not one, but two or more intermediate levels, and find the average.
Extrapolation - finding a member of a number of speakers in the long term (for the future). Widely used in the planning of the extrapolation of production. Communication concept correlation.
Functional relationship y = 5x
Distinguish two types of bonds honey various phenomena and their signs of functional and statistical.
Functional called this relationship, when a change in the value of one of the variables of the second change in a certain way, that is, the value of one variable corresponds to one or more precisely the set values ??of another variable. The functional connection is possible only in the case where the variable y depends on x and not on any other factors are not independent, but in reality is impossible.
Statistical relationship exists when a change in the value of one variable from the second can to a certain extent take any value, but its statistical characteristics vary in defining the law.
The most important special case of the statistical relationship - correlation. When correlation to different values ??of one variable are associated with different mean values ??of another variable, ie with changes in the value of characteristic x natural way changes the average value of the sign in.
Correll communication can occur in different ways:
· Causal relationship resultant variable variation of the variation factor variable.
· Correlation may arise between two corollaries one reason (fires, number of firefighters, fire size)
· The relationship attributes each of which cause and effect at the same time (labor productivity and s / charge)
In statistics taken to distinguish between the following types of dependencies:
1. The pair correlation - the relationship between 2myapriznakami RESULT factor-m, or between two factorial.
2. The partial correlation - the relationship between productive and one factor variable with a fixed value other factor variable.
3. The multiple correlation - the dependence of the effective characteristic of two or more factor variables included in the study.
The objective of the correlation analysis is to measure the closeness of the relationship between signs. Regression examines the contact form below.
The problem of regression analysis - determining an analytical expression of communication.
Correlation and regression analysis as a general concept involves changing the closeness of the connection and the establishment of an analytical expression svyazi.§8.2. Terms used and restrictions CRA.
1. The existence of a mass of data, as correlation is a statistical
2. QUALITY homogeneity required population.
3. submission aggregate distribution in scoring and factor variables, normal distribution, which is associated with the use of the method of least kvadratov.Indeksy.
Index - a summary measure of comparison of economic phenomena, consisting of the elements are not additive. To analyze such elements need to find a common unit of measurement of these elements.
The index method is most widely used for the analysis of economic developments and for the calculation of the rate dynamics. It can also be used to compare the performance, both homogeneous and heterogeneous, or for one time period and over several periods. It provides an opportunity to identify the role of each factor in the change sredney.Obschie and individual indices
Individual indices give the characteristic changes of individual elements of a complex phenomenon.
General indices give a characterization of complex phenomena in general. Often do not calculate the overall index and sub-index, ie Not all elements of the phenomenon, but only part of it.
Of all these indexes, group indexes are of great economic importance because they reveal patterns in the development of the whole phenomenon. In statistics group indices are used in the whole industry in the national economy, as well as on the individual product groups.
Any index is obtained by comparing the two absolute levels of the phenomenon under study. But calculated the same way and dynamic indexes, when take the levels of various periods. The level, which compares called reporting or current; and the period is compared with the level - basic.
Thus each index each index characterizes the level of the phenomenon under study in the reporting period compared with baseline. And if this level in the reporting period more than in the baseline, then the index is greater than one. In the first case, the difference between the index, expressed as a percentage, shows the percentage of the base period level above or below the reporting, and in the second case - on how many percent of the level of the reporting period less bazisnogo.Agregatny index
Is the aggregate index, which is a ratio of two absolute amounts of production costs, calculated, with the same number of products of the reporting period.
- The prices of the base period,
- The price of the reporting period,
- The quantity of goods in kind of the reporting period.
For the calculation of the overall feature you need, above all, to move from a set of elements that are not directly measurable summation, to another set whose elements can be added. And this transition is performed via commensurator (weights) inserted into the index. Such commensurator index is determined based on the economic analysis of the essence of the studied phenomenon. The system of interconnected indexes.
