At the heart of any statistical research There are three interrelated stages of work:

1) statistical observation;

2) summary and grouping of observational data;

3) scientific processing and analysis of the summary results. Each subsequent stage of statistical research can be carried out provided that the previous (preceding) stages of work have been carried out.

Statistical observation is the first stage of statistical research.

Statistical observation- this is a systematic, scientifically organized collection of information about a particular set of social and, in particular, economic phenomena or processes.

Statistical observations are very diverse and differ in the nature of the phenomena being studied, the form of organization, the time of observation, and the completeness of the coverage of the phenomena being studied. In this connection, a classification of statistical observations according to individual characteristics .

1. According to the form of organization statistical observations are divided into reporting and specially organized statistical observations.

Reporting- this is the main organizational form of statistical observation, which boils down to collecting information from enterprises, institutions and organizations about various aspects of their activities on special forms called reports. Reporting is mandatory. Reporting is divided into main and current, depending on the length of the period in relation to which it is prepared.

Basic reporting also called annual and contains the widest range of indicators covering all aspects of the enterprise.

Current reporting presented throughout the year for various time intervals.

However, there are data that are fundamentally impossible to obtain on the basis of reporting and data that are inappropriate to include in it. It is to obtain these two types of data that specially organized statistical observations are used - various surveys and censuses.

Statistical Surveys- These are such specially organized observations in which the studied set of phenomena is observed for a certain period of time.

Census- this is a form of specially organized statistical observation, in which the studied set of phenomena is observed on a certain date (at a certain moment).

2. On the basis of time all statistical observations are divided into continuous and discontinuous.

Continuous (current) statistical observation is an observation that is carried out continuously in time. With this type of observation, individual phenomena, facts, events are recorded as they occur.

Discontinuous statistical observation- this is an observation in which the observed phenomena, facts, events are recorded not continuously, but after periods of time of equal or unequal duration. There are two types of discontinuous monitoring - periodic and one-time. periodic called discontinuous observation, which is carried out at intervals of time of equal duration. one-time called observation, which is carried out through periods of time of unequal duration or having a one-time character.

3. On the basis of completeness of coverage of the studied mass phenomena, facts, events, statistical observations are divided into continuous and non-continuous, or partial.

Continuous observation aims to take into account all phenomena, facts, events, forming the totality under study, without exception.

Discontinuous observation aims to take into account only a certain part of the phenomena, facts, events that form the totality under study.

Main stages of statistical research

Consider the most important method of statistics - statistical observation.

Usage various ways and techniques of statistical methodology

requires the availability of comprehensive and reliable information about the studied

object. The study of mass social phenomena includes the stages of collecting

statistical information and its primary processing, information and grouping

observation results in certain aggregates, generalization and analysis

received materials.

At the first stage of statistical research, primary

statistical data, or raw statistical information that

is the foundation of the future statistical building. For the building to be

solid, solid and high-quality should be its basis. If when collecting

primary statistical data, an error was made or the material turned out to be

poor quality, it will affect the correctness and reliability of both

theoretical as well as practical findings. Therefore, statistical

observation from the initial to the final stage - obtaining the final

materials - should be carefully thought out and clearly organized.

Statistical observation gives raw material to summarize, start

which serves as a summary. If during statistical observation about each of its

unit receive information that characterizes it from many sides, then the data

summaries characterize the entire statistical population and its individual parts.

At this stage, the population is divided according to the signs of difference and combined according to

signs of similarity, total indicators are calculated for groups and in

in general. Using the grouping method, the studied phenomena are divided into the most important

types, characteristic groups and subgroups according to essential features. Via

groupings are limited qualitatively homogeneous in a significant respect

totality, which is a prerequisite for the definition and application

summary indicators.

At the final stage of the analysis with the help of generalizing indicators

relative and average values ​​are calculated, a summary assessment is given

variations of signs, the dynamics of phenomena is characterized, indices are applied,

balance constructions, indicators are calculated that characterize the tightness

connections in the change of signs. For the most rational and clear

presentation of digital material, it is presented in the form of tables and graphs.

