Absolute values- these are the results of statistical observations. In statistics, unlike mathematics, all absolute quantities have a dimension (unit of measurement), and can also be positive and negative.
Units absolute values reflect the properties of units of the statistical population and can be simple, reflecting 1 property (for example, the mass of the cargo is measured in tons) or complex, reflecting several interrelated properties (for example, tonne-kilometer or kilowatt-hour).
Units absolute values can be 3 types:
- Natural- used to calculate quantities with homogeneous properties (for example, pieces, tons, meters, etc.). Their disadvantage is that they do not allow the summation of heterogeneous quantities.
- Conditionally natural- are applied to absolute quantities with homogeneous properties, but manifesting them differently. For example, the total mass of energy resources (firewood, peat, coal, petroleum products, natural gas) is measured in t.e.f. - tons of standard fuel, since each type has a different calorific value, and 29.3 mJ/kg is taken as the standard. Similarly, the total number of school notebooks is measured in standard units. - conventional school notebooks size 12 sheets. Similarly, canning production products are measured in u.c.b. - conventional cans with a capacity of 1/3 liter. Similar products detergents is reduced to a conditional fat content of 40%.
- Cost units of measurement are expressed in rubles or other currencies, representing a measure of the value of an absolute value. They make it possible to summarize even heterogeneous values, but their disadvantage is that it is necessary to take into account the inflation factor, therefore statistics always recalculate cost values in comparable prices.
Absolute values can be momentary or interval. Momentary absolute values show the level of the phenomenon or process being studied at a certain point in time or date (for example, the amount of money in your pocket or the value of fixed assets on the first day of the month). Interval absolute values are the final accumulated result for a certain period (interval) of time (for example, salary for a month, quarter or year). Interval absolute values, unlike moment ones, allow subsequent summation.
The absolute statistical value is denoted X, and their total number in the statistical aggregate is N.
The number of quantities with the same attribute value is indicated f and is called frequency(repetition, occurrence).
By themselves, absolute statistical values do not provide a complete picture of the phenomenon being studied, since they do not show its dynamics, structure, and relationships between parts. Relative statistical values are used for these purposes.
Concept and types of relative quantities
Relative statistic is the result of the relationship between two absolute statistical quantities.
If absolute quantities are correlated with the same dimension, then the resulting relative quantity will be dimensionless (the dimension will be reduced) and is called coefficient.
Often used artificial dimension of coefficients. It is obtained by multiplying them:
- for 100 - get interest (%);
- for 1000 - get ppm (‰);
- for 10,000 - get prodecimal(‰O).
The artificial dimension of coefficients is used, as a rule, in colloquial speech and when formulating results, but it is not used in the calculations themselves. Most often, percentages are used, in which it is customary to express the obtained values of relative values.
More often instead of a name relative statistic a shorter synonymous term is used - index(from lat. index- indicator, coefficient).
Depending on the types of correlated absolute values when calculating relative values, different results are obtained. types of indexes: dynamics, plan task, plan implementation, structure, coordination, comparison, intensity.
Dynamics index
Dynamics index(growth coefficient, growth rate) shows how many times the phenomenon or process being studied has changed over time. It is calculated as the ratio of the absolute value in the reporting (analyzed) period or point in time to the base (previous):
The criterion value of the dynamics index is “1”, that is: if iD >1 - there is an increase in the phenomenon over time; if iD =1 - stability; if iD
If you subtract its criterion value “1” from the dynamics index and express the resulting value as a percentage, you will get the following criterion value “1”:
If T>0, then the phenomenon grows; Т=0 – stability, Т In some textbooks the dynamics index is called growth rate or growth rategrowth rate, regardless of the result obtained, which can show not only growth, but also stability or decline. Therefore, the more logical and more often used names are precisely And .
For example, a car dealership sold 100 cars in January, and 110 cars in February. Then the dynamics index will be iD = 110/100 = 1.1, which means an increase in car sales by a car dealership by 1.1 times or 10%
Schedule task index
Schedule task index is the ratio of the planned absolute value to the basic value:
For example, a car dealership sold 100 cars in January, and planned to sell 120 cars in February. Then the plan target index will be iпз = 120/100 = 1.2, which means planning sales growth by 1.2 times or 20%
Plan execution index
Plan execution index is the ratio of the actual absolute value obtained in the reporting period to the planned one:
For example, a car dealership sold 110 cars in February, although it was planned to sell 120 cars in February. Then the plan fulfillment index will be iвп = 110/120 = 0.917, which means the plan is 91.7% fulfilled, that is, the plan is underfulfilled by (100%-91.7%) = 8.3%.
