Types of statistical data. Preliminary data analysis

Statistical data can be presented in the form of statistical tables, statistical graphs and statistical charts.

Statistical tables are drawn up as a result of summarizing and grouping the available observation data. Statistical tables necessarily contain summary indicators and consist of a subject and a predicate.

Subject of the table shows what the table is about, it is located on the left and represents the contents of the rows.

Table predicate located at the top and represents the contents of the graph. The predicate shows what features characterize the subject.

Statistical graphs. The construction of statistical graphs is the final stage of summarizing and grouping statistical data. Graphic representation is the most effective form of presenting statistical data from the point of view of their perception.

Schedule called a conditional, visual representation of statistical quantities and their relationships using geometric lines and figures.

Each graph must include the following elements: a graphic image, a graph field, scale guidelines and a coordinate system.

Graphic image - geometric signs, a set of points, lines, figures with the help of which statistical quantities are depicted.

Graph field represents a space in which geometric signs are placed.

The scale references of a statistical graph are determined by the scale and scale bar.

Statistical graph scale - this is a measure of converting a numerical value into a graphic one,

Scale scale - a line whose specific points can be read as specific numbers. The scale consists of a line (the scale carrier) and a number of points marked on it, arranged in a certain order.

Uniform scale is the length of a segment taken as a unit and measured in some measure.

To place geometric signs in the graph field, a coordinate system is required. The most common system is rectangular coordinates.

According to the method of constructing, graphs are divided into line graphs, diagrams, cartograms, and map diagrams.

The class of linear graphs includes: polygon, cumulate and Lorenz curve.

Polygon called a broken line whose segments connect points X and/j (X j - characteristic value; - frequency).

The polygon is used for a discrete distribution series.

Cumulates- a broken line, compiled from accumulated frequencies or frequencies, the coordinates of the points of which are X ( And f. (X j- value of the characteristic, for an interval series - upper limit of values (X.);/ ( - accumulated frequency).

The starting point of the broken line of the interval distribution series is the lower limit of the value ( X") in the first group.

Lorenz curve, or concentration curve, is called the relative concentration curve of the total value of the attribute. It is a broken line, the coordinates of the points of which on the abscissa axis are the accumulated relative frequencies, and on the ordinate axis the accumulated (cumulative total) value of the attribute Xj.

The closer the Lorenz curve is to a straight line, the more uniform the distribution of the characteristic is, i.e. concentration is less. The greater the curvature of the curve, the more uneven the distribution, i.e. concentration is greater.

Statistical charts. The class of charts primarily includes a histogram (bar chart), as well as bar charts, ribbon charts, pie charts, linear charts, square charts, pie charts, curly charts, etc.

Bar chart - this is a stepped figure consisting of rectangles, the bases of which are equal to the size of the interval in the group, and the heights are equal to the density in the group (absolute or relative).

When constructing bar charts, data is depicted in the form of bars of the same width but different heights, depending on numerical values depicted quantities on a certain scale.

A variety of bar charts are strip and strip charts. They depict the dimensions of a feature in the form of horizontally located rectangles of the same width, but of different lengths, in proportion to the depicted values. The beginning of the stripes should be on the same vertical line.

Pie charts It is convenient to use to depict the structure of a phenomenon; in this case, the circle is divided into sectors proportional to the shares of parts of the phenomena. The circle is taken as a whole (100%) and is divided into sectors, the arcs of which are proportional

the values of individual parts of the displayed quantities. The arc of each sector (or the value of the central angle) is determined by the formula

where 360° is the area of the circle;

d- the specific gravity of the depicted phenomenon in percent.

If statistical data is presented in absolute values, then the formula for determining the arc takes the form:

Where b- the magnitude of the depicted phenomenon in absolute values.

For building circular And square diagrams it is necessary to carry out preliminary calculations, since the available statistical data (/)) correspond to the areas of geometric shapes (circles or squares).