3. Statistical observation: concept, basic forms.

This is a scientific and organizational work to collect data. Forms: stat. 1) reporting, cat. based on documentary accounting. since 1998, 4 unified forms of federal state supervision have been introduced: FP-1 (project issue), FP-2 (investment), FP-3 (financial state of organizations), FP-4 (number of -t workers, labor), 2) specially organized observation (census), 3) a register is a s-ma pok-lei, which characterizes each unit of observation: registers of us- niya, pr-ty, construction sites and contractors. org-tions, retail and wholesale trade. Types of observation: 1) continuous, non-continuous (selective, qualified based on the main array method, monograph). Observation is current, period., One-time. Observation methods: direct, documentary, survey (forwarding agent, questionnaire, private, correspondence). Statistical observations are carried out according to the plan, which includes: program-methodological issues (goals, tasks), organizational issues (time, place). As a result of the observations, errors occur, the cat reduces the accuracy of the observations, therefore, data control is carried out (logical and counting). As a result of checking the authentic data, the following observation errors are revealed: random. errors (registration errors), intentional errors, unintentional (system. and non-system.), errors of representativeness (representativeness).

Program-methodological issues of statistical observation.

Program and methodological issues of statistical observation

Each observation is carried out with a specific purpose. When conducting it, it is necessary to establish what is to be examined. The following questions need to be addressed:

Object of observation - a set of objects, phenomena, from which information should be collected. When defining an object, its main distinctive features(signs). Any object of mass observations consists of their individual units, so it is necessary to decide what is the element of the totality that will serve as the unit of observation.

Unit of observation - this is an integral element of the object, which is the carrier of signs subject to registration and the basis of the account.

Qualification are certain quantitative restrictions for the object of observation.

sign - this is a property that characterizes certain features and characteristics inherent in the units of the studied population.

Organizational issues of statistical observation.

The observation program is drawn up in the form of forms (questionnaires, forms), in which primary data are entered. A necessary addition to the forms is an instruction that explains the meaning of the questions.

The organizational issues of the program include:

terms of observation;

critical moment of observation;

preparatory work;

The period of observation to which the recorded information is referred. It is called the objective observation time. This might be a certain period of time (day, decade, month) or a certain moment. The moment to which the recorded information relates is called the critical moment of observation.

For example, the critical moment of the micro-census of 1994. was 0.00 am on the night of February 13-14. By establishing the critical moment of observation, one can determine the true state of affairs with photographic accuracy.

Preparatory work provides for the provision of observation with documents, as well as the compilation of a list of reporting units, forms, instructions.

Documents m. will be filled in during the observation or based on its results.

Important place in the system preparatory work has the selection and training of personnel, as well as briefing those who will participate in the observation.

Statistical methodology- a system of techniques, methods and methods aimed at studying quantitative patterns that manifest themselves in the structure, dynamics and relationships of socio-economic phenomena. The methodology is basis of statistical research.

Stages of statistical research:

1. statistical observation, or collection of information;

2. summary and grouping of the results of statistical observation, or processing of information;

3. analysis of the received information.

Statistical observation- this is a mass, systematic, scientifically organized observation of the phenomena of social and economic life, which consists in registering selected features for each unit of the population.

Process statistical observation includes the following steps:

1) preparation of observation;

2) conducting mass data collection;

3) preparation of data for automated processing;

4) development of proposals for improving statistical observation.

Summary- a set of sequential operations to summarize statistical observation data to characterize the statistical population as a whole and its individual parts (calculation of intermediate and general results). grouping - delimitation of the total statistical population into groups of qualitatively homogeneous units. The results of the statistical summary and grouping are presented in the form of statistical tables.

Analysis or research the essence of the studied phenomena, explores the structure, dynamics and interrelationships of social phenomena and processes.

Has the following steps:

1) statement of facts and their assessment;

2) establishment characteristic features and the causes of each phenomenon;

3) comparison of one phenomenon with others (including with the standard);

4) formulation of hypotheses, conclusions and suggestions.

5) Statistical verification of the hypotheses put forward using special statistical indicators

38. Statistical forecasting methods based on indicators of a series of dynamics. The forecasting process based on statistical methods is divided into two stages. First, inductive, is to generalize the data observed over a more or less long period of time, and to present the relevant statistical patterns in the form of a model. A statistical model is obtained either in the form of an analytically expressed development trend, or in the form of an equation depending on one or more factors-arguments. In a number of cases, when studying complex complexes of economic indicators, they resort to the development of so-called interdependent systems of equations, consisting mainly of equations characterizing statistical dependencies. The process of constructing and applying a statistical model for forecasting, whatever form the latter may have, necessarily includes the choice of the form of an equation that describes the dynamics or the relationship of phenomena, and the estimation of its parameters using one method or another. The second stage, the prediction itself, is deductive. At this stage, based on the found statistical patterns, the expected value of the predicted feature is determined.