Multiplying the indices of the planned task and plan execution, we obtain the dynamics index:
In the previously discussed example about a car dealership, if we multiply the obtained values of the indices of the planned task and the implementation of the plan, we obtain the value of the dynamics index: 1.2 * 0.917 = 1.1.
Structure index
Structure index(share, specific gravity) is the ratio of any part of a statistical aggregate to the sum of all its parts:
The structure index shows what proportion a particular part of the population makes up of the entire population.
For example, if in the group of students under consideration there are 20 girls and 10 young men, then the structure index (proportion) of girls will be equal to 20/(20+10) = 0.667, that is, the proportion of girls in the group is 66.7%.
Coordination Index
Coordination Index- this is the ratio of one part of the statistical population to another part of it, taken as the basis of comparison:
The coordination index shows how many times more or what percentage one part of the statistical population is compared to another part taken as the basis of comparison.
For example, if in a group of students of 20 girls and 10 young men, we take the number of girls as a basis for comparison, then the coordination index of the number of young people will be 10/20 = 0.5, that is, the number of young people is 50% of the number of girls in the group.
Comparison index
Comparison index- this is the ratio of values of the same absolute value in the same period or point in time, but for different objects or territories:
Where A, B are characteristics of the objects or territories being compared.
For example, in January 2009, the number of residents in Nizhny Novgorod was approximately 1280 thousand people, and in Moscow - 10527 thousand people. Let's take Moscow as object A (since it is customary to put a larger number in the numerator when calculating the comparison index), and Nizhny Novgorod as object B, then the comparison index for the number of residents of these cities will be 10527/1280 = 8.22 times, that is, in Moscow the number there are 8.22 times more residents than in Nizhny Novgorod.
Intensity index
Intensity index- this is the ratio of the values of two interrelated absolute quantities with different dimensions related to the same object or phenomenon.
For example, a bread store sold 500 loaves of bread and earned 10,000 rubles, then the intensity index will be 10,000/500 = 20 [rubles/loaf of bread], that is, the selling price of bread was 20 rubles. for a loaf.
Most fractional quantities are intensity indices.
4.1. The concept of absolute and relative magnitude in statistics
When studying mass social phenomena, statistics in their conclusions rely on numerical data obtained in specific conditions of place and time. results statistical observation are registered primarily in the form of primary absolute values. Thus, the bulk of national economic absolute indicators are recorded in primary accounting documents. The absolute value reflects the level of development of the phenomenon.
In statistics, all absolute values are named, measured in specific units and, unlike the mathematical concept of absolute value, can be both positive and negative (losses, decline, losses, etc.).
Natural units of measurement can be simple (tons, pieces, meters, liters) and complex, which are a combination of several different quantities (freight turnover railway transport expressed in tonne-kilometres, electricity production - in kilowatt-hours). Statistics also use absolute indicators expressed in conventional natural units of measurement (for example, various types of fuel are converted into conventional fuel).
Cost units of measurement are used, for example, to express the volume of heterogeneous products in cost (monetary) form - rubles. When using cost measures, price changes over time are taken into account. This disadvantage of cost measures is overcome by the use of “constant” or “comparable” prices of the same period.
Labor units of measurement (man-days, man-hours) take into account the total labor costs of the enterprise and the labor intensity of individual operations.
From the point of view of a specific study, a set of absolute values can be considered as consisting of indicators individual, characterizing the size of a characteristic in individual units of the population, and total, characterizing the final value of a characteristic for a certain part of the population.
Since absolute indicators are the basis of all forms of accounting and methods of quantitative analysis, it is necessary to distinguish momentary And interval absolute values. The first ones show the actual presence or level of a phenomenon at a certain moment, date (for example, the presence of stocks of materials or working capital, the amount of work in progress, the number of residents, etc.). The second is the final accumulated result for the period as a whole (the volume of production per month or year, population growth for a certain period, the amount of gross grain harvest for the year and for the five-year period, etc.).
The absolute value itself does not give a complete picture of the phenomenon being studied, does not show its structure, the relationship between individual parts, or development over time. It does not reveal relationships with other absolute indicators. These functions are performed by relative indicators determined on the basis of absolute values.
