Statistical indicators: absolute and relative values
- Statistical indicators, their types.
- Absolute value.
- Relative values.
Statistical indicators, their types
Each unit of a statistical population can be characterized using statistical indicators. Statistical indicator – This is a quantitative and qualitative generalizing characteristic of any property of a group of units or a population as a whole, and this is what distinguishes it from a feature. For example: the average salary in Ukraine is a statistical indicator, and the salary of a specific person is a sign.
A statistical indicator is a generalizing characteristic of the object under study, which combines its qualitative and quantitative certainty. Qualitative the content of the indicator depends on the essence of the object being studied (phenomenon, process) and is reflected in its name (number of goods sold, daily revenue, annual profit, etc.). Quantitative The side of the phenomenon is represented by the number and its meter. The connecting link between qualitative content and numerical expression is indicator model, which reveals the statistical structure of the indicator, establishes what, where, when, how subject to measurement. It justifies units of measurement and computational operations. The indicator model reflects the rules for its construction and calculation.
Indicators are classified:
1. According to the calculation method:
- primary,are determined by summarizing and grouping data and are presented in the form of absolute values;
- derivatives, are calculated on the basis of primary or secondary indicators and have the form of average or relative values.
2. Based on time for:
- interval, characterize the state of an object (phenomenon, process) for a certain time (day, month, year). For example, the volume of products sold during the year, the production capacity of the enterprise put into operation during the quarter, the shift output of the worker, etc.;
- momentary, characterize a phenomenon at a certain point in time. For example, the attendance of workers at the beginning of the shift, the availability of taxis at the time of ordering, the state of the enterprise’s balance sheet accounts at the beginning and end of the year (quarter), working capital balances at the beginning of the month, etc.
3. Based on the relationship between the object being studied, pairs of mutually inverse (direct and inverse) statistical indicators are distinguished, which exist in parallel and characterize the same phenomenon. Straight the indicator increases with the increase in the phenomenon, o brotherly, on the contrary, decreases. For example, production output per unit of time is a direct indicator, and time spent per unit of production is an inverse indicator.
Absolute and relative values can be expressed in statistical terms.
Absolute value
In statistics, absolute indicators are called total indicators that characterize either the size of a characteristic for individual units of the population (for example: the size of the salary of an individual employee) or the total value of the characteristic for a set of objects (the wage fund of an enterprise). Absolute values are named numbers, i.e. having a unit of measurement. Depending on the specific research problem and the nature of the phenomenon, they use natural, labor and cost (monetary) units.
Cost meters make it possible to evaluate the activity of heterogeneous objects. For example: the production volume of a machine-building plant is measured in units of output; volume of work of cargo transport vehicles – in tons, ton-kilometers; passenger ATP – in passengers, passenger-kilometers; taxi fleet in paid kilometers. The production volume indicators of the above enterprises are expressed in different natural units of measurement and therefore they are not comparable. If it is necessary to compare these enterprises, the results of their work should be considered in value terms, i.e. in income.
IN labor units of measurement (person-day, person-hour) take into account labor costs at the enterprise or the labor intensity of individual operations of the technological cycle.
If there is a need to bring together several varieties of products for the same consumer purpose, the volume of this phenomenon is expressed in conditionally natural units. Conversion into conventional units is carried out using special reduction coefficients. For example, the fuel balance is compiled in tons of standard fuel. The standard is coal, the calorific value of which is 7000 cal per 1 kg. Calorific conversion factors for Donetsk coal - 0.9; natural gas - 1.2, etc.
When solving a certain range of analytical problems, absolute values are presented in the form of balances, in which indicators are grouped by sources of formation and by areas of use. Dynamic balances are also widely used, which are compiled according to the following scheme:
(balances at the beginning of the period) + (receipts) - (expenses) = (balances at the end of the period).
Based on the ratio of absolute values presented in the form of balances, the balance of processes is assessed. For example, the balance of income and expenses of the population, the balance of export-import operations, etc.