It should be emphasized that the results obtained cannot be regarded as something final. When evaluating and using them, factors, conditions or limitations that were not taken into account when developing a statistical model should be taken into account, and the detected statistical characteristics should be adjusted in accordance with the expected change in the circumstances of their formation. In short, the prognostic estimates found using statistical methods are important material which, however, must be critically considered. At the same time, the main thing is to take into account possible changes in the very trends in the development of economic phenomena and objects.

39. Statistical tables, their types, constituent elements and rules for constructing tables. Statistical table - a form of the most rational presentation of the resulting statistical summary and grouping of numerical (numerical) data. By appearance it is a combination of vertical and horizontal lines containing side and top headers. The statistical table contains the subject and the predicate.

The subject of the table represents the statistical population referred to in the table, i.e. a list of individual or all units of the population or their groups. Most often, the subject is placed on the left side of the table and contains a list of strings.

41. STRUCTURAL MEAN FASHION AND ITS DEFINITION. The value of the average is determined by all the values ​​of the attribute found in the given distribution series. There are such structural averages as: (1) mode (2) median (3) quartile (4) decile (5) percentile Mode is the most common variant of the series. Fashion is used, for example, in determining the size of clothes, shoes, which are in greatest demand among buyers. The mode for a discrete series is the variant with the highest frequency. When calculating the mode for the interval variation series, you must first determine the modal interval (by the maximum frequency), and then the value of the modal value of the attribute according to the formula: where:

Predicate of the table - indicators with the help of which the characteristic of the phenomenon displayed in the table is given.

If the subject of the table contains a simple list of any objects, the table is called simple. The subject of a simple table does not contain any groupings of statistical data. If the subject of a simple table contains a list of territories, then such a table is called territorial.

A simple table contains only descriptive information, its analytical capabilities are limited. A deep analysis of the studied population, the relationship of signs involves the construction of more complex tables - group and combination.

Group tables contain in the subject a grouping of units of the object of observation according to one essential attribute. The simplest type of group table are tables that represent distribution series. The group table can be more complex if the predicate contains not only the number of units in each group, but also a number of other important indicators that quantitatively and qualitatively characterize the subject groups. Such tables are often used to compare summary indicators across groups, which makes it possible to draw certain practical conclusions.

Combination tables are called statistical tables, the subject of which is a group of units formed according to one attribute, divided into subgroups according to one or more characteristics. Unlike simple and group tables, combination tables allow us to trace the dependence of the indicators of the predicate on several features that formed the basis of the combination grouping in the subject.

Basic rules for constructing statistical tables:

1) the title should reflect the object, sign, time and place of the event;

2) columns and lines should be numbered;

3) columns and lines must contain units of measurement;

4) the information compared during the analysis is placed in adjacent columns (or one under the other);

5) the numbers in the table are put down in the middle of the column, strictly one under the other; it is advisable to round numbers with the same degree of accuracy;

6) the absence of data is indicated by the multiplication sign ( ), if this position is not to be filled in, the absence of information is indicated by an ellipsis (...), or n.d., or n. St., in the absence of a phenomenon, a dash (-) is put;

7) to display very small numbers use the designation 0.0 or 0.00; if the number is obtained on the basis of conditional calculations, then it is taken in brackets, doubtful numbers are accompanied by a question mark, and preliminary ones - by the sign (*).

40. Structural mean median and its definition. Median- this is the numerical value of the attribute for that unit of the population, which is in the middle of the ranked series (built in ascending or descending order of the values ​​of the studied attribute). median sometimes called middle option, because it divides the population into two equal parts in such a way that on both sides of it there is the same number of units of the population. If all units of a series are assigned serial numbers, then the serial number of the median will be determined by the formula (n + 1): 2 for series, where n is odd. If a row with even number of units, then median will be the average value between two adjacent options, determined by the formula: n:2, (n+1):2, (n:2)+1.