Relative value in statistics, it is a general indicator that gives a numerical measure of the relationship between two compared absolute values. Since many absolute values are interrelated, relative values of one type in some cases can be determined through relative values of another type.
The main condition for the correct calculation of relative values is the comparability of the compared indicators and the presence of real connections between the phenomena being studied. Thus, according to the method of obtaining, relative indicators are always derivative values, defined in the form of coefficients, percentages, ppm, prodecimille, etc. However, it must be remembered that these indicators, dimensionless in form, can, in essence, be assigned a specific, and sometimes quite complex, unit of measurement. For example, relative indicators of vital statistics, such as birth or death rates, calculated in ppm (), show the number of births or deaths per year per 1,000 average annual population; the relative value of the efficiency of using working time is the amount of production per one man-hour worked, etc.
4.2. Types and relationships of relative quantities
Relative values form a system of interrelated statistical indicators. Based on the content of the expressed quantitative relationships, the following types of relative quantities are distinguished.
1. Relative magnitude of task completion. It is calculated as the ratio of the level actually achieved in a given period to the planned level. Thus, in 1988, 6,103 thousand washing machines were produced. under the plan (government order) 6481 thousand pieces. The relative level of plan implementation was
Consequently, the planned target was underfulfilled by 5.8%.
In practice, there are two types of relative indicators of plan implementation. In the first case, actual and planned levels are compared (this is the example discussed above). In the second case, the absolute value of the increase or decrease in the indicator is established in the plan target and the degree of implementation of the plan according to this value is checked accordingly. So, if it was planned to reduce the cost per unit of production by 24.2 rubles, and the actual reduction was 27.5 rubles, then the planned target for reducing the cost was completed with an increase of 27.5: 24.2 = 1.136 times, i.e. the plan was exceeded by 13.6%. The indicator of plan fulfillment in terms of cost level in this case will be less than one. If the actual cost of the product was 805.8 rubles. with the planned 809.1 rubles, then the value of the plan was 805.8: 809.1 = 0.996, or 99.6%. The actual level of expenditure per product turned out to be 0.4% lower than planned.
In analytical calculations when studying relationships, an assessment of plan implementation by indicator level is more often used. An assessment of the implementation of the plan for changing the level is usually given for illustration purposes, especially if it is planned to reduce the absolute value of costs, costs by type, etc.
The relative values of the dynamics, the planned task and the implementation of the plan are related by the relation i=i pl.z. × i issue pl.
2. Relative magnitude of dynamics. Characterizes changes in the level of development of a phenomenon over time. It is obtained by dividing the level of a characteristic in a certain period or point in time by the level of the same indicator in the previous period or point.
Thus, according to the fuel and energy balance of the USSR, resources in 1980 were estimated at 2171.1 million tons of equivalent fuel (standard fuel), and in 1987 - at 2629.1 million tons of equivalent fuel. The relative magnitude of the dynamics was .
Thus, the volume of fuel and energy resources has increased over 7 years by 1.211 times (growth coefficient, growth index, index). In percentage terms this is 121.1% (rate growth).
In other words, over 7 years the volume of resources increased by 21.1% (rate growth). On average, each year the volume of resources increased compared to the previous year by , or by 2.77% (average annual growth rate or index and average annual growth rate).
3. Relative values of structure. They characterize the shares and specific gravity of the constituent elements in the overall total. As a rule, they are obtained in the form of percentages:
For analytical calculations, it is preferable to use the coefficient representation, without multiplying by 100.
The set of relative values of the structure shows the structure of the phenomenon being studied.
Let us consider, for example, the structure of the formation and distribution of fuel and energy resources (FER) in Russia in the form of a fuel and energy balance (FEB) (Table 4.1.).
Table 4.1
Sources of formation of fuel and energy resources in Russia
From the table 4.1. It can be seen that the main part of the resources is formed through the extraction of fuel. Approximately 8–9% of annual resources were available at the beginning of the year in the form of reserves.
5. Relative coordination values (RCVs). They characterize the relationship of parts of a given population to one of them, taken as a basis for comparison. OVC show how many times one part of a population is larger than another or how many units of one part are per 1, 10, 100, 1000, ... units of another part. Relative values of coordination can be calculated both by absolute indicators and by structural indicators.
Thus, taking as a basis for comparison the supply of fuel resources for export in 1987, we see that for each conventional ton of export supplies there are 2.342 times more resources consumed within the country for energy production, and 2.363 times more resources intended for production. technological purposes. The level of balances at the end of the year is 57.8% compared to annual export supplies
(9,20: 15,91 = 242: 418,3 = 0,578).