The index method is widely used in the analysis of economic situations, especially when the process is dynamic, but always as a result not want to analyze the final data and intermediate results, which largely depend on several factors. Therefore, this phenomenon separate indexes linked index number and tseny.Izuchenie relationships between economic phenomena.
To study the force (tightness) relations factor and productive traits calculate empirical correlations. For this we need to have a clear idea of ??the factorial and productive characteristics. If every value of factor variable corresponds to only one resultant variable, such a relationship between the values ??is called functional. These ties are expressed by formulas and are widely used in mathematics, physics, and astronomy.
In economic phenomena manifested dependence of the distribution of values ??of resultant variable values ??from several factors. This kind of communication is called stochastic. In the particular case of the stochastic is a correlation. In this regard, the same factor variable value may correspond to different values ??of the most effective feature.
The shape of the connection are:
1. straight - connection when the value of resultant variable changes uniformly, in line with the change in the characteristic factor. Mathematically, this relationship is represented by a linear equation and graph - a straight line;
2. curvilinear - change under the influence of resultant variable factor variable is uneven or the direction of one sign leads to the reversal of the other.
To determine the closeness of the connection between the factorial and effectiveness of signs used index "index determination."
This indicator shows what proportion of the total variation resultant variable "y" is due to the studied factor 'x'. Then, the index of correlation:
Where x and y - signs.
- Abnormalities that characterize koleblimost znacheniyot.
When a functional link if znacheniyapolnostyu coincide with the corresponding individual values, then = 0. When correlation or no connection :.
Calculation of the total index value of the empirical correlation:
- Straight bond
- Curvilinear relationship.
If the calculations were as follows correlation values, then:
0.1-0.3 weak link Scale Chertok
0.3-0.5 moderate relationship
0.7-0.9 high bond
0,9-0,99 very high bond
Theoretical Foundations of Statistics.
The term "statistics" is used in different meanings. Under practical statistics mean the collection, storage, processing and analysis of digital data describing the population, economy, culture, education and other phenomena in society.
Statistics also referred to a special science, t. E. A discipline that studies the phenomena in society with their quantitative aspects. As an academic discipline statistics is an important unit of the curriculum of training businessmen, managers, economists, highly qualified personnel.
Between the statistical science and practice there is a close relationship and dependence. Statistical science uses these practices, summarizes them and develop methods of statistical research. In turn, in practice apply theoretical principles of statistical science to address specific management problems.
Statistics has a long history. Its emergence and development were due to the needs of society: count of the population, livestock, land records, property, etc. The earliest information about such works in China belong to the V century BC II tys.do In ancient Rome, held qualifications (counting) of free citizens and their property.
With the development of social production, the growth of domestic and foreign trade increases the need for statistical information. This expanded the scope of the statistics, has led to the improvement of its methods and techniques.
Various practices of accounting and statistical work has become, subject to theoretical generalizations. Formation of statistical science.
It is believed that the foundations of statistical science U.Petti laid by the English economist (1623-1687). In connection with the work U.Petti "political arithmetic", "Miscellaneous about money" and others. Marx called it "a kind of inventor statistics". U.Petti followers formed a research area, called "political arithmetic".
The founder of the other directions of development of statistical science recognized G.Konring German scientist (1606-1681), who developed a system for describing the state of the device. His successor, Professor of Philosophy and Law G.Ahenval (1719-1772) for the first time in the University of Marburg (1746) began to teach a new discipline, which he called statistics. The main content of this course was to describe the political situation and the attractions of the state. State management is reflected in a number of papers MV Lomonosov (1711-1765), in which the consideration of population, natural resources, finance, trade Russia illustrated by statistics. This direction is the development of statistics has been called descriptive.
Somewhat later, Professor, University of Gottingen A.Shlitser (1736-1809) refuted the notion that statistics should only describe the political structure of the state. The subject of statistics, A.Shlitseru is the whole of society.
Further development of statistics carried out by many scholars and practitioners. Among them we mention the Belgian statistics A.Ketle (1796-1874), who made a significant contribution to the theory of stability of statistical indicators.