In discrete variational series with an odd number of population units, this is a specific numerical value in the middle of the series.

Finding the median in interval variational series requires a preliminary determination of the interval in which the median is located, i.e. median interval- this interval is characterized by the fact that its cumulative (cumulative) frequency is equal to half the sum or exceeds the half sum of all frequencies of the series.

X Me - the lower limit of the median interval

h Me - the value of the median interval;

S Me-1 - the sum of the accumulated frequencies of the interval preceding the median interval;

• f Me is the local frequency of the median interval.

The frequency of the interval following the modal

42. The essence and meaning of graphs, their main elements. In statistics schedule called illustrative image The representation of statistical quantities and their relationships using geometric points, lines, figures or geographic maps.

Graphs attach presentation of statistics greater visibility than tables, expressiveness, facilitate their perception and analysis. Allows you to visually assess the nature of the phenomenon under study, its inherent patterns, development trends, relationships with other indicators, the geographical resolution of the studied phenomena. Even in ancient times, the Chinese said that one image replaces a thousand words. Whenever possible, it is recommended to always start the analysis of statistical data with their graphic representation. The graph allows you to immediately get a general idea of ​​the entire set of statistical indicators. The graphical method of analysis acts as a logical continuation of the tabular method and serves the purpose of obtaining generalizing statistical characteristics of the processes inherent in mass phenomena.
With the help of graphic statistic images p solved tasks stat.studies:

1) a visual representation of the magnitude of indicators (phenomena) in comparison with each other;

2) characterization of the structure of any phenomenon;

3) change of the phenomenon in time;

4) the progress of the plan;

5) the dependence of a change in one phenomenon on a change in another;

6) the prevalence or distribution of any quantities across the territory

In each graph, the following are distinguished (distinguished): main elements:

• 1) spatial reference points (coordinate system);
• 2) graphic image;
• 3) chart field;
• 4) scale landmarks;
• 5) schedule explication;
• 6) name of the chart

43. Essence and meaning of averages. average value- a generalized characteristic of the level of attribute values, obtained per unit of population. The average value is calculated for signs that are qualitatively homogeneous and differ only quantitatively, which are inherent in all phenomena in a given set.

Average values ​​are general (reflect the population as a whole) and group (reflect the feature by groups). They are divided into 2 categories - power and structural .

to power include - harmonic mean, geometric mean, arithmetic mean, mean square. The most common - cf. arithmetic. Wed harmonic used as the inverse of arithmetic. RMS used in calculating the indicators of variation, cf. geometric– in the analysis of dynamics.

to structural are the mode and the median. Fashion- the value of the studied trait with the highest frequency. Median- the value of the feature that comes to the middle of the ranged series. Fashion is used in commercial practice to study consumer demand and record prices. In a discrete series, the mode is the variant with the highest frequency. In the interval variation series, the mode is the central variant of the interval, which has the highest frequency. Using the median allows you to get more accurate results than using other forms of averages. The property of the median is that the sum of the absolute deviations of the trait values ​​from the median is less than from any other value. determine the accumulated frequencies for this ranked series; according to the accumulated frequencies, we find the median interval.

1. STAGES OF STATISTICAL RESEARCH

The process of studying socio-economic phenomena through a system of statistical methods and quantitative characteristics - a system of indicators, is called statistical research.

The main stages of statistical research are:

1) statistical observation;

2) summary of received data;

3) statistical analysis.

If necessary, a statistical study may contain an additional stage - a statistical forecast.

Statistical observation - scientifically organized collection of data on phenomena and processes public life by registering according to a previously developed program for observing their essential features. Observation data are primary statistical information about the observed objects, which is the basis for obtaining their general characteristics. Observation acts as one of the main methods of statistics and as one of the most important stages statistical research.

Conducting a statistical study is impossible without a high-quality information base obtained in the course of statistical observation. Therefore, from the moment of changing the idea of ​​statistics as a descriptive science, special rules for conducting observation and special requirements for its results - statistical data are being developed. That is, observation is one of the main methods of statistics.

Observation is the first stage of statistical research, the quality of which determines the achievement of the final objectives of the study.

1.1. Observation is carried out according to a specially prepared program.

The program includes a list of characteristics of the object of study, data on which must be obtained as a result of observation.