To construct a circle, you need to find the radius of the circle using the formula

To construct a square, you need to find the side of the square based on the formula for the area of the square:

Barbarian Sign used to visually characterize three interrelated quantities - this is a rectangle in which the base is one indicator, the height is another, and the product of the base and the height characterizes the value of the derived third indicator.

Shape charts are constructed in two ways: the compared statistical quantities (/)) are depicted by figures - symbols of different sizes in proportion to the volumes of these aggregates, or by different numbers of identical signs-symbols, each of which is given a certain numerical value.

To graphically depict the spatial distribution of any statistical indicator, cartograms are used, which can be background or point.

Cartogram is a combination of a diagram and a geographical map.

On background cartograms, the distribution of the phenomenon under study across the territory is depicted by various territorial colorings

nal units with different densities of color or shading of varying intensity.

On a dot cartogram, the symbols for the graphic representation of statistical data are points located within certain territorial units. Each point is given a specific numerical value.

A cartogram is used in cases where there is a need to show the territorial distribution of any one statistical feature in the aggregate in order to identify the pattern of distribution of this feature.

Automated methods for constructing diagrams. Charts can be created in an automated way based on observation data generated and grouped in a table. To ensure the clarity of the diagram, the data block must meet certain requirements:

data should be systematized by quantity and by groups, columns and rows;
data for different categories must be comparable;
headings of tables, rows, columns should be short and clear so as not to take up much space and ensure a correct understanding of the meanings of the constructed diagram;
The data should be arranged in one or more rectangular ranges with text labels in the top row and left column.

As part of an integrated package Microsoft Office spreadsheet information is processed using the program Microsoft Excel. A spreadsheet is the computer equivalent of a regular spreadsheet.

Table processor - special program(software package) that provides processing of information presented in tabular form.

Microsoft Excel defines the first row of data, starting with the first cell in the upper left corner of the existing selected non-date data range and ending with the remaining selected rows and columns.

To build diagrams in the spreadsheet processor, it is possible to use a special diagram wizard using a plotter Microsoft Graph. The Chart Wizard is launched by clicking on the icon in the standard toolbar. It is recommended that you first select the range of cells containing the data used to create charts. Diagrams are constructed in four stages:

1) choosing the type and type of diagram;
2) clarification of the data range and arrangement of rows in rows or columns. The result of constructing a diagram when positioned

series in rows and columns can vary significantly. By default, the window displays the chart view for the selected range of cells. If you have not previously selected the data, you must do this in this window by clicking on the stylized table icon in the field Range and highlighting the data in the table. Tab "row" allows you to add and delete rows, specify the ranges in which the corresponding rows are presented, category axis labels;

3) specifying the title of the diagram and completing the necessary signatures;
4) placing the diagram on a spreadsheet (on the current or a separate worksheet).

To edit chart elements, you must double-click, after which you will be taken to the corresponding window for changing the parameters of the selected element. Significant help is provided by a context-sensitive menu that can be called up on individual diagram elements.

Statistical data must be adequate, firstly to the object of study, and secondly to the time at which they are collected and used.

This chapter describes the sources of statistical data, their types and methods of obtaining, as well as techniques for describing and presenting numerical and non-numerical data.

After studying this chapter, YOU should be able to:

-build a statistical research program;
-identify sources of statistical information;
-summarize and group statistical data and generate statistical tables;
- display grouping results in the form of diagrams;
- assess the main characteristics: relative value, average value, dispersion, standard deviation, median, mode, range.

Obtaining initial data

Obtaining information about the object of study is one of the main tasks of statistical research.

Statistical research should be guided by the goals and requirements for the results. They determine the methods of statistical analysis, on the basis of which the collection of initial data is organized. In the process of statistical research, one should be wary of the following mistakes: goals are not clearly formulated, observation methods are applied incorrectly.

Obtaining initial data for statistical research can be done in two ways:

-an active experiment, specially organized to determine statistical dependencies;
-statistical observation.