Relative values
Relative value in statistics, it is a general indicator, which is the quotient of two absolute indicators and gives a numerical measure of the relationship between them. In this case, the numerator of the fraction contains the value that is being compared, and the denominator contains the value with which it is being compared. The last one is called base or basis of comparison. If the comparison base is taken as one, then the relative value will be expressed in the form of a coefficient and will show how many times the compared value is greater or less than the base. So, if we compare the number of students of the fourth (21 people) and second (49 people) years of the specialty “Accounting and Auditing”, we get a relative value in the form of a coefficient (49:21 = 2.33), which shows that students of the second the rate is 2.33 times more. The basis of comparison can be 100, 1000, 10000 or 100000 units. Then the relative value is expressed respectively in percentage (%), ppm (0/00), prodecimiles (0/000) and prosantimiles 0/0000).
The choice of one form or another of a relative quantity depends on its absolute value. If the value being compared is 2 times or more greater than the comparison base, then the form of the coefficient is usually chosen (as in the example given). If the relative value is close to unity, as a rule, it is expressed as a percentage, but if it is very small, then in ppm, etc. For example, 0.0025 can be expressed as 0.25% or 2.5 0/00, or 25 0/000.
In accordance with the analytical function, the following types of relative values are distinguished: relative values of dynamics, plan task, implementation of plan task, structure, comparison, intensity, coordination.
Relative dynamics() characterize a change in the level of a phenomenon over time, calculated by dividing the level of a characteristic in the analyzed period or point in time by the level of the same characteristic in the previous period or point in time. Relative values can be basic, when one year is taken as the base of comparison, and chain – when the previous year is taken as the base of comparison.
For example, the electricity production of nuclear power plants in Ukraine is characterized by the following data.
Then a) the basic relative values of the dynamics of electricity production: 
; 
; 
;.
b) chain relative values of production dynamics): 
; 
; 
.
Relative value of the planned target() is calculated as the ratio of the level planned for the upcoming period to the level actually established in the current period. For example, production volume in 2003 was 100,000 units. conditional products, production of 110,000 pieces is planned for 2004. products. Then
Relative value of plan task fulfillment() represents the ratio of the level actually achieved in a given period to the planned level. Example: production of 110,000 units was planned for 2004. conditional products, 105,000 pieces were actually produced. 
There is the following relationship between the relative values of dynamics, plan target and plan implementation 
Example. It was planned to increase production by 5%; actual growth was 7.5%. It is necessary to determine the degree of completion of the planned task. 
Thus, the planned target was exceeded by 2.38%.
Relative magnitudes of structure show the specific gravity (share) of individual parts in the entire aggregate. They are calculated by dividing the number of units in individual parts by the total number of units in the aggregate. The relative values of the structure are called shares, their sum is 1 or 100%. The use of shares is the basis for a comparative analysis of the composition of populations of different sizes and an assessment of structural shifts over time. The difference between the shares is called percentage points.
Relative comparison values() are called indicators that represent the quotient of the division of absolute values of the same name, relating to different populations, but to the same period or moment. For example, on January 1, 1996, 2,630 thousand people lived in Kiev, 1,555 thousand in Kharkov. people Then 
shows that in Kyiv the population is 69% larger than in Kharkov, and 
indicates that in Kharkov the population is 41% less than in Kyiv. (The absolute values of the same name are the urban population, the aggregates are different cities).
Relative intensity values– show the degree of distribution or level of development of a particular phenomenon in a certain environment. They are calculated by comparing opposite quantities. An example is population density, which is determined by dividing the population by the area of the territory where it lives, or labor productivity. These indicators are usually determined per 100, 1000, etc. units of the population being studied.
Relative coordination values characterize the relationship between the individual parts of one whole. Calculated by dividing one part by another.
Example. The urban population of Ukraine as of January 1, 1996 was 34.8 million people, the rural population was 16.5 million people.
When studying the urban population, they calculate 
. The obtained value shows that the urban population is greater than the rural population by 2 times or 110%.
If we take the number of rural population as the basis of comparison, then the relative indicator of coordination is equal to 
. This means that in Ukraine in 1996 the rural population was 53% less than the urban population. (Whole: population of Ukraine, parts: urban and rural population.)
