Organization of statistical research. Methods and main stages of statistical research

Stages of statistical research.

Stage 1: Statistical observation.

Stage 2: Consolidation and grouping of observation results into specific aggregates.

Stage 3: Generalization and analysis of the received materials. Identification of relationships and scales of phenomena, determination of patterns of their development, development of forecast estimates. It is important to have comprehensive and reliable information about the object being studied.

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”. For a “building” to be durable, its foundation must be sound and of high quality. If an error is made during the collection of primary statistical data or the material turns 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 aspects, then these summaries characterize the entire statistical aggregate and its individual parts. At this stage, the population is divided according to signs of difference and united according to signs of similarity, and total indicators are calculated for groups and as a whole. Using the grouping method, the phenomena being studied are divided into the most important types, characteristic groups and subgroups according to essential characteristics. 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, using general indicators, relative and average values ​​are calculated, an assessment of the variation of characteristics is given, the dynamics of phenomena are characterized, indices and balance sheets are used, indicators are calculated that characterize the closeness of connections in changes in characteristics. For the purpose of the most rational and visual presentation of digital material, it is presented in the form of tables and graphs.

Cognitive value of statistics thing is:

1) statistics provide digital and meaningful coverage of the phenomena and processes being studied and serve as the most reliable way to assess reality; 2) statistics provide evidentiary power to economic conclusions and allow one to verify various “current” statements and individual theoretical propositions; 3) statistics has the ability to reveal the relationships between phenomena, 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.

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

Planfulness statistical observation lies in the fact that it is prepared and carried out according to a developed plan, which includes issues 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 a large number of cases of manifestation of a given process, sufficient to obtain true data characterizing not only individual units, but the entire population as a whole.

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

The following requirements apply to statistical observation:

1) completeness of statistical data (completeness of coverage of units of the population being studied, 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 study must begin with the formulation of its goals and objectives. After this, the object and unit of observation are determined, a program is developed, and the type and method of observation are selected.

Observation object- 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 - existing, i.e., actually located in a given area at the time of the census, or permanent, i.e., permanently living in a given area. When surveying industry, it is necessary to establish which enterprises will be classified as industrial. In a number of cases, one or another qualification is used to limit the object of observation. Census- a restrictive criterion that must be satisfied by all units of the population being studied. So, for example, when taking a census of production equipment, it is necessary to determine what is classified as production equipment and what is classified as hand tools, what equipment is subject to the census - only operating equipment or also under repair, in a warehouse, or in reserve.

Unit of observation is called a component of the object of observation, which serves as the basis for calculation and has characteristics that are subject to registration during observation.

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 the unit of observation, along with the person, will be each household.

Surveillance program- this is a list of issues on which information is collected, or a list of characteristics 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 instructions (or instructions on the forms themselves) explaining the meaning of the question. The composition and content of the questions in the observation program depend on the objectives of the study and on the characteristics of the social phenomenon being studied.

To get an idea of ​​a particular phenomenon and draw conclusions, it is necessary to conduct a statistical study. The subject of statistical research in health care and medicine can be the health of the population, the organization of medical care, various sections of the activities of medical institutions, and environmental factors that influence the state of health.

The methodological sequence of performing a statistical study consists of certain stages.

Stage 1. Drawing up a research plan and program.

Stage 2. Collection of material (statistical observation).

Stage 3. Material development, statistical grouping and summary

Stage 4. Statistical analysis of the phenomenon under study, formulation of conclusions.

Stage 5. Literary processing and presentation of the results obtained.

Upon completion of the statistical study, recommendations and management decisions are developed, the research results are implemented into practice, and effectiveness is assessed.

In conducting a statistical study, the most important element is adherence to a strict sequence in the implementation of these stages.

First stage statistical research - drawing up a plan and program - is preparatory, at which the purpose and objectives of the study are determined, a research plan and program is drawn up, a program for summarizing statistical material is developed, and organizational issues are resolved.

When starting a statistical study, you should accurately and clearly formulate the purpose and objectives of the study and study the literature on this topic.