Active experimentation is used in technical and economic research, when, for example, the task is to optimize technological process modes according to economic criteria.

When conducting a statistical study of socio-economic processes, it seems possible to use only observation. The program is the basis of this method of obtaining information. It consists of three main stages:

-definition of the research object;
- selection of a population unit;
- determination of the system of indicators to be registered.

The object of observation is a set of units of the phenomenon being studied, about which statistical information can be collected. To clearly define the object of observation, the following questions should be answered:

-What? (what elements will we study);
-Where? (where the observation will be conducted _;
-When? (for what period).

From the point of view of organizing statistical observation, there are two main forms: reporting and specially organized statistical observation.

Reporting as a form of observation is characterized by the fact that statistical authorities systematically receive from enterprises, institutions and organizations, within a specified period of time, information about the conditions and results of work over the past period, the volume and content of which are determined by approved reporting forms.

Specially organized statistical observation is the collection of information in the form of censuses of one-time records and surveys. They are organized to study those phenomena that cannot be covered by mandatory reporting.

Types of statistical observation are distinguished by the time of data recording and the degree of coverage of units of the population being studied. Based on the nature of data recording over time, observation can be classified:

-continuous (for example, accounting of manufactured products);
-periodic (accounting statements);
- one-time, in case of need for information, for example, a population census.

According to the degree of coverage of units of the population being studied:

-incomplete, selective, when not the entire population is examined, but some part of it;
- continuous, i.e. description of all units of the population;
-monographic, when typical objects are described in detail.

The main ways to obtain statistical information are direct observation, documentary methods and surveys.

The method of direct observation is characterized by the fact that representatives of state statistics bodies or other organizations record data in statistical documents after personal inspection, recalculation, measurement or weighing of observation units.

With the documentary method of observation, various documents serve as the source. This method is used when enterprises and institutions compile statistical reporting based on primary accounting documents.

When conducting a survey, the source of information is the responses of the respondents. The survey can be organized in different ways: by expedition method, self-registration, correspondence method and questionnaire method.

With the expedition method, representatives of statistical bodies ask the person being surveyed and, from his words, record information on observation forms.

In the self-registration method, surveyed units (enterprises or citizens) are given a survey form and given instructions on how to fill it out. Completed forms are sent by mail within the specified period.

With the correspondent method, information is reported to statistical bodies by voluntary correspondents.

The questionnaire method of data collection is based on the principle of voluntary completion of questionnaires by recipients.

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Groupings in criminal legal statistics allow us to give the most complete and comprehensive criminological and criminal legal characteristics based on a wide variety of criteria:

Ш by type - articles of the Criminal Code,
Sh on the object of the attack,
Ш on a territorial basis - district, region, region, republic,
W ratio of mercenary and violent crimes,
Ш according to the time of commission of crimes, etc.),
The identity of the criminals (by gender, age, education, social status, place of residence, etc.),
Ш causes and conditions conducive to the commission of crimes, as well as measures of social and legal control over them.

At the same time, it is very important to compare various groupings from criminal law statistics not only with each other, but also with groupings from other branches of statistics (demographic, socio-economic, etc.), reflecting interrelated phenomena.

Differences in the purpose of the grouping and the tasks that they solve in statistical analysis are expressed in their existing classification: typological, structural, analytical.

The most important task of groupings in statistics is to divide the studied mass of population units into characteristic types, i.e. into groups homogeneous in essential characteristics. This problem is solved using a typological grouping.

Typological groupings- this is the differentiation of the studied population into homogeneous groups, types according to an essential qualitative feature.

The main goal of a typological grouping is to distinguish one type of phenomenon from another by statistical means. This type of grouping is largely determined by established ideas about what types of phenomena constitute the content of the population being studied.

In legal statistics, these are three types of legal relations: criminal law, administrative law and civil law, which define its sections.