When preparing an observation, it is necessary to determine in advance:

1. An observation program in which:

a) the object of observation is defined, i.e. the set of units of the phenomenon that needs to be investigated. Moreover, it is necessary to distinguish the unit of observation from the reporting unit. Reporting unit - a unit that provides statistical data, may consist of several population units, or may coincide with a population unit. For example, in a population survey, the unit might be a household member and the reporting unit might be the household.

b) the boundaries of the object of observation are determined.

c) the characteristics of the object of observation are determined, information about which must be obtained as a result of observation.

2. Time of observation of an object - the time at which or for which information about the object under study is recorded.

3. Timing of the observation. That is, the time period for data collection and the end date of the observation are determined. The terms of observation affect the time of completion of the statistical study as a whole and the timeliness of its conclusions.

4. Means and resources needed for monitoring: the number of qualified specialists; material resources; means of processing the results of observation.

5. Requirements for statistical data. The main requirements are: a) reliability, i.e. information about the object of study should reflect its real state at the time of observation; b) comparability of data, i.e. information obtained as a result of observation should be comparable, which is ensured by a unified methodology for collecting and analyzing data, by units of measurement, etc.

1.2. There are several types of statistical observation.

1. By coverage of population units:

a) solid;

b) non-continuous (selective, monographic, according to the method of the main array)

2. By the time of registration of facts: a) current (continuous); b) discontinuous (periodic, one-time)

3. According to the method of collecting information: a) direct observation; b) documentary observation; c) survey (questionnaire, correspondent, etc.)

Summary - the process of bringing the received data into the system, their processing and calculation of intermediate and general results, the calculation of interrelated analytical values.

The next stage of the statistical study is the preparation of the information obtained during the observation for analysis. This stage is called summary.

The summary includes:

— systematization of information obtained during observations;

- their grouping;

- development of a system of indicators characterizing educated groups;

- creation of development tables for grouped data;

— calculation of derived values ​​according to development tables.

In the literature on the theory of statistics, one often encounters the consideration of summaries and groupings as independent stages research. However, it should be noted that the concept of a summary includes actions for grouping statistical data, so here the concept of “summary” is adopted as the name of the research stage.

Statistical analysis- study characteristic features structures, connections of phenomena, trends, patterns of development of socio-economic phenomena, for which specific economic-statistical and mathematical-statistical methods are used. Statistical analysis is completed by the interpretation of the obtained results.

Statistical forecast - scientific identification of the state and probable ways of development of phenomena and processes, based on a system of established cause-and-effect relationships and patterns.

EXERCISE 1

As a result of a sample survey wages 60 employees of an industrial enterprise received the following data (Table 1).

Build an interval series of distribution according to the resultant attribute, forming five groups with equal intervals.

Determine the main indicators of variation (dispersion, standard deviation, coefficient of variation), mean power value (mean value of the feature) and structural means. Depict graphically in the form of: a) histograms; b) cumulates; c) ogives. Make a conclusion.

DECISION

1. Let's determine the range of variation according to the performance indicator - according to the length of service according to the formula:

R \u003d Xmax - Xmin \u003d 36 - 5 \u003d 31

where Xmax is the maximum amount of assets

Xmin - the minimum amount of assets

2. Determine the value of the interval

i \u003d R / n \u003d 31/5 \u003d 6.2

taking into account the obtained value of the intervals, we group the banks and obtain

3. Let's build an auxiliary table

Feature group	Meaning of values ​​in a group x i	Quantity feature frequency (frequency) fi	in % of the total ω	Accumulated frequency Si	Interval midpoint	* f i	ω
I 5 – 11,2	6,8,7,5,8,6,10,9,9,7, 6,6,9,10,7,9,10,10, 11,8,9,8, 7, 6, 9, 10		43,3	43,3		210,6	350,73		46,24	1202,24
II 11,2 – 17,4	16,15,13,12,14,14, 12,14,17,13,15,17, 14		21,7		14,3	185,9	310,31		0,36	4,68
III 17,4 – 23,6	18,21,20,20,21,18, 19,22,21,21,21,18, 19		21,7	86,7	20,5	266,5	444,85		31,36	407,68
IV 23,6 –29,8	28,29,25,28, 24				26,7	133,5	221,61	11,8	139,24	696,2
V 29,8 – 36	36,35,33,				32,9	98,7	164,5
TOTAL						895,2	1492		541,2	3282,8

4. The average value of the attribute in the studied population is determined by the weighted arithmetic formula:

of the year

5. Dispersion and standard deviation of a feature is determined by the formula

Definition of volatility

Thus, V>33.3%, therefore, the population is heterogeneous.