The goal determines the main direction of the research and, as a rule, is not only theoretical, but also practical in nature. The goal is formulated clearly, clearly, unambiguously.

To reveal the set goal, research objectives are determined.

An important point in the preparatory stage is the development of an organizational plan. The organizational plan of the study provides for the determination of the place (administrative and territorial boundaries of observation), time (specific terms of observation, development and analysis of material) and the subject of the study (organizers, performers, methodological and organizational management, sources of funding for the study).

Pl A n research d ov A nia includes:

Definition of the object of study (statistical population);

Scope of research (continuous, non-continuous);

Types (current, one-time);

Methods of collecting statistical information. Research program includes:

Definition of the unit of observation;

List of questions (accounting characteristics) to be registered in relation to each observation unit*

Development of an individual accounting (registration) form with a list of questions and characteristics to be taken into account;

Development of table layouts, into which the research results are then entered.

A separate form is filled out for each observation unit; it contains the passport part, clearly formulated program questions posed in a certain sequence and the date of filling out the document.

Medical registration forms used in the practice of medical treatment institutions can be used as registration forms.

Sources for obtaining information can be other medical documents (medical histories, and individual outpatient records, child development histories, birth histories), reporting forms from medical institutions, etc.

To ensure the possibility of statistical development of data from these documents, information is copied onto specially designed accounting forms, the content of which is determined in each individual case in accordance with the objectives of the study.

Currently, in connection with machine processing of observation results using a computer, program questions can be formalized , when questions in an accounting document are presented in the form of an alternative (yes, no) , or ready-made answers are offered, from which a specific answer must be selected.

At the first stage of statistical research, along with the observation program, a program* is compiled for summarizing the data obtained, which includes establishing the principles of grouping, identifying grouping characteristics , determination of combinations of these characteristics, drawing up layouts of statistical tables.

Second phase- collection of statistical material (statistical observation) - consists of registering individual cases of the phenomenon being studied and the accounting characteristics characterizing them on registration forms. Before and during this work, the surveillance performers are instructed (oral or written) and provided with registration forms.

In terms of time, statistical observation can be current or one-time.

At current observation Yu Denia the phenomenon is studied for a specific period of time (week, quarter , year, etc.) by daily recording the phenomenon as each case occurs. An example of current observation is the recording of the number of births , dead, sick , discharged from the hospital, etc. This takes into account rapidly changing phenomena.

At one-time observation Yu Denia statistical data is collected at a certain (critical) point in time. One-time observations include: population census, study of the physical development of children, accounting of hospital beds at the end of the year, certification of medical institutions, etc. This type also includes preventive examinations of the population. A one-time registration reflects the state of the phenomenon at the time of study. This type of observation is used to study slowly changing phenomena.

The choice of type of observation over time is determined by the purpose and objectives of the study. For example, characteristics of hospitalized patients can be obtained as a result of the ongoing registration of those leaving the hospital (ongoing surveillance) or from a one-day census of patients in the hospital (one-time observation).

Depending on the completeness of coverage of the phenomenon being studied, a distinction is made between continuous and non-continuous research.

At completely The study examines all units of observation included in the population, i.e. general population. A continuous study is carried out in order to establish the absolute size of a phenomenon, for example, the total population, the total number of births or deaths, the total number of people sick with a particular disease, etc. The continuous method is also used in cases where information is necessary for operational work (accounting for infectious diseases , doctors’ workload, etc.)

At not continuous The study examines only a portion of the population. It is divided into several types: questionnaire, monographic, main array, selective. The most common method in medical research is the sampling method.

Monographic method- gives a detailed description of individual units of the population that are characteristic in some respect and a deep, comprehensive description of objects.

Main Array Method- involves the study of those objects in which a significant majority of observation units are concentrated. The disadvantage of this method is that a part of the population remains uncovered by the study, although small in size, but which may differ significantly from the main array.

Questionnaire method is the collection of statistical data using specially designed questionnaires addressed to a specific circle of people. This study is based on the principle of voluntariness, therefore the return of questionnaires is often incomplete. Often the answers to the questions posed bear the imprint of subjectivity and randomness. This method is used to obtain an approximate characteristic of the phenomenon being studied.