Mathematic statistics developed in the works F.Galtona (1822-1911), K.Pirsona (1857-1936), V.Gosseta (1876-1936), R. Fisher (1890-1962), M.Mitchela (1874-1948 ), and others. So, K.Pirson made a significant contribution to the theory quantify the relationship between phenomena. V.Gosset, who wrote under the pseudonym Student, developed the theory of a small sample. R. Fisher developed the methods of quantitative 'analysis. M.Mitchelu's idea of ??"economic barometer."
Representatives of the mathematical sciences in the statistics say the basis of statistics probability theory, constitutes one of the branches of applied mathematics.
In the development of statistics prominence belongs to the representatives of national science and practice. In the era of Peter I in the works of IK Kirilov (1689-1737) and VN Tatishcheva (1686-1750) Statistics treated primarily as a descriptive science. But in the second half of the XIX century. the fore cognitive significance statistics. Thus, B.C. Poroshin (1809-1868) in the "critical study of the basics of statistics" stressed that science can not limit ourselves to just one description. In the book of II Sreznevsky (1812-1880) "The experience of the subject matter and elements of statistics and political economy," noted that the statistics in the abyss of chance finds "normality".
Prominent statistician DP Zhuravskiy (1810-1856) in his work "On the sources and use of statistical data" considered the science of statistics "categorical calculus." In the works of St. Petersburg Polytechnic Institute Professor AA Chuprova (1874-1926) Statistics acts as a method of studying mass phenomena of nature and society.
St. Petersburg University professor YE Janson (1835--1893) in the "Theory of Statistics" Statistics called social sciences. This look at the statistics and held prominent economist AI Chuprov (1842-1908), who in his work "The course statistics" noted the need for mass statistical studies using the method of quantitative observations of a large number of factors in order to describe social phenomena, sweeping laws and determine their causes.
In the works of the famous scientist AA Kaufman (1874-1919) presents a look at the statistics as "the art of measuring political and social phenomena."
Development of statistics in Russia is closely linked to 'set up after the abolition of serfdom, the County statistics, which enjoyed a well-deserved reputation for objectivity and professionalism.
Experience in the development of statistics in Soviet times was generalized in the works of VI Khotimsk, B.C. Nemchinova, VN Starovsky, BS -Yastremskogo And other scientists.
Thus, the history of the development of statistics shows that the statistical science developed as a result of theoretical generalization vakopleig-south humanity excellence accounting and statistical work, primarily due to management needs of society.
In the preparation of the management and staff of higher savings eskgos kvalyfikagrli for business' their statistical education consists of a series of training disgschgtgt. First of all - this is a general theory of statistics is a basic course of study as obscheprofessgyunalnoy dgyugschglgty sotsislno-ekonomgteskoy statistics and prof-iliruyugtsgss disciplines: business statistics, statistical evaluation methods and prognozguovaniya market for goods and services, and others depending on spetsiapizatsii.
In order to study their subject statistics develops and applies a variety of methods, which together form the statistical methodology. Application of statistical methods for the study of specific predetermined objectives posed in this case depends on the nature and source of information.
Common basis for the development and application of statistical methodology are the principles of the dialectical approach to the study of the phenomena of social life. This is primarily a requirement of the facts characterizing the phenomena, in their entirety, in the relationship and interdependence, which is very important in the statistical study of causal relationships.
Important provisions of the dialectical method of cognition is to examine the phenomenon under study in the development, moving from the beginning to the disappearance. In accordance with this general epistemological requirement is that statistics studies the dynamics of socio-economic phenomena in their historical implications.
In the statistical study of the socio-economic phenomena are guided by the position of materialist dialectics of transition from quantitative to qualitative changes. This is important in the study of quantitative changes in the mass social and economic phenomena for understanding the deep qualitative changes.
Statistics based on dialectical categories of chance and necessity, and the unit of mass, individual and general.