6. Definition of fashion

Mode is the value of the feature that occurs most frequently in the studied population. In the studied interval variational series, the mode is calculated by the formula:

where

xM0
– the lower limit of the modal interval:

i M0 is the value of the modal interval;

f M0-1 f M0 f M0+1 are the frequencies (frequencies) of the modal, premodal, and postmodal intervals, respectively.

The modal interval is the interval having the highest frequency (frequency). In our problem, this is the first interval.

7. Calculate the median.

Median is a variant located in the middle of an ordered variational series, dividing it into two equal parts, so that half of the population units have attribute values ​​less than the median, and half more than the median.

In the interval series, the median is determined by the formula:

where is the beginning of the median interval;

- the value of the median interval

is the frequency of the median interval;

is the sum of accumulated frequencies in the pre-median interval.

The median interval is the interval in which the ordinal number of the median is located. To determine it, it is necessary to calculate the sum of the accumulated frequencies up to a number exceeding half of the totality.

According to Gr. 5 auxiliary table we find the interval, the amount of accumulated often exceeds 50%. This is the second interval - from 11.6 to 18.4, and it is the median.

Then

Consequently, half of the employees with work experience less than 13.25 years, and half - more than this value.

6. Draw a series in the form of a polygon, a histogram, a cumulative straight line, an ogive.

Graphical representation plays an important role in the study of variational series, as it allows in a simple and visual form to analyze statistical data.

There are several ways to graphically represent series (histogram, polygon, cumulate, ogive), the choice of which depends on the purpose of the study and on the type of variation series.

The distribution polygon is mainly used to display a discrete series, but you can also build a polygon for an interval series if you first bring it to the maternity one. The distribution polygon is a closed broken line in a rectangular coordinate system with coordinates (x i , q i), where x i is the value of the i-th feature, q i is the frequency or frequency of the i-ro feature.

A distribution histogram is used to display an interval series. To build a histogram on the horizontal axis, successively lay off segments equal to the intervals of the sign, and on these segments, as on the bases, rectangles are built, the heights of which are equal to the frequencies or particulars for a series with equal intervals, densities; for a series with unequal intervals.

Cumulate is a graphic representation of a variational series, when the accumulated frequencies or particulars are plotted on the vertical axis, and the values ​​of the feature are plotted on the horizontal axis. The cumulate serves for graphical representation of both discrete and interval variational series.

Conclusion: Thus, the main indicators of the variation of the studied series were calculated: the average value of the feature - work experience is 14.9 years, the dispersion is calculated equal to 54.713, in turn, the standard deviation of the feature is 7.397. The mode has a value of 9.13, in the modal interval is the first interval of the studied series. The median of the series is 13.108, dividing the series into two equal parts, which indicates that in the organization under study, half of the employees have less than 13.108 years of work experience, and half have more.

TASK 2

We have the following initial data characterizing the dynamics for 1997-2001. (table 2).

Table 2 Initial data

Year	1997	1998	1999	2000	2001
Production of granulated sugar, thousand tons	1620	1660	1700	1680	1700

Determine the main indicators of a series of dynamics. Present the calculation in the form of a table. Calculate the average annual values ​​of indicators. In the form of a graphic image - a polygon, indicate the dynamics of the analyzed indicator. Make a conclusion.

DECISION

Given

Year	years
	1997	1998	1999	2000	2001
	1620	1660	1700	1680	1700

1) The average level of dynamics is calculated by the formula

2) We calculate chain and basic growth rates as follows:

1. Absolute growth is determined by the formula:

Аib = yi – y0

Aic \u003d yi - yi-1

2. The growth rate is determined by the formula: (%)

Trb = (yi / y0) *100

Trc \u003d (yi / yi-1) * 100

3. The growth rate is determined by the formula: (%)

Tnrb \u003d Trb -100%:

Тnрц = Трц - 100%

4. Average absolute growth:

y n
is the final level of the dynamic series;

y 0
– the initial level of the dynamic series;

n c
is the number of chain absolute increments.