Based on the relative values of coordination, it is possible to restore the original relative indicators of the structure if we calculate the ratio of the relative value of coordination of a given part (RVC) to the sum of all RVCs (including the one taken as the basis of comparison):
For example, the share of export supplies is
1: (2.342 + 2.364 + 1 + 0.578) = 0.1591, or 15.9%.
6. Relative comparison values (RCVs). Characterize the comparative sizes of the same absolute values, relating to the same period or point in time, but to different objects or territories. Using these indicators, capacities are compared various types equipment, labor productivity of individual workers, production of products of this type by different enterprises, regions, countries. For example, in oil and gas production in 1985, the USSR exceeded the United States: in oil - 1.36 times, in gas - 1.24 times. The level of electricity production (billion kWh) in the USSR was 1544:2650 = 0.583, or 58.3%, compared to the US level.
With known growth coefficients (dynamic indices) and the initial ratio of levels, one can find the condition for equality of levels in the upcoming period t:
.
Hence OBC a / b =Y a / Y b =(i a / i b) t,
those. 
.
The found t value shows after what period of time the level of the phenomenon being studied at object A will become equal to the level of the same phenomenon at object B.
In particular, with the average annual growth rate of electricity production in the USA being 4.5% and in the USSR 6.9% (according to data for 1961–1985)
.
By comparing indicators of the dynamics of different phenomena, we obtain another type of relative comparison values - lead (lag) coefficients according to the rate of growth or gain. So, if labor productivity at an enterprise increased by 12%, and the wage fund increased by 7.5%, then the coefficient of labor productivity advance in terms of growth rates will be 112: 107.5 = 1.042; the advance coefficient in terms of growth rate is 12: 7.5 = 1.60.
7. Relative intensity values. Characterize the degree of distribution or development of a given phenomenon in a particular environment. They represent the ratio of the absolute level of one indicator, characteristic of the environment being studied, to another absolute indicator, also inherent in this environment and, as a rule, being a factor sign for the first indicator. Thus, when studying demographic processes, indicators of fertility, mortality, natural increase, etc. are calculated. as the ratio of the number of births (deaths) or the amount of population growth per year to the average annual population of a given territory per 1000 people. If the obtained values are very small, then the calculation is made for 10,000 people. Thus, as of 1987, we have a total of K births for the country as a whole. = 19.8 , K natural increase = 9.9 . Including in the city of Novosibirsk. = 15.2 , K see = 9.1 , K marriage rate = 10.9 , K development. = 5.2 etc.
Relative values of intensity are, for example, indicators of product output per unit of working time, costs per unit of production, labor intensity, efficiency of use production assets etc., since they are obtained by comparing different quantities that relate to the same phenomenon and the same period or moment in time. The method of calculating relative intensity values is used to determine average levels (average output level, average labor costs, average cost of products, average price, etc.). Therefore, it is widely believed that relative intensity values are one way of expressing average values.
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Types of absolute values
Types and relationships of relative quantities
The concept of absolute and relative magnitude in statistics
When studying mass social phenomena, statistics in their conclusions rely on numerical data obtained in specific conditions of place and time. The results of statistical observation are recorded primarily in the form of primary absolute values. The absolute value reflects the level of development of the phenomenon.
Absolute statistical values show the volume, size, levels of various socio-economic phenomena and processes. They reflect levels in physical measures of volume, weight, etc. In general, absolute statistical quantities are named numbers. They always have a certain dimension and units of measurement. The latter determine the essence of absolute value.
Natural- such units that reflect the size of objects, things in physical measures (weight, volume, area, etc.).
Monetary (cost)– are used to characterize many economic indicators in value terms.
Labor– used to determine labor costs (man-hour, man-day)
Conditionally natural– units that are used to bring together several varieties use values(t.u.t = 29.3 MJ/kg; soap 40% fat content).
Individual– reflect the size of quantitative characteristics of individual units of the population being studied.
Are common– express the size and magnitude of quantitative characteristics of the entire population being studied as a whole.
Absolute values reflect the availability of certain resources; this is the basis of material accounting. They most objectively reflect economic development.
Absolute values are the basis for calculating various relative statistical indicators.
Relative magnitude in statistics is a generalizing indicator that gives a numerical measure of the relationship between two compared absolute values. Since many absolute values are interrelated, relative values of one type in some cases can be determined through relative values of another type.