Sampling method- comes down to the study of some specially selected part of observation units to characterize the entire population. The advantage of this method is that it produces results with a high degree of reliability, as well as a significantly lower cost. The study involved fewer performers , In addition, it requires less time.

In medical statistics, the role and place of the sampling method is especially great, since medical workers usually deal only with part of the phenomenon being studied: they study a group of patients with a particular disease, analyze the work of individual departments and medical institutions , evaluate the quality of certain events, etc.

According to the method of obtaining information during statistical observation and the nature of its implementation, several types are distinguished:

1) direct observation(clinical examination of patients , conducting laboratory , instrumental studies , anthropometric measurements, etc.)

2) sociological methods: interview method (face-to-face survey), questionnaire (correspondence survey - anonymous or non-anonymous), etc.;

3) documentary research A tion(copying information from medical records and reports, information from official statistics of institutions and organizations.)

Third stage- grouping and summary of material - begins with checking and clarifying the number of observations , completeness and correctness of the information received , identifying and eliminating errors, duplicate records, etc.

For the correct development of the material, encryption of primary accounting documents is used , those. designation of each characteristic and its group with a symbol - alphabetic or digital. Encryption is a technique , facilitating and accelerating material development , increasing the quality and accuracy of development. Ciphers - symbols - are generated arbitrarily. When encoding diagnoses, it is recommended to use the international nomenclature and classification of diseases; when encrypting professions - with a dictionary of professions.

The advantage of encryption is that, if necessary, after completing the main development, you can return to the development material in order to clarify new connections and dependencies. Encrypted accounting material makes this easier and faster , than unencrypted. After verification, the characteristics are grouped.

Grouping- division of the totality of the studied data into homogeneous ones , typical groups according to the most essential characteristics. Grouping can be carried out according to qualitative and quantitative criteria. The choice of grouping characteristic depends on the nature of the population being studied and the objectives of the study.

Typological grouping is made according to qualitative (descriptive, attributive) characteristics, for example, by gender , profession, disease groups, severity of the disease, postoperative complications, etc.

Grouping by quantitative (variational) characteristics is carried out on the basis of the numerical dimensions of the characteristic , For example , by age , duration of the disease, duration of treatment, etc. Quantitative grouping requires solving the issue of the size of the grouping interval: the interval can be equal, but in some cases it can be unequal, and even include so-called open groups.

For example , When grouped by age, open groups can be defined: up to 1 year . 50 years and older.

When determining the number of groups, they proceed from the purpose and objectives of the study. It is necessary that groups can reveal the patterns of the phenomenon being studied. A large number of groups can lead to excessive fragmentation of the material and unnecessary detailing. A small number of groups leads to a blurring of characteristic features.

Having finished grouping the material, proceed to the summary.

WITH vodka- generalization of individual cases , obtained as a result of statistical research, into certain groups, their calculation and inclusion in table layouts.

A summary of statistical material is carried out using statistical tables. Table , not filled with numbers , called a layout.

Statistical tables can be lists , chronological, territorial.

The table has a subject and a predicate. The statistical subject is usually placed along horizontal lines on the left side of the table and reflects the main, main feature. The statistical predicate is placed from left to right along vertical columns and reflects additional accounting characteristics.

Statistical tables are divided into simple , group and combinational.

IN simple tables presents the numerical distribution of material according to one characteristic , its components (Table 1). A simple table usually contains a simple list or summary of the entire phenomenon being studied.

Table 1

Distribution of deaths in hospital N. by age

IN group tables a combination of two characteristics is presented in connection with each other (Table 2).

table 2

Distribution of deaths in hospital N. by gender and age

IN combine A qi O these tables the distribution of material according to three or more interrelated characteristics is given (Table 3).

Table 3

Distribution of deaths in hospital N. due to various diseases by age and gender

When compiling tables, certain requirements must be met:

Each table should have a title that reflects its contents;

Inside the table, all columns should also have clear, short titles;

When filling out a table, all cells of the table must contain the appropriate numeric data. Cells in the table that are left blank due to the absence of this combination are crossed out (“-”), and if there is no information in the cell, “n.s.” is entered. or "...";

After filling out the table, the vertical columns and horizontal rows are summed up in the bottom horizontal row and the last vertical column on the right.