All variety of statistical methods for the study of commercial activity in the course "General Theory of Statistics" are classified according to their intended use in sequentially executed while the three main stages of economic and statistical studies:
1) collection of primary statistical information;
2) statistical summary and processing of primary information;
3) analysis of statistical information.
In the first stage of statistical research solved the problem of obtaining relevant to the task of values ??studied traits of individual units statistical population. To carry out this initial stage of statistical research methods are used mass surveillance. The requirement for mass units of observation due to the fact that the studied statistical regularities seen in quite a large array of data on the basis of the law of large numbers.
The main content of the law of large numbers is that the summary statistical characteristics of the elements of chance are mutually compensating actions, although they may appear in the evidence of individual units of a statistical population. For example, under conditions of developed market relations each store buyer chooses the product he requires at the moment. But in general, the store probably relatively accurately predict both the total volume and structure of demand during the year, some seasons and even days of the week. To identify specific patterns of consumer demand is necessary statistical information showing the specificity of demand by day of week, time of year and for the whole year.
In the second stage of statistical research gathered during mass surveillance information is subject to statistical analysis, including receipt totals for the target population as a whole and its individual parts, ordering units in the population on the basis of similarity, etc.
The most important method of the second stage of statistical research is the method of statistical groupings, allows you to select the target population in the socio-economic classes. The main content of the second stage of statistical research is to switch on the characteristics of the unit to the summary (summarizing) indicators set as a whole or its parts (groups). Delimitation qualitatively similar materially groups of socio-economic phenomena - a prerequisite scientific application in the statistical study of the method of generalizing statistics. Violation of the principles of good homogeneity of the studied population results in atypical characteristics affect results significantly.
On the third and final stage of statistical research analyzes the statistical information based on the application of generalizing statistical indicators: absolute, relative and average values, statistical and other factors.
Analysis of statistical information allows to reveal causal relationships of the phenomenon, and to determine the effect of the interaction of various factors, to evaluate the effectiveness of management decisions, the possible economic and social consequences of the evolving situation. Compared generalizing statistical indicators of the phenomena studied are defined quantitative estimates of their prevalence in space and development time, set the characteristics of relationships and dependencies. By comparing the unit with a common measure of an individual are determined, it differs from other units of the target population.
In the analysis of statistical data are widely used tabular and graphical methods.
In the "General Theory of Statistics" are considered the main categories and methods of statistical science, the nature of statistical aggregates, cognitive properties of modern computing.
Presenting the basic course of statistical science, "General Theory of Statistics" fundamental academic discipline, the study of which begin to form the required professional economists highest quality merchants and managers. Provide the foundation for learning and statistical methodology knowledge of the laws of socio-economic conditions in the market economy.
Statistics in its essence is designed to determine the nature and form of this phenomenon in relation to the set according to a fixed number of elements included in the study, which have an impact on the phenomenon under investigation.
Statistical problems in a market economy.
Fundamental questions of implementation of radical economic reform in Russia from the command-administrative forms of governance to economic. This presents statistics as an integral part of management of the national economy new challenges tasks.
Based on the change management role and place of firms, inter-regional relations and relations outside world, the basic statistics on its modern stage are:
1) a comprehensive study taking place in society profound transformation of economic and social processes on the basis of evidence-based system of indicators;
2) synthesis and forecasting trends in the development of the national economy;
3) vmvlenie available reserves efficiency of social production;
4) timely provision of reliable information legislature, administrative, executive and administrative bodies, as well as the general public.
With changes in the socio-political role of statistics as a factor in the formation of social consciousness is of particular importance substantial expansion of transparency and accessibility of summary statistical information, while maintaining the principle of confidentiality of individual data. This is one of the very neobhodimk towards democratization of society. Extension publications statistical information to better see the situation on the ground, in some regions, focus on the shortcomings and deficiencies to correct them.
Return statistics broad public purpose defines the main directions of its development: the improvement of statistical information analysis, streamlining reporting to ensure its accuracy.