Denominator (base of comparison, base) is the value with which comparison is made.
Comparable (reported, current) value – it is the quantity that is being compared.
The relative value shows how many times the compared value is greater or less than the base value or what proportion the first is in relation to the second. In some cases, a relative quantity shows how many units of one quantity are per unit of another.
Important property– relative magnitude abstracts differences in absolute magnitudes and makes it possible to compare phenomena whose absolute sizes are not directly comparable.
The main condition for the correct calculation of relative values is the comparability of the compared indicators and the presence of real connections between the phenomena being studied. Thus, according to the method of obtaining, relative indicators are always derivative values, defined in the form of coefficients, percentages, ppm, prodecimille, etc. However, it must be remembered that these indicators, dimensionless in form, can, in essence, be assigned a specific, and sometimes quite complex, unit of measurement. For example, relative indicators of vital statistics, such as birth or death rates, calculated in ppm (‰), show the number of births or deaths per year per 1,000 average annual population; the relative value of the efficiency of using working time is the amount of production per one man-hour worked, etc.
Relative statistical indicators is a generalizing characteristic expressed as a numerical measure of the ratio of two compared absolute values. These indicators are used to study the structure of the phenomenon being studied, to compare its level of development with the level of development of another phenomenon, to assess changes occurring in the phenomenon being studied, etc.
A relative statistical indicator is obtained by dividing one absolute indicator by another.
IN general view the formula for the relative statistical indicator will look like this:
Relative indicators can be expressed in the form of coefficients, percentages, ppm and prodecimal.
If the comparison base is taken as one, then the relative indicator is expressed in the form of a coefficient. If the comparison base is taken to be one hundred units, then the relative indicator is expressed as a percentage. If the comparison base is taken as a thousand units, then the relative indicator is expressed in ppm (tenth of a percent), if ten thousand - in prodecimal (hundredth of a percent).
Speakers;
Plan and implementation of the plan;
Structures;
Coordination;
Intensity and level economic development;
Comparisons.
Relative dynamics indicator characterizes the change in the phenomenon being studied over time and represents the ratio of indicators characterizing the phenomenon in the current period and the previous (or base) period.
OPD =
The indicator calculated in this way is called the growth (decrease) coefficient. It shows how many times the indicator of the current period is greater (less) than the indicator of the previous (base) period. Expressed as a percentage, the relative indicator of dynamics is called the growth (decrease) rate.
T r = (y i / y i-1) *100%
T r = (y i / y o)*100%
Example: population of the Russian Federation according to the 2002 population census. amounted to 145,181.9 thousand people, according to the 1989 census. - 147021.9 thousand people. Determine the coefficient and rate of growth (decrease).
Consequently, the population decreased by 1.3%.
Relative indicator of plan (forecast) (RPP) and plan implementation (RPVP) are used by all subjects of financial and economic activities carrying out current and strategic planning and are calculated using the formula:
The relative indicator of the plan characterizes the intensity of the plan task, and the relative indicator of the plan’s implementation characterizes the degree of its implementation.
Example: actual turnover of the company for 2008. amounted to 2 billion rubles. Market analysis showed that in 2009. it is possible to increase turnover to 2.6 billion rubles. Actual turnover for 2009 amounted to 2.5 billion rubles. Define AKI and APVP.
OPP==130% or 1.3 times
VPVP==96%
Calculations show that the planned target for 2009 is 1.3 times higher than the actual level for 2008, but the plan for 2009 is only 96% fulfilled.
Relative structure indicators(OPS) characterize the shares (specific gravities) components aggregate in its total volume. They characterize the structure of the aggregate and its structure.
OPS=(*100%)
OPVs are usually expressed in the form of odds or percentages. The sum of the coefficients should be 1, and the sum of the percentages should be 100%, since the specific weights are given to a common basis.
The set of relative values of the structure shows the structure of the population.
Relative coordination indicators(GPC) characterize the ratio of parts of a given statistical population to one of them, taken as a basis for comparison. They show how many times one part of the population is larger than the other or how many units of one part of the population are one, ten, hundred, etc. units of another population.
The part that has the greatest share or is a priority in a given population is selected as the basis for comparison.
Relative indicators of intensity and level of economic development(OPI) characterize the degree of distribution or level of development of the phenomena or processes being studied in a certain environment. They are formed as a result of comparison of opposite, but in a certain way interconnected quantities.