The concept of absolute and relative quantities
Absolute and relative quantities, reflecting the corresponding characteristics, cannot exist without each other.
Absolute values in economic analysis
Definition 1
The absolute value expresses the quantitative dimensions of a certain phenomenon without relating it to others, without assessing the changes and deviations that occur. The absolute value characterizes the volume and level of the process (phenomena), being always named numbers.
Absolute quantities have a dimension, that is, a unit of measurement.
Classification of absolute values:
- natural,
- labor,
- monetary, etc.
Average and relative values
The ratio of several absolute values is expressed using average and relative values.
Note 2
To determine relative values, it is necessary to divide one indicator by another, which is taken as the base one.
The following indicators can be the basic value:
- Plan data
- Factual data,
- Information from previous years
- Indicators of other enterprises, etc.
Relative comparison values can be expressed as a percentage (based on the base, which is taken as 100) or in the form of coefficients (in this case, the base is one).
Classification of absolute values
Absolute values can be of two types:
- Individual absolute values characterizing the size of a characteristic of a specific unit. Examples of such values may be the size of employees’ wages or a bank deposit. These dimensions are determined directly during the observation process, and they are recorded in the primary accounting documentation.
- Total absolute values reflecting the final indicator of a characteristic in a set of objects. This size acts as the sum of the number of units (size of the population) or the volume of varying characteristics.
Classification of relative quantities
The main condition for calculating relative values is the comparability of units and the existence of a real connection between the phenomena under study. The value with which the comparison is made, which is in the denominator in the fraction, acts as the basis or basis of the relationship. In accordance with her choice, the result can be expressed in various fractions of a unit, then a network of tenths, hundredths (percent), thousandths (tenth of a percent, ppm), ten-thousandths (hundredth of a percent prodecimal).
The units that are compared can be either the same name or different ones. If the units have different names, then their name is formed depending on the units used (c/ha, rubles/person, etc.).
In economic analysis, several types of relative values are used:
- Speakers,
- The relative value of the structure, characterizing the share of certain parts of the population being studied in its total volume;
- The value of the plan target, expressing the ratio of planned indicators for the future to the actual existing values for the current period;
- intensity,
- Comparisons,
- Coordination,
- Degrees of economic development.
The calculation of relative values is carried out by determining the ratio of the number in a certain part to their total number (or volumes). These units are expressed as a percentage or a simple multiple. For example, calculating the share of the urban population.
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 carriers (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. Similarly, detergent products are 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 inhabitants 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.
Absolute and relative errors are used to assess the inaccuracy in highly complex calculations. They are also used in various measurements and for rounding calculation results. Let's look at how to determine absolute and relative error.
Absolute error
Absolute error of the number call the difference between this number and its exact value.
Let's look at an example
: There are 374 students in the school. If we round this number to 400, then the absolute measurement error is 400-374=26.
To calculate the absolute error, you need to subtract the smaller number from the larger number.
There is a formula for absolute error. Let us denote the exact number by the letter A, and the letter a - the approximation to the exact number. An approximate number is a number that differs slightly from the exact one and usually replaces it in calculations. Then the formula will look like this:
Δa=A-a. We discussed above how to find the absolute error using the formula.
In practice, absolute error is not sufficient to accurately evaluate a measurement. It is rarely possible to know the exact value of the measured quantity in order to calculate the absolute error. Measuring a book 20 cm long and allowing an error of 1 cm, one can consider the measurement to be with a large error. But if an error of 1 cm was made when measuring a wall of 20 meters, this measurement can be considered as accurate as possible. Therefore, in practice, determining the relative measurement error is more important.
Record the absolute error of the number using the ± sign. For example , the length of a roll of wallpaper is 30 m ± 3 cm. The absolute error limit is called the maximum absolute error.
Relative error
Relative error They call the ratio of the absolute error of a number to the number itself. To calculate the relative error in the example with students, divide 26 by 374.
We get the number 0.0695, convert it to percentage and get 6%. The relative error is denoted as a percentage because it is a dimensionless quantity. Relative error is an accurate estimate of measurement error. If we take an absolute error of 1 cm when measuring the length of segments of 10 cm and 10 m, then the relative errors will be equal to 10% and 0.1%, respectively. For a segment 10 cm long, an error of 1 cm is very large, this is an error of 10%. But for a ten-meter segment, 1 cm does not matter, only 0.1%.