In criminal statistics, in particular, this could be, for example, the gender distribution of persons who committed crimes.

This grouping according to a qualitative characteristic, when there are only two values of this characteristic, and one of them excludes the other, is called alternative in statistics.

The sequence of actions for carrying out this type of grouping is elementary:

1) the type of phenomenon that should be highlighted is determined - in our case, registered crimes;
2) a grouping characteristic is selected as the basis for describing the type - in our case, the gender of the persons who committed the crimes;
3) the boundaries of the intervals are established (in our case, for all persons identified as having committed crimes);
4) the grouping is drawn up in a table, the selected groups (based on a combination of grouping characteristics) are combined into the intended types, and the number (specific gravity) of each of them is determined.

When typological grouping, that is, when summing up units into qualitatively homogeneous categories, these categories should, as noted, be determined on the basis of the provisions of the relevant science and the norms of the law. For example, the grouping of punishments by type is carried out by criminal law (judicial) statistics in full accordance with Art. 43-59 of the Criminal Code, establishing with exhaustive completeness the exact qualitative characteristics of their individual types (fine, correctional labor, imprisonment, etc.

Structural groupings- this is the distribution of typically homogeneous groups according to quantitative characteristics, which can change (vary). In the scientific literature, this type of grouping is sometimes called variational. With their help, criminal statistics study, for example, the structure of criminals according to varying characteristics: age, number of convictions, terms of imprisonment, wages and other quantitative characteristics.

Structural, or variational, grouping of statistics can be done to examine the changing structure of typically homogeneous groups of crimes, offenders, civil claims, and other indicators. For the structural grouping of material, it is necessary to have homogeneous aggregates, divided according to the value of the changing (varying) characteristic.

If the typological grouping is based on qualitative characteristics, then the variational grouping is based on quantitative ones (proportion of crimes, persons, cases, age of offenders, sentence terms, number of convictions, number of completed classes, amount of damage, amount of claim, terms of investigation and consideration of criminal or civil cases). affairs, etc.) .

Quantitative shifts in the structure of the phenomena under study over several years indicate changes in objective trends and patterns, investigative or judicial practice, and the effectiveness of the activities of law enforcement or other legal bodies. Taking, for example, absolute and relative conviction rates over many years, we will identify trends in judicial practice and its relationship with actual crime. Having studied the dynamics of the absolute numbers of recorded crimes of a certain type, the dynamics of its share in the structure of all crime, we will discover trends in the development of this act.

Structural groupings can be built on the basis of the share distribution of crimes by areas and objects of criminal encroachment, subjects of the Federation, regions and territories

Structural differences in this case may reveal the peculiarities of the criminological situation in a particular region.

Structural (variational) groupings are adjacent to the rows of distribution of population units according to varying characteristics.

Analytical groupings- this is a distribution according to dependence, the relationship between two or more heterogeneous groups of phenomena or their characteristics (for example, the distribution of thefts by place and time of their commission; those convicted of motor vehicle crimes - by the driver’s work experience, etc.).

Analytical groupings are of great importance for all branches of legal statistics. They make it possible to identify many hidden dependencies and relationships, which is important for making practical decisions and the development of legal science. Other types of groupings, as well as other statistical techniques, also have analytical potential, but the analytical grouping itself directly pursues the establishment of dependencies between the phenomena under study. By the nature of their tasks, correlational groupings are close to the analytical grouping, when the dependence between the phenomena or processes under study can be measured relatively accurately.

All types of considered groupings are usually used together when analyzing socio-legal, tortological and criminological aspects. For example, to establish the social danger and severity of the crimes committed, we can divide their totality into categories of acts and forms of guilt (typological grouping). To determine the effectiveness of the fight against crime of various law enforcement agencies (internal affairs, drug control, customs service, prosecutor's office, security service), we can study the variation in the detection rate of crimes in the mentioned departments (variation grouping).