This indicator is calculated per hundred, thousand, ten thousand, etc. units of the population under study and is used in cases where it is impossible to determine the scale of distribution of the phenomenon based on the value of the absolute indicator. For example, when studying demographic processes, indicators of fertility, mortality, and natural population growth (loss) are calculated as the ratio of the number of births (deaths) or the amount of natural growth per year to the average annual population of a given territory per 1000 or 10,000 people.
K r =‰
K m=‰
to natural increase =‰
Relative indicators of the level of economic development characterize the efficiency of resource use and production efficiency. These are indicators of product output, costs per unit of production, efficiency of use of production assets, etc.
Relative Comparison Index OPS p characterizes the comparative sizes of absolute indicators of the same name, relating to different objects or territories, but for the same period of time.
They are obtained as quotients from the division of absolute indicators of the same name that characterize different objects belonging to the same period or point in time.
OPS r=
Using these indicators, you can compare labor productivity in different countries, compare prices for different products and economic indicators for various enterprises.
Statistics studies the quantitative side of mass phenomena and processes with the help of statistical quantities, which are divided into absolute and relative quantities.
Absolute values characterize sizes in specific conditions of time and place. They characterize the entire population.
Absolute units:
1) natural, reflecting the natural properties of a phenomenon - 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 quantities;
2) conditionally natural(used to summarize consumer products of different forms);
3) combined. They are obtained by multiplying or dividing two natural units of measurement;
4) cost (monetary). They eliminate the shortcomings of previous units of measurement and 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 quantities, which are used in comparisons and comparisons and act as a measure of ratio.
Relative quantities are abstract statistical quantities that express the quantitative relationship between two quantities.
Types of relative quantities: 1) relative magnitudes of dynamics 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 dynamics characterize changes in a phenomenon over time. In statistics, these indicators are called growth rates; 2) relative levels of plan implementation is the ratio of the actual value of the indicator (y1) to its planned value (ypl) for the same period:
OVVP = Y 1 / Y pl × 100%.
This relative value shows the degree of implementation of the plan as a percentage; 3) relative amount of planned task fulfillment– this is the ratio of the planned value of the indicator (uPL) to the actual value achieved in the previous period, i.e. in the base period (y0):
OVPP = Y pl/ Y 0 × 100%.
Shows by what percentage 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 structure– shows the composition of the phenomenon, expressed in the form of a fraction or specific gravity. Proportion (d) is the ratio of a part to the whole, that is, 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 structure are used in statistics to characterize structural changes;
5) relative magnitude of coordination– shows the ratio of the parts of the whole, i.e. the ratio of all parts successively to one of them, taken as the base. The smallest value is taken as the base. The relative magnitude 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 certain environment;
7) relative comparison value– this is the ratio of quantities of the same name that characterize 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 sizes. 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 characteristic being studied in one number. A distinctive feature of averages is that they represent general indicators.
average value– this is a general indicator that expresses the typical level (size) of a varying characteristic per unit of a population (qualitatively homogeneous).
The average value reflects what is common in each unit of the population. It captures common features, general patterns that appear due to the law of large numbers. Speaking about average values, we 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 populations under study;
3) characteristics of changes in the level of the phenomenon over time;
4) identification and characterization of connections between the populations being studied.
P principles for constructing averages:
1) average values can be calculated only for qualitatively homogeneous populations;
2) average values should not be abstract, i.e., only quantitative indicators. They must provide a qualitative and 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; harmonic mean; mean square; geometric mean.
To correctly calculate average values, it is necessary to introduce concepts such as options and frequencies.
As a result of summaries and groupings we get statistical series, i.e. series of digital indicators. According to their content, such series divided into distribution series And dynamics series .
Distribution series characterize the distribution of population units according to any one characteristic, the varieties of which are ordered in a certain way. There are two types of distribution series - attribute and variation series.
Attribute series are formed as a result of grouping data according to qualitative characteristics (for example, population distribution by gender). There are as many groups in these series as there are variants of the qualitative trait.
Variation series- this is an ordered series of values of a varying quantitative characteristic and the number of units that have a given value of the characteristic (for example, the distribution of workers by wages).
The following elements are distinguished in the variation series of distribution:
1) options(x or x1, x2 ... xn) is a series of numerical values of a quantitative characteristic (for example, length of service, wage, age). Options can be either absolute or 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 indicated by an absolute number; if, by convention, frequencies are expressed as percentages of the total or shares, then they are called relative frequencies (or) frequencies f:
f = m / Σ m .
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