There are systematic and random errors. Systematic is the error that remains unchanged during repeated measurements. Random error arises as a result of the influence of external factors on the measurement process and can change its value.
Rules for calculating errors
There are several rules for the nominal estimation of errors:
- when adding and subtracting numbers, it is necessary to add up their absolute errors;
- when dividing and multiplying numbers, it is necessary to add relative errors;
- When raised to a power, the relative error is multiplied by the exponent.
Approximate and exact numbers are written using decimal fractions. Only the average value is taken, since the exact value can be infinitely long. To understand how to write these numbers, you need to learn about true and dubious numbers.
True numbers are those numbers whose rank exceeds the absolute error of the number. If the digit of a figure is less than the absolute error, it is called doubtful. For example , for the fraction 3.6714 with an error of 0.002, the correct numbers will be 3,6,7, and the doubtful ones will be 1 and 4. Only the correct numbers are left in the recording of the approximate number. The fraction in this case will look like this - 3.67.
What have we learned?
Absolute and relative errors are used to assess the accuracy of measurements. Absolute error is the difference between an exact and an approximate number. Relative error is the ratio of the absolute error of a number to the number itself. In practice, relative error is used since it is more accurate.
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A statistical indicator is a quantitative characteristic of a socio-economic process or phenomenon.
A set of interrelated statistical indicators, having a single-level or multi-level structure, forms a system of statistical indicators.
A distinction is made between indicators - categories and specific statistical indicators. Indicator - category reflects the essence, general distinctive properties of specific statistical indicators. But after being tied to a specific place (object), it becomes specific. For example, the population size is a qualitative definition, and the population size of Leninogorsk as of 01/01/2010. - a specific statistical indicator.
In terms of the coverage of aggregate units, indicators can be individual and summary. Summary are divided into:
Volumetric - obtained by adding the characteristic values of individual units of the population
Calculated - calculated using various formulas and used to measure relationships, variations, characteristics of structural changes, etc.
According to the time factor, indicators can be momentary - for a date and interval - for a period from ... to ...
On a spatial basis, indicators can relate to the federal, regional and local levels.
From the point of view of specific objects and forms of expression, indicators can be absolute, relative, average.
Statistical indicators expressing the dimensions (volumes, levels) of socio-economic phenomena in units of measure, weight, volume, length, area, cost, etc. are called absolute statistical values. They always have a certain dimension, certain units of measurement.
The choice of units of measurement of absolute values is determined by the essence, properties of the phenomenon being studied, as well as the objectives of the study. Statistics uses a large number of different units of measurement. In the most general classification, they can be reduced to three types: natural, monetary (cost) and labor.
Natural It is customary to call such units of measurement that are expressed in measures of weight, volume, length, area, etc. Such units of measurement are used to characterize the volume of various types of products, the size of sales of goods, the capacity of power plants, etc. These are the production of fabrics - in linear and (or) square meters, the production of gas - in cubic meters, electricity - in kilowatt-hours.
In some cases they are used conditionally natural units. They are used to bring together several varieties of the same use value. One of them is taken as a standard, and the others are recalculated using special coefficients into units of measure of this standard. Thus, in the practice of our statistics, all types of fuel are converted into standard fuel with a calorific value of 29.3 MJ/kg (7000 kcal/kg).
Soap with different contents of fatty acids is converted to 40% fatty acid content, canned food of different volumes is converted into conventional cans with a volume of 353.4 cm3, freight cars are converted into two-axle cars, etc.
If, for example, there are 100 tons of soap with a fatty acid content of 40% and 100 tons with a fatty acid content of 60%, then, recalculating to 40% soap, we get 100 + 100. 60/40 = 250 conventional tons of soap.
Labor units of measurement such as man-hours, man-days, etc., are used to determine labor costs for the production of products, for performing some work, for accounting for the labor intensity of individual operations of the technological process.