Tables must have a single sequential numbering.

In studies with a small number of observations, summaries are performed manually. All accounting documents are divided into groups in accordance with the attribute code. Next, the data is calculated and recorded in the appropriate cell of the table.

Currently, computers are widely used in sorting and summarizing material. . which allow not only to sort the material according to the characteristics being studied , but perform calculations of indicators.

Fourth stage- statistical analysis is a critical stage of the study. At this stage, statistical indicators are calculated (frequency , structures , average size of the phenomenon being studied), their graphic representation is given , dynamics are being studied , trends, connections between phenomena are established . forecasts are given, etc. Analysis involves interpreting the data obtained and assessing the reliability of the research results. Finally, conclusions are drawn.

Fifth stage- literary treatment is final. It involves the finalization of the results of a statistical study. The results can be presented in the form of an article, report, report , dissertations, etc. For each type of design there are certain requirements , which must be observed when processing the results of statistical research in literature.

The results of medical and statistical research are introduced into healthcare practice. There are various options for using the research results: familiarization with the results to a wide audience of medical and scientific workers; preparation of instructional and methodological documents; preparation of rationalization proposals and others.

Processing of collected primary data, including their grouping, generalization and presentation in tables, constitutes the second stage of statistical research, which is called summary.

There are 3 main forms of presenting processed statistical data: text, tabular and graphic.

At the third stage of the statistical study, based on the final data of the summary, scientific analysis of the phenomena under study: various generalizing indicators are calculated in the form of average and relative values, certain patterns in distributions, dynamics of indicators, etc. are identified. Based on the identified patterns, forecasts are made for the future.

Statistical observation is the first stage of statistical research. Almost always, in accordance, of course, with the goals and objectives of research, work begins with taking into account facts and collecting primary material. Primary material is the foundation of statistical research. The success of the entire study as a whole depends on the quality of statistical observation. It must be organized in such a way that the result is objective, accurate data about the phenomenon being studied. Incomplete, inaccurate data that does not sufficiently characterize the process, especially if it distorts it, leads to errors. And an analysis carried out on such a basis will be erroneous. It follows that the recording of facts and the collection of primary material must be carefully thought out and organized.

It should be noted once again that statistical observations are always massive. The law of large numbers comes into force - the larger the population, the more objective the results obtained will be.

Statistical observation can be divided into three stages: 1. Preparation of observation. This is the formulation of the observation program, the definition of indicators grouped into layouts of the final statistical tables.

The questions that make up the content of the program should follow from the purpose of the study or the hypothesis to which the study is supposed to be devoted to confirming. An important element is the layout of the final statistical tables. They are the project for developing observation results, and only if they are available it is possible to identify all the issues that need to be included in the program and avoid including unnecessary information.

2. Direct collection of material. This is the most labor-intensive stage of the study. Statistical reporting, as a special form of organizing data collection, is inherent only in state statistics. All other information is collected through a variety of static tools. It is necessary to point out two main requirements for the collected data: reliability and comparability. And what is extremely desirable (in market conditions it increases many times) is timeliness.

3. Control of the material before its analysis. No matter how carefully the observation tools are compiled and the instructions given to the performers, the observation materials always require control. This is explained by the massive nature of statistical work and the complexity of their content.

The object of any statistical study is a set of units of the phenomenon being studied. The object can be the population during the census, enterprises, cities, company personnel, etc. In short, the object of observation is the statistical population under study. It is very important to define the boundaries of the population being studied, which clearly define the population being studied. For example, if the goal is to study the activities of small enterprises in the region, then it is necessary to determine what form of ownership it belongs to (state, private, joint, etc.), by what criterion the enterprises will be selected: industry characteristics, sales volume, time since registration, status (active, inactive, temporarily idle), etc. The population must be homogeneous, otherwise additional difficulties will arise in the analysis process and errors are almost always inevitable.

Along with defining the object of observation and the boundaries, it is important to define the unit of population and the unit of observation. A population unit is an individual component element of a statistical population. An observation unit is a phenomenon, an object, the characteristics of which are subject to registration. The set of observation units constitutes the object of observation. For example, the goal: to study the influence of various factors on the productivity of workers at the mines of Ispat-Karmet OJSC. In this case, the population is determined by the goal itself - miners working at the Ispat-Karmet mines, the unit of the population is the miner, as a carrier of information, and the unit of observation is the mine. Briefly: the unit of the population is what is being examined, the unit of observation is the source of information.
To carry out statistical observation, it is necessary to collect data on a given basis, namely: to designate a statistical population that consists of materially existing objects, the unit and purpose of a one-time survey of the object, and to draw up a statistical observation program.

At the first stage, it is formed sample collected data according to the indicated characteristics, the data is ordered in ascending order. Then you should draw up a table of frequency distributions and sequentially fill in the corresponding columns in the table.

At the second stage, in order to process the collected primary data, it is necessary to group and generalize the selected elements according to a given characteristic, and identify the numerical characteristics of the sample. This stage of statistical research is called summary. Summary – scientific processing of primary data in order to obtain generalized characteristics of the phenomenon under study according to a number of characteristics essential to it, i.e. primary materials are brought together, forming statistical aggregates, which are characterized by final absolute generalizing indicators. At the summary stage, we move from the characterization of individual varying characteristics of units of the population - to the characteristics of the entire population as a whole or to the characteristics of their general manifestation in the mass.

Should be found scope according to the formula:

R=x(max) – x(min);

fashion M(0), which shows the value that occurs most often, median M(e), which characterizes the average value (it does not exceed half of the members of the series), corresponds to the option in the middle of the ranked variation series. The position of the median is determined by its number: Nme = (n+1) /2, where n is the number of units in the aggregate and arithmetic mean for the designated group, which is calculated by the formula:

The results of the work can be presented graphically in the form of a histogram and frequency distribution polygon.

The data obtained reflect what is common to all units of the population under study. As a result of statistical observation, objective, comparable, complete information should be obtained, allowing at subsequent stages of the study to provide scientifically based conclusions about the nature and patterns of development of the phenomenon being studied.

Practical task

Conduct a statistical study to find out information about growth 2 5 randomly selected students of Tomsk Polytechnic University.

Make a frequency distribution table, find the range, mode, median and arithmetic mean height value (in cm) for the designated young men.

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 conducting a statistical study are:

1) statistical observation;

2) summary of the data obtained;

3) statistical analysis.

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

Statistical observation is a scientifically organized collection of data about the phenomena and processes of social life through registration according to a pre-developed program for observing their essential features. Observation data represents 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 of statistical research.

Conducting a statistical study is impossible without a high-quality information base obtained during statistical observation. Therefore, since the change in ideas about statistics as a descriptive science, special rules for conducting observations and special requirements for its results - statistical data - have been 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 research object, data about 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 determined, i.e. that set of units of a phenomenon that needs to be investigated. Moreover, it is necessary to distinguish the observation unit from the reporting unit. A reporting unit is a unit providing statistical data; it may consist of several population units, or may coincide with a population unit. For example, in a population survey, the unit might be the household member and the reporting unit might be the household.

b) the boundaries of the observation object are determined.

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

2. Time of observation of an object - the time as of which or for which information about the object being studied is recorded.

3. Timing of observation. That is, the period of time for data collection and the date of completion of observation are determined. The observation period affects the completion time of the overall statistical study and the timeliness of its conclusions.

4. Funds and resources required for monitoring: number of qualified specialists; material resources; means for processing observation results.

5. Requirements for statistical data. The main requirements are: a) reliability, i.e. information about the object of research should reflect its real state at the time of observation; b) comparability of data, i.e. information obtained as a result of observation must 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, based on the bulk method)

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

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

Summary is the process of bringing the received data into the system, processing it and calculating intermediate and general results, calculating interrelated quantities of an analytical nature.

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

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 quantities using development tables.

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

Statistical analysis is a study of the characteristic features of the structure, relationships of phenomena, trends, patterns of development of socio-economic phenomena, for which specific economic-statistical and mathematical-statistical methods are used. Statistical analysis concludes with the interpretation of the results obtained.

Statistical forecast is a scientific identification of the state and probable paths 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 of wages of 60 employees of an industrial enterprise, the following data were obtained (Table 1).

Construct an interval distribution series based on the effective attribute, forming five groups with equal intervals.

Determine the main indicators of variation (variance, standard deviation, coefficient of variation), the average power value (the average value of the characteristic) and structural averages. Represent it graphically in the form of: a) a histogram; b) cumulates; c) ogives. Draw a conclusion.

SOLUTION

1. Let us determine the scope of variation according to the effective attribute - according to production experience using the formula:

R = Хmax – Хmin = 36 – 5 = 31

where Xmax is the maximum size of assets

Хmin – minimum asset size

2. Determine the size of the interval

i = R/n = 31/5 = 6.2

Taking into account the obtained intervals, we group the banks and obtain

3. Let's build an auxiliary table

4. The average value of a characteristic in the population under study is determined by the arithmetic weighted formula:

of the year

5. The variance and standard deviation of a characteristic are determined by the formula

Determination of variability

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

6. Definition of fashion

Mode is the value of a characteristic that occurs most frequently in the population being studied. In the interval variation series under study, the mode is calculated using the formula:

Where

x M0
– lower limit of the modal interval:

i M0– the value of the modal interval;

f M0-1 f M0 f M0+1– frequencies (frequencies) of modal, pre-modal and post-modal intervals, respectively.

A modal interval is the interval that has the greatest frequency (frequency). In our problem, this is the first interval.

7. Calculate the median.

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

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

where is the beginning of the median interval;

– value of the median interval

– frequency of the median interval;

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

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

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

Then

Consequently, half of the workers with work experience are less than 13.25 years, and half have more than this value.

6. Let us depict the series in the form of a polygon, a histogram, a cumulative line, or an ogive.

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

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

A distribution polygon is mainly used to depict a discrete series, but you can also construct a polygon for an interval series if you first convert it to a discrete series. 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 construct a histogram, segments equal to the intervals of the characteristic are laid out sequentially on the horizontal axis, and on these segments, as on bases, rectangles are constructed, the heights of which are equal to the frequencies or particulars for a series with equal intervals, densities; for a series with unequal intervals.

Cumulates are a graphical representation of a variation series, when accumulated frequencies or particulars are plotted on the vertical axis, and characteristic values ​​are plotted on the horizontal axis. The cumulate is used for graphical representation of both discrete and interval variation series.

Conclusion: Thus, the main indicators of variation of the series under study were calculated: the average value of the attribute - production experience is 14.9 years, the dispersion was calculated to be 54.713, in turn, the standard deviation of the attribute is 7.397. The mode has a value of 9.13, and the modal interval is the first interval of the series being studied. The median of the series, equal to 13.108, divides the series into two equal parts, indicating 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

The following initial data are available that characterize the dynamics for 1997 – 2001. (table 2).

Table 2 Initial data

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

SOLUTION

Given

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

2) Chain and base growth rates are calculated as follows:

1. Absolute growth is determined by the formula:

Аib = yi – y0

Aic = yi – yi-1

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

Trb = (yi / y0) *100

Trc = (yi / yi-1)*100

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

Тnрb = Трb –100%:

Tnrts = Trts – 100%

4. Average absolute increase:

y n
– final level of the time series;

y 0
– initial level of the dynamic series;

n c
– number of chain absolute increases.

5. Average annual growth rate:

6. Average annual growth rate:

3) Absolute content of 1% increase:

A = Xi-1/100

We summarize all calculated indicators in a table.

5) Average annual value

7. Let's depict it graphically in the form of 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 increases were in 1998 and 1999 – 40 operations each. The highest chain growth rate was observed in 1998 - 102.5%, and the lowest chain growth rate in the number of transactions was in 2000 - 98.8%.

TASK 3

There are data on sales of goods (see table 3)

Table 3 Initial data on sales of goods

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

Draw a conclusion based on the calculated indicators.

SOLUTION

Let's create an auxiliary table

Conclusion: As we can see, the total increase in trade turnover for the year was (-26,300) conventional units, including the impact of a change in the quantity of goods sold by - 16,000 and due to changes in the price of goods - 10,300 conventional units. The overall increase in trade turnover was 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 product “P” by 120% and product “C” by 110%, a slight increase in sales of product “T” is only 103%. Sales of goods “P” decreased quite significantly - only 66.7% of sales in the base year, sales of goods “N” were slightly higher - 87.5% and goods “O” - 90.9% of the corresponding indicator for the base year. The individual price index shows that the price increased only for the product “O” - by 105.3%, while at the same time for all other product names - “N”, “P”, “R”, “S”, “T” the individual price index indicates negative dynamics (decrease), respectively – 90.9%; 93.3%;, 96.3%, 88.9; 93.8.

The general index of physical sales volume indicates a slight decrease in total sales volume 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 a general decrease in trade turnover by 87.2%.

TASK 4

From the initial data of table No. 1 (select rows from 14 to 23) based on two characteristics - 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 characteristics (resultative and factorial). Draw a conclusion.

SOLUTION

Initial data

Straight-line dependence

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

To solve the system we use the method of determinants.

Parameters are calculated using formulas

Statistical observation consists in the collection of primary statistical material, in a scientifically organized registration of all significant facts related to the object under consideration. This is the first stage of any statistical research.

The grouping method makes it possible to systematize and classify all facts collected as a result of mass statistical observation. This is the second stage of statistical research.

The method of generalizing indicators allows you to characterize the phenomena and processes being studied using statistical values ​​- absolute, relative and average. At this stage of statistical research, the relationships and scales of phenomena are identified, the patterns of their development are determined, and forecast estimates are given.

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. For a building to be durable, its foundation must be sound and of high quality. If an error is made during the collection of primary statistical data or the material turns 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 - obtaining final materials - must be carefully thought out and clearly organized. Statistical observation provides the source material for generalization, the beginning of which is a summary. If, during statistical observation, information is obtained about each of its units that characterizes it from many aspects, then these summaries characterize the entire statistical aggregate and its individual parts. At this stage, the population is divided according to signs of difference and united according to signs of similarity, and total indicators are calculated for groups and as a whole. Using the grouping method, the phenomena being studied are divided into the most important types, characteristic groups and subgroups according to essential characteristics. With the help of groupings, populations that are qualitatively homogeneous in significant respects are limited, which is a prerequisite for the definition and application of generalizing indicators.

At the final stage of the analysis, using general indicators, relative and average values ​​are calculated, a summary assessment of the variation of characteristics is given, the dynamics of phenomena are characterized, indices and balance sheets are used, indicators are calculated that characterize the closeness of connections in changes in characteristics. For the purpose of the most rational and visual presentation of digital material, it is presented in the form of tables and graphs.

Statistical observation - the first stage of statistical research

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

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

The systematic nature of statistical observation lies in the fact that it is prepared and carried out according to a developed plan, which includes issues of methodology, organization, technology for collecting information, quality control of the collected material, its reliability, and presentation of the final results. The massive nature of statistical observation suggests that it covers a large number of cases of manifestation of a given process, sufficient to obtain true statistical data characterizing not only individual units, but the entire population as a whole.

Finally, the systematic nature of statistical observation is determined by the fact that it must be carried out either systematically, continuously, or regularly. The study of trends and patterns of socio-economic processes characterized by quantitative and qualitative changes is possible only on this basis. From the above it follows that the following requirements are imposed on statistical observation:

• 1) completeness of statistical data (completeness of coverage of units of the population being studied, aspects of a particular phenomenon, as well as completeness of coverage over time);
• 2) reliability and accuracy of data;
• 3) their uniformity and comparability.

Programmethodological and organizational issues of statistical observation

Any statistical study must begin with a precise formulation of its purpose and specific objectives, and thereby the information that can be obtained during the observation process. After this, the object and unit of observation are determined, a program is developed, and the type and method of observation are selected.