5. Average annual growth rate:

6. Average annual growth rate:

3) Absolute content of 1% increase:

A \u003d Xi-1 / 100

All calculated indicators are summarized in a table.

Indicators	years
	1997	1998	1999	2000	2001
Number of surgeries per period	1620	1660	1700	1680	1700
2. Absolute growth
Aic
3. Growth rate
Trib		102,5	104,9	103,7	104,9
trits		102,5	102,4	98,8	101,2
4. Growth rate
Тпib
Tpits
5. Meaning of 1% increase		16,2	16,6	17,0	16,8

5) Average annual value

7. Draw graphically as a polygon.

Thus, the following is obtained. The largest absolute and relative increase in surgical operations for the period was in 1999 and amounted to 1700, the absolute increase compared to the base year was 80 operations, the growth rate compared to the base year 1997 was 104.9%, and the base growth rate was 4.9 %. The largest chain absolute gains were in 1998 and 1999 - 40 operations each. The highest chain growth rate was observed in 1998 - 102.5%, and the smallest chain growth rate in the number of transactions was in 2000 - 98.8%.

TASK 3

There is data on the sale of goods (see table 3)

Table 3 Initial data on the sale of goods

	Product	Base year		Reporting year
		quantity	price	quantity	price
		1100		1000
			1350		1300
		1650		1700

Determine: a) individual indices ( i p , i q); b) common indices (I p , I q , I pq); c) an absolute change in trade due to: 1) the quantity of goods; 2) prices.

Make a conclusion based on the calculated indicators.

DECISION

Let's create an auxiliary table

View	basic		Reporting		Work		Indices
	Quantity, q 0	Price, p 0	Qty, q 1	Price, p 1	q 0 * p 0	q 1 * p 1	i q \u003d q 1 / q 0	i p \u003d p 1 / p 0	q 1 * p 0
					44000	35000	0,875	0,909	38500
	1100		1000		41800	40000	0,909	1,053	38000
					7500	8400	1,200	0,933	9000
		1350		1300	40500	26000	0,667	0,963	27000
					45000	44000	1,100	0,889	49500
	1650		1700		26400	25500	1,030	0,938	27200
TOTAL					205200	178900			189200

Conclusion: As you can see, the total increase in turnover for the year amounted to (-26300) conventional units, including the impact of changes in the quantity of goods sold by - 16000 and due to changes in the price of goods - 10300 conventional units. The total increase in trade turnover amounted to 87.2%. It should be noted that according to the calculated indices of the quantity of goods by assortment, there is a slight increase in turnover for goods "P" by 120% and goods "C" by 110%, a slight increase in the sale of goods "T" - only 103%. The sales of goods "P" decreased quite significantly - only 66.7% of sales in the base year, sales of goods "H" - 87.5% and goods "O" - 90.9% of the corresponding indicator of the base year slightly higher. The individual price index shows that the price increased only for the product "O" - by 105.3%, at the same time for all other types of goods - "N", "P", "R", "S", "T" the individual price index indicates a negative trend (decrease), respectively - 90.9%; 93.3%;, 96.3%, 88.9; 93.8.

The overall index of the physical volume of sales indicates a slight decrease in the total volume of sales by 94.6%; the general price index indicates a general decrease in the price of goods sold by 92.2%, and the general trade turnover index indicates an overall decrease in trade turnover by 87.2%.

TASK 4

From the initial data of table No. 1 (select lines from 14 to 23), on two grounds - length of service and wages, conduct a correlation-regression analysis, determine the parameters of correlation and determination. Construct a graph of the correlation between two signs (resultant and factorial). Make a conclusion.

DECISION

Initial data

Production experience	Salary
	1800
	2500
	1750
	1580
	1750
	1560
	1210
	1860
	1355
	1480

Straight Line Dependency

The parameters of the equation are determined by the least squares method, by the system of normal equations

To solve the system, we use the method of determinants.

Parameters are calculated by formulas

Stages of statistical research.

Stage 1: Statistical observation.

Stage 2: Reduction and grouping of the results of observation into certain populations.

Stage 3: Generalization and analysis of the received materials. Identification of interrelations and scales of phenomena, determination of patterns of their development, development of predictive estimates. It is important to have comprehensive and reliable information about the object under study.

At the first stage of statistical research, primary statistical data, or initial statistical information, is formed, which is the foundation of the future statistical "building". In order for the “building” to be durable, solid and of high quality, its foundation must be. If a mistake was made in the collection of primary statistical data or the material turned out to be of poor quality, this will affect the correctness and reliability of both theoretical and practical conclusions. Therefore, statistical observation from the initial to the final stage must be carefully thought out and clearly organized.

Statistical observation provides the source material for generalization, the beginning of which is summary. If, during statistical observation, information is obtained about each of its units that characterizes it from many sides, then these reports characterize the entire statistical aggregate and its individual parts. At this stage, the population is divided according to the signs of difference and combined according to the signs of similarity, the total indicators are calculated for the groups and as a whole. Using the grouping method, the studied phenomena are divided into the most important types, characteristic groups and subgroups according to essential features. With the help of groupings, qualitatively homogeneous populations are limited, which is a prerequisite for the definition and application of generalizing indicators.

At the final stage of the analysis, with the help of generalizing indicators, relative and average values ​​are calculated, an assessment of the variation of signs is given, the dynamics of phenomena is characterized, indices and balance constructions are applied, indicators are calculated that characterize the closeness of relationships in changing signs. For the purpose of the most rational and visual presentation of digital material, it is presented in the form of tables and graphs.

The cognitive value of statistics thing is:

1) statistics provides a digital and meaningful coverage of the phenomena and processes under study, serves as the most reliable way to assess reality; 2) statistics gives probative force to economic conclusions, allows you to check various "walking" statements, individual theoretical positions; 3) statistics has the ability to reveal the relationship between phenomena, to show their form and strength.

1. STATISTICAL OBSERVATION

1.1. Basic concepts

Statistical observation - this is the first stage of statistical research, which is a scientifically organized accounting of facts characterizing the phenomena and processes of social life, and the collection of data obtained on the basis of this accounting, scientifically organized according to a single program.

However, not every collection of information is a statistical observation. One can talk about statistical observation only when statistical regularities are studied, i.e. those that manifest themselves in a mass process, in a large number of units of some set. Therefore, statistical observation should be planned, massive and systematic.

Plannedness statistical observation lies in the fact that it is prepared and carried out according to a developed plan, which includes questions of methodology, organization, collection of information, quality control of the collected material, its reliability, and presentation of the final results.

Mass the nature of statistical observation suggests that it covers big number cases of manifestation of this process, sufficient to obtain truthful data characterizing not only individual units, but the entire population as a whole.

Systematic statistical observation is determined by the fact that it must be carried out either systematically, or continuously, or regularly.

The following requirements are imposed on statistical observation:

1) completeness of statistical data (completeness of coverage of units of the studied population, aspects of a particular phenomenon, as well as completeness of coverage over time);

2) reliability and accuracy of data;

3) their uniformity and comparability.

Any statistical research must begin with the formulation of its goals and objectives. After that, the object and unit of observation are determined, a program is developed, and the type and method of observation are selected.

Object of observation- a set of socio-economic phenomena and processes that are subject to research, or the exact boundaries within which statistical information will be recorded . For example, during a population census, it is necessary to establish which population is subject to registration - cash, that is, actually located in a given area at the time of the census, or permanent, that is, permanently living in a given area. When surveying industry, it is necessary to establish which enterprises will be classified as industrial. In some cases, one or another qualification is used to limit the object of observation. Qualification- a restrictive feature that all units of the studied population must satisfy. So, for example, in the census of production equipment, it is necessary to determine what is attributed to production equipment and what to hand tool, what equipment is subject to the census - only operating or also under repair, in stock, reserve.

Unit of observation called component object of observation, which serves as the basis for counting and has features that are subject to registration during observation.

So, for example, in a population census, the unit of observation is each individual person. If the task is also to determine the number and composition of households, then each household will be the unit of observation along with the person.

Observation program- this is a list of issues on which information is collected, or a list of signs and indicators to be registered . The observation program is drawn up in the form of a form (questionnaire, form), in which primary information is entered. A necessary addition to the form is an instruction (or indications on the forms themselves), explaining the meaning of the question. The composition and content of the questions of the observation program depend on the objectives of the study and on the characteristics of the social phenomenon being studied.