In a market economy, they are of great importance and widespread use. cost units of measurement that give a monetary assessment of socio-economic phenomena and processes.
These are: gross domestic product, trade turnover, income and expenses of the population, etc.
Absolute statistical indicators are divided into volume indicators and level indicators.
Volume indicators make it possible to characterize the size of the entire population or its parts. Thus, the economically active population in Russia in 1998 amounted to 72,572 thousand people, including 38,355 thousand men, 34,217 thousand women. They can also express the total value of any characteristic of the entire population or its part.
Level indicators characterize the magnitude of the load of a unit of one population with elements of another population (for example, in Russia in 1999, the number of inhabitants per 1 km2 of territory was 8.6 people). They can also determine the degree of saturation of a particular set with elements of some characteristic of a given or another set. (in Russia in 1998, the average cost of living per capita per month was 493.3 rubles; in 1998 in Moscow, the average retail price for a women's demi-season coat made of wool and wool blend fabrics was 2128.16 rubles per piece ).
There are also difference absolute indicators. They represent the absolute size in the difference between two absolute indicators in time or space. An example of an absolute gel difference in time (called the absolute growth rate) is the difference between the production of confectionery products in Russia in 1998 (1310 thousand tons) and in 1992 (1829 thousand tons), equal to 519 thousand tons. The absolute size of confectionery production in Russia has decreased by this value over six years
Relative indicators are called statistical indicators, defined as the ratio of the absolute value being compared to the comparison base. The quantity with which the comparison is made (the denominator of the fraction) is usually called the base, base of comparison or basic quantity. Numerator is the quantity being compared. It is also called the current or reporting value.
For example, dividing the urban population by the entire population of the country, we obtain the indicator “share of urban population”.
The compared quantities can be of the same name or different. If values of the same name are compared, then the relative indicators are expressed in abstract numbers. As a rule, the comparison base is taken to be 1,100, 1000 or 10000. If the base is 1, then the relative value shows what proportion of the base the current value is. If the comparison base is 100, then the relative value is expressed as a percentage (%), if the comparison base is 1000 - in ppm (%o), 10000 - in prodecimille (%oo).
When comparing different values, the names of the relative values are formed from the names of the compared values (population density of the country: people/km2; yield: c/ha, etc.).
Depending on the tasks, content and meaning of the expressed quantitative relationships, relative indicators of the plan target, plan implementation, dynamics, structure, coordination, comparison, intensity, and level of economic development are distinguished.
Relative indicators of the planned target(OPPP) are used for the purpose of long-term planning of the activities of entities in the financial and economic sphere, as well as for comparing the actually achieved results with those previously planned.
Example In the first quarter, the retail turnover of a trade association amounted to 250 million rubles; in the second quarter, retail turnover is planned at 350 million rubles. Determine the relative value of the planned target.
Solution: GPV * 100% = 140%. Thus, in the second quarter it is planned to increase the retail turnover of the trade association by 40%.
Relative indicators of plan implementation(OPVP) express the relationship between the actual and planned levels of the indicator. They are usually expressed as a percentage. The method for calculating relative indicators of plan implementation depends on the type and form in which the plan indicators are given. Planned indicators can be set in the form of absolute and average values. If the plan target is set in the form of absolute and average values, the degree of implementation of the plan is determined by dividing the actually achieved value of the indicator by the value provided for by the plan
When the plan is specified as a relative indicator (compared to the baseline level), the implementation of the plan is determined from the ratio of the relative value of the dynamics with the relative value of the plan target
If the planned target provides for a decrease in the level of the indicator, then the result of comparing the actual level with the planned one, which is less than 100% in value, will indicate that the plan has been exceeded.
Relative indicators of dynamics(OPD) are statistical quantities that characterize the degree of change in the phenomenon being studied over time. They represent the ratio of the level of the process or phenomenon under study for a given period of time and the level of the same process or phenomenon in the past.
The value calculated in this way shows how many times the current level exceeds the previous (basic) one or what proportion of the latter it constitutes. This indicator can be expressed as shares or percentages.