In order to establish the causes and conditions of growth or (decrease in crime in a city, region, country), a number of analytical groups should be applied.

Statistical methods

Statistical methods- methods of statistical data analysis. There are methods of applied statistics, which can be used in all areas of scientific research and any sectors of the national economy, and other statistical methods, the applicability of which is limited to one or another area. This refers to methods such as statistical acceptance control, statistical control of technological processes, reliability and testing, and planning of experiments.

Classification of statistical methods

Statistical methods of data analysis are used in almost all areas of human activity. They are used whenever it is necessary to obtain and justify any judgments about a group (objects or subjects) with some internal heterogeneity.

It is advisable to distinguish three types of scientific and applied activities in the field of statistical methods of data analysis (according to the degree of specificity of the methods associated with immersion in specific problems):

a) development and research of general-purpose methods, without taking into account the specifics of the field of application;

b) development and research of statistical models of real phenomena and processes in accordance with the needs of a particular area of activity;

c) application of statistical methods and models for statistical analysis of specific data.

Applied Statistics

A description of the type of data and the mechanism for its generation is the beginning of any statistical study. Both deterministic and probabilistic methods are used to describe data. Using deterministic methods, it is possible to analyze only the data that is available to the researcher. For example, with their help, tables were obtained that were calculated by official state statistics bodies based on statistical reports submitted by enterprises and organizations. The obtained results can be transferred to a wider population and used for prediction and control only on the basis of probabilistic-statistical modeling. Therefore, only methods based on probability theory are often included in mathematical statistics.

We do not consider it possible to contrast deterministic and probabilistic-statistical methods. We consider them as sequential steps of statistical analysis. At the first stage, it is necessary to analyze the available data and present it in an easy-to-read form using tables and charts. Then it is advisable to analyze the statistical data on the basis of certain probabilistic and statistical models. Note that the possibility of deeper insight into the essence of a real phenomenon or process is ensured by the development of an adequate mathematical model.

In the simplest situation, statistical data are the values of some characteristic characteristic of the objects being studied. Values can be quantitative or provide an indication of the category to which the object can be classified. In the second case, they talk about a qualitative sign.

When measuring by several quantitative or qualitative characteristics, we obtain a vector as statistical data about an object. It can be thought of as a new kind of data. In this case, the sample consists of a set of vectors. There are part of the coordinates - numbers, and part - qualitative (categorized) data, then we are talking about a vector of different types of data.

One element of the sample, that is, one dimension, can be the function as a whole. For example, describing the dynamics of the indicator, that is, its change over time, is the patient’s electrocardiogram or the amplitude of the beat of the motor shaft. Or a time series describing the dynamics of a particular company’s performance. Then the sample consists of a set of functions.

Sample elements can also be other mathematical objects. For example, binary relationships. Thus, when surveying experts, they often use ordering (ranking) of objects of examination - product samples, investment projects, options for management decisions. Depending on the regulations of the expert study, the sampling elements can be various types of binary relations (ordering, partitioning, tolerance), sets, fuzzy sets, etc.

So, the mathematical nature of sample elements in various problems of applied statistics can be very different. However, two classes of statistical data can be distinguished - numerical and non-numerical. Accordingly, applied statistics is divided into two parts - numerical statistics and non-numerical statistics.

Numerical statistics are numbers, vectors, functions. They can be added and multiplied by coefficients. Therefore, in numerical statistics, various sums are of great importance. The mathematical apparatus for analyzing the sums of random elements of a sample is the (classical) laws of large numbers and central limit theorems.

Non-numerical statistical data are categorized data, vectors of different types of features, binary relations, sets, fuzzy sets, etc. They cannot be added and multiplied by coefficients. Therefore, it makes no sense to talk about sums of non-numeric statistics. They are elements of non-numerical mathematical spaces (sets). The mathematical apparatus for analyzing non-numerical statistical data is based on the use of distances between elements (as well as measures of proximity, indicators of difference) in such spaces. With the help