The main means of improving the reliability of statistical information is to further improve the methodology of its formation. Will review the existing techniques that are not free from the desire for embellishment of the fruits of economic and social development. Thus, in the years 1985-1987 for details. national income, real incomes corrections were made to eliminate the effect of reducing the production and sale of alcoholic beverages. As a result of overstatement growth rate of national income. Official publications of those years were reported exceeded state revenues over expenditures. But all incomes declined, increased costs due to future earnings. Untrue statement of the constancy of prices for consumer goods. Previously published indices list prices are only displayed price changes carried out in the law. But they do not appear raise prices of new products, the impact of pent-up demand, other forms of hidden price rises and so on
Clearly, the statistics need to get rid of all segregating administrative-command system, to overcome the current practice of obtaining statistical indicators such as direct closed method of their calculation. This creates fragmentation statistics, the discrepancy calculation parameters conjugate international standards.
Very important is a critical review of the current during the prevalence of costly methods of management practices forming the statistical reporting, which is mainly built on a solid, very abundant and costly information. This negates the use of statistical methods for studying mass sovdyulno-economic phenomena. Necessary to find ways to a significant reduction in reporting, especially urgent reporting overloaded operational technical parameters required osvobozhdekie enterprises from micromanaging their pro-vodsttzennoy and commercial activities.
Before statistical science raises important problems of theoretical justification volume and structure statnsteleskoy information meeting modern and persibktkznsh conditions for economic development, the transition to functional management principles.
It is very important to solve the problem of the transition from a solid to a discontinuous reporting types of statistical observation: one-time recording, sampling and monographic surveys. This follows directly from changes in the situation of the company uslovkyah market economy, from a variety of forms of cooperation, dynamism of their organizational processes.
Application of statistical methods of non-continuous observation increases responsiveness occurring ko?yunkturnye changes, provides management information to allow timely decisions. Periodic sample surveys have become a major tool for statistical observation of changes in mass social and economic phenomena, with the situation in the region.
Increasingly necessary and important to collect statistical information are one-time accounting methods. On their basis are solved questions of analysis of accumulated economic potential, the study of living standards, security of supplies. Statistical information should characterize the formation of a mixed economy, the development of various forms of ownership and entrepreneurship, the social structure of the national economy.
Need to re-evaluate the results of statistical development, which consist not only in accounting and reports, but also contain analytical conclusions. Of particular importance is the increased focus prognostic analysis. It must contain elements of foresight, identify critical points of growth, indicate the possible consequences of the evolving situation.
The transition to a market economy necessitates the introduction of a statistical and accounting system of national accounts (SNA). Widely used in the world SNA best meets the characteristics and requirements of the market.
Statistics fixed and current assets.
7.1. Classification of fixed assets by natural-material characteristics.
Under the asset in statistics to understand the totality of production material and real values ??are repeatedly involved in the production of goods and services, it does not change their natural form, are not included in the result of real work and transfer their value to the manufactured product (service) immediately, and in part by the extent of wear.
Revolving funds, in contrast to the main, take part in one production cycle, immediately transferring their value to the product manufactured and mutating in the labor process.
With the transition to international statistical methodology all fixed assets are considered to be manufacturing.
7.2. Methods of assessment of fixed assets revaluation.
The following types of valuation of fixed assets, depending on the age and the state of: full replacement cost, ie, value of a new production facility in terms of the time when it was made, in operation; full replacement cost, ie, cost of reproduction of each of a fixed asset in the present conditions of its production; the original cost less depreciation (residual); replacement cost less depreciation.
7.3. Indicators of movement and use of fixed assets.
Fixed assets can be determined on the date and for the period. In the first case it will be the torque figures in the second - the average for the period (interval). The cost of fixed assets at the end of the period is determined by the balance scheme:
FK.P. = FN.P. + FPOST. - FVYB.
where FK.P.- value of fixed assets at the end of the period;
FN.P.- value of fixed assets at the beginning of the period;
FPOST.- value received fixed assets;
FVYB. -The cost of fixed assets disposed of during the period.
Period average value of fixed assets may be defined by the formula of average chronological or simplified way as half the sum of residues of fixed assets at the beginning and end of the period.
where F1 ... .Fn- value of fixed assets in the i- th time;
n - number of points; - period average value of fixed assets.
The current status of fixed assets is assessed using indicators of wear and life.
where A is the amount of annual depreciation charges on time;
PF - the original value of fixed assets at the time.
Complete understanding of the process of reproduction of fixed assets can be obtained on the basis of the balance sheet method. Balance Allows you to give a detailed description of not only the existence of fixed assets, but also to track their movement, calculate the coefficients of the renovation and replacement. Depending on the purpose of the study in the practice of statistics are made up of fixed assets balances of two types: the full original (book) or full replacement value and cost adjusted for depreciation (initial or replacement).
The balance of the full original cost characterizes the process of reproduction from a position of changing the amount (volume) of fixed assets, and the balance sheet at cost adjusted for depreciation - to change their value, taking into account the physical condition.
Indicators of movement of funds are public and private factors inflow and outflow of capital assets.
The total retirement rate (kS) is calculated by dividing the total value of all retired for the year of fixed assets for the full value of fixed assets at the beginning of the year.
Specific indicators are the retirement rate due to dilapidation and deterioration, transfer to other companies, losses from natural disasters, etc.
The total revenue ratio (Kpost) is calculated by dividing the total value of all received during the year of fixed assets for the full value of fixed assets at the end of the year.
It can also be decomposed into a number of partial factors characterizing the state received fixed assets - new input factor and input factor other funds.
To characterize the use of fixed assets used scorecard that includes generalizing and private technical and economic indicators. Generalising indicators reflect the use of fixed assets, and private - use of individual species.
The most common indicator of fixed assets is capital productivity, which is calculated by the formula:
where FOTD- level of return on assets;
- The level of return on assets of the fixed assets;
Q - the result of production (amount of work performed and services rendered or output, services) in monetary terms;
- Period average value of fixed assets;
- Period average value of the active part of the funds.
Effect of changes in factors on the increase (decrease) in the amount of work performed and services rendered is determined as follows:
a) increase (decrease) the volume of work performed or services rendered under the influence of changes in the value of fixed assets:
somewhere period average value of fixed assets during the reporting period and the base;
dAKT.- share of the fixed assets in their total cost;
* - return on assets of the fixed assets of the base period.
b) increase (decrease) the volume of work performed or services rendered under the influence of changes in the share of the fixed assets:
7.4. Indicators of material consumption and production efficiency is-use of working capital.
In statistics, revolving funds are used indicators: the presence and composition of the working capital, replenishment and disposal of revolving funds, the turnover of prisoners in their working capital sufficiency of the production process, and others.
Efficiency of working capital is characterized by the speed of circulation, turnover, namely the number of revolutions of funds for the period (turnover ratio - Kobori); Average duration of one turnover in days - transoms.
Turnover ratio (Kobori) indicates how much produced (Q) or sold (R) products and accounts for 1 ruble revolving funds, how many times during the period turned in the production of the average balance of current assets ():
Kobori = or = Kobori.
Average prodolzhitelnostodnogo turnover in days (transoms) is calculated by dividing the number of calendar days in the period (D) on the speed of revolving funds for this period (Kobori).
7.5. Composition, availability and use of park equipment.
Types of valuation of fixed assets.
One of the major tasks of statistics is to determine the volume of fixed assets and their depreciation in value. Valuation of fixed assets has several features. Since fixed assets are functioning for a long time, they objectively inherent in some estimates.
The most important and most useful in the practice of social and economic statistics are the following types of:
The full original value of fixed assets - the actual cost of putting them into action. It reflects the total amount of actual expenses incurred during the creation or at the time of acquisition of fixed assets. This estimate remains unchanged in accounting for the duration of the operation of fixed assets. The full original cost of fixed assets on the basis of relevant documents (acts of commission and others.) Are credited to the balance of the organization in the future are shown in their reporting.
The full original value of fixed assets, net of depreciation - is that part of their costs, which they retained after a certain period of their operation. Sometimes this type of evaluation is called the residual value of fixed assets. It is equal to the full amount of the original cost less depreciation. If disposed of dilapidation and depreciation of fixed assets used as scrap, the cost estimated sales of scrap will be a liquidation value of fixed assets.
Full replacement cost of fixed assets is the cost of reproduction in the present conditions, ie, at the time when it is determined. Due to scientific and technical progress, and many other factors full replacement cost of fixed assets varies over time and practically can only be determined during the general revaluation of inventories and fixed assets.
Replacement cost of fixed assets, net of depreciation can be determined according to the revaluation of inventories and fixed assets, during which, by the inspection of objects in nature and with the help of various documents define the actual wear objects. It is equal to the full replacement cost of fixed assets, net of cash express their wear.
Statistical study of the formation and use of sinking funds.
The nature of the circuit value of fixed assets determines the existence of a special economic category - depreciation. In practice, takes the form of amortization of depreciation included in the cost of production and designed for simple reproduction of fixed assets and maintain them in working order. Produced during the lifetime of objects depreciation accumulated in the sinking fund, and the size of contributions to these funds are determined by the depreciation rates.
When calculating the depreciation rates take into account the initial cost of fixed assets, standard terms of their service (amortization period) required for the period costs of major repairs and upgrades, and resale value of fixed assets, defined as the ability of the object proceeds in liquidation less the costs of its liquidation ( the cost of scrap metal obtained by dismantling the machine is completely worn out, building materials obtained by dismantling the building to be demolished, and others.
Indicators of availability, traffic, condition and use of fixed assets.
The wide availability of fixed assets with the distribution of its intended use, and the types of industry the production sector is characterized by the statistics most often as of a certain date (for example, at the beginning and end of the year). Such data can be obtained directly from the balance sheet assets. However, in some cases, requires the presence of the characteristic of fixed assets on average over a given period, as in this period is their inflow and outflow. To calculate the average for the period of availability of fixed assets Statistics uses the arithmetic and chronological. Thus, the average value of fixed assets in the past month is determined by the arithmetic mean as half the sum of the data on the availability of fixed assets at the beginning and end of the month, the average annual availability (average annual volume of fixed assets) according to the volume of fixed assets at the beginning and end of each month of the year calculated as average chronological.
According to the balance of fixed assets in full and the residual value determined by the generalized characteristics of their condition - coefficients life and depreciation of fixed assets.
Coefficient of life of fixed assets characterizes the magnitude of their value has not yet been transferred to the product, and is defined as the ratio of the cost of fixed assets subject to wear their full value. It can be calculated at the beginning and end of the reporting period.
Direct characterization of the degree of depreciation of fixed assets is given by the coefficient of wear, which is defined as the ratio of depreciation of fixed assets to their full value, or as an addition to one (100%) of the coefficient life of fixed assets.
According to the data available in the balance of fixed assets are determined and generalized characteristics of the intensity of their movement - the coefficients of income, renovation and replacement (including retirement due to dilapidation and deterioration) of fixed assets. These coefficients are calculated from data on the total value of fixed assets. Input factor of fixed assets [R) - the ratio of the value received in the reporting period to the value of fixed assets at the end of this period. In determining the rate of renewal of fixed assets (Cob) prinimayutne into account the entire value of fixed assets received, but only received cost of new fixed assets. The economic content of these factors is that they represent the percentage of all new or just arrived in the reporting period, the fixed assets in their total volume at the end of this period. Since fixed assets are not less than one year retirement rate Kg defined as the ratio of retired full cost during the period of fixed assets to their full value at the beginning of the reporting period. Retirement rate of fixed assets due to dilapidation and deterioration Kvvychislyayut without gratuitous transfer of fixed assets to other organizations.
When calculating the coefficients of the inflow and outflow of capital assets for long periods of time, be aware that different types of fixed assets are substantially different terms of service. Therefore, for the common values ??of the coefficients of receipt and disposal of fixed assets may be hidden very significant differences in the intensity update their individual species.
Mechanization and automation of production processes, improvement of working conditions are quantitative generalization expressed in terms of capital-. Theoretically correct to define capital-workers
According to the replacement cost of fixed assets adjusted for depreciation and the number of workers employed in the most completed change (as when working more than one shift the same objects of fixed assets used by several workers in different shifts). However, in practice, enjoy full cost or the carrying value of fixed production assets on a certain date or the average for the period and subject to the availability of necessary information is determined by dividing the capital-value of fixed assets or on the number of workers employed in the most filled with change, or the average payroll number workers or all rabotayuschih.Sistema National Accounts
System of National Accounts is a balance of interrelated indicators that characterize the production, distribution, redistribution, and end use of the final product and national income. At the heart of the construction of the SNA is the concept of "economic circuit", the core of which is the economic cycle.
The system of national accounting determine the quantitative value the most important macroeconomic indicators. To this end, for each of the economic actors and the national economy as a whole system is composed of functional accounts reflecting part of the subject in the following business processes:
- The production of goods and services;
- Generation of income;
- The distribution of income;
- Redistribution of income;
- The use of income;
- Change of property;
- Lending and finansirovanie.Pokazateli SNA.
Although most often as an indicator of total income is used GNP, SNA and other applicable measures of income that differ from the GNP for some components.
Net national product can be obtained from the GNP, subtracting the depreciation (cost of depreciation of fixed capital):
NNP = GNP - a / a, where a / s - depreciation
NNP = C + NI + G + NE, where NI - net investments = I - A / O.
Indirect taxes on business - is the difference between the prices. Which consumers buy goods and sales prices of firms. This VAT, excise taxes, import duties, taxes on monopoly activities, etc. If NNP subtract from net indirect taxes on business, ie, indirect taxes net of subsidies to business, get the national income-figure representing the total income of all residents.
ND = NNP - k / n, where k / n -kosvennye taxes.
Rate of personal income is obtained by subtracting from the national income in social security contributions, undistributed corporate profits, corporate income taxes, and adding the amount of transfer payments. It is also necessary to deduct net interest and add personal income earned in the form of interest, including interest on the public debt. Personal income PI.
Disposable personal income is calculated decrease in personal income in the amount of personal income tax and certain non-tax payments to the state.
DI = PI - T, where T - taxes.
Disposable personal income is used for household consumption and saving.
Consumption (C) - the most important and the largest component of the GNP.
Savings (S) is defined as income minus consumption.
Gross national disposable income is obtained by summing the GNP and net transfers from abroad (donation, donations, humanitarian aid and so on.) Less similar transfers sent abroad. Gross national disposable income is used for final consumption and national saving.
Indices of Balaclava., Paasche, Fisher.
Inflation and its impact on the deviation of nominal GDP is expressed in terms of the real price index.
Price index - commensurator relationship between the total price of a particular set of goods and services, so-called "market basket", for a given period and the total cost of a market basket "in the base period. The base period is changed in 10-15 years.
Consumer price index CPI - consumer price index.
1. Index Layspersa:
2. Paasche index:
3. Fisher index:
Where Pt - price in the current period
Qt - the contents of the "market basket" in the current period
Po - price in the base period
Qo - the contents of the "market basket" in the base period
2. Growth rates of growth, and their computation.
Communication concept correlation.
General and individual indices
Study of tightness.
Theoretical Foundations of Statistics. Statistical methods.
Statistical problems in a market economy
Statistics fixed and current assets.
Types of valuation of fixed assets.
Statistical study of the formation and use of sinking funds.
Indicators of availability, traffic, condition and use of fixed assets.
SNA. Indices of Balaclava., Paasche, Fisher.