If data is available for several periods of time, comparison of each given level can be made either with the level of the previous period, or with some other one taken as the basis of comparison (base level). The first ones are called relative indicators of dynamics with a variable comparison base, or chain, the second - relative indicators of dynamics with a constant base of comparison, or basic. Relative indicators of dynamics are otherwise called growth rates and growth coefficients.
There is the following relationship between the relative indicators of the plan target, plan implementation and dynamics: GPZ. OPVP = OPD. Based on this relationship, from any two known indicators it is always possible to determine a third unknown value.
Relative structure indicators(OPS) represent the relationship between the part and the whole. They characterize the structure and composition of a particular set of socio-economic phenomena. From the definition of relative indicators of the structure it follows that when calculating them, the value of the whole (the overall result for any indicator) is taken as the basis for comparison, and the values of the indicators of individual parts of this whole are compared.
Relative coordination indicators(GPC) represent the ratio of one part of a population to another part of the same population
As a result of this division, we get how many times this part of the totality is greater (less) than the basic one, or how many percent of it it is, or how many units of this structural part are per 1 unit, per 100, per 1000, etc. units of other -th part taken as the basis of comparison.
Relative intensity indicators(OPI) characterize the degree of saturation or development of a given phenomenon and represent the ratio of the indicator under study to the size of its inherent environment
A type of relative intensity indicators are relative indicators of the level of economic development (OPUER). They characterize output per capita and are very significant when assessing the state of the state’s economy.
Since volumetric production indicators are interval in nature, and the population indicator is momentary, the calculation uses the average population for the period (for example, the average annual):
Relative comparison indicators(OPSR) represent the ratio of quantities of the same name relating to different objects (enterprises, firms, districts, regions, countries, etc.):
Using this indicator, you can compare the population, the size of the territory, the size of the cultivated area across countries, regions, districts, etc.
Averages are the most common values in statistics. They represent a generalized quantitative characteristic of a characteristic in a statistical aggregate. They give a generalized description of similar phenomena according to one of the varying characteristics.
The most important property of average values is the ability to reflect what is common to all units of the population. The average value reflects the typical level of the attribute when it is calculated from a qualitatively homogeneous population. If the population is not homogeneous, the general average should be supplemented with group averages, which are calculated as a result of preliminary grouping of the population data.
The most common types of averages used in statistics include:
Arithmetic, which can be simple and weighted.
Arithmetic mean simple used when calculations are carried out using ungrouped data. To do this, the sum of the values of the varying indicators is divided by their total number.
Weighted arithmetic mean, used when the value of a variable characteristic is repeated. In this case, the frequency of repetition of such a value is determined and the average is calculated from the grouped data using the formula:
or by the formula:
When calculating the weighted average based on data from an interval series, it is necessary to move from interval values to median values.
Harmonic mean weighted - used when the numerator of the initial ratio of the average is known, but its denominator is not known. In this case, the calculation is carried out according to the formula:
Where w i = x i m i
Place weighted can be used in cases where the values w i for units of the population are equal (planned duration of the working day). It is calculated using the formula:
Geometric mean unweighted calculated by the formula:
Harmonic mean weighted calculated by the formula:
The mode and median are most often used in statistics. Fashion represents the value of the characteristic being studied that is repeated with the greatest frequency.
The median is the value of the attribute that falls in the middle of the ranked (ordered) population. The main property of the median is that the sum of the absolute deviations of the attribute values from the median is less than from any other value.
Based on the grouped data, the mode is determined from the table.
The median value of the characteristic is calculated using the formula:
Where P- volume of the aggregate.
In an interval series, the mode is calculated using the formula:
Where, X 0 - lower limit of the modal interval (interval with the highest frequency), h - width of the modal interval; mMo - modal interval frequency;
T Mo-1 - frequency of the interval preceding the modal one;
T Mo+1 is the frequency of the interval following the modal one.
In an interval series, the median is calculated using the formula:
Where: x0 is the lower limit of the median interval (the first interval in which the accumulated frequency exceeds half of the total sum of frequencies); h - width of the median interval; T i - frequency of the i-th interval;
S M e -1 - accumulated frequency of the interval preceding the median;
T Me - frequency of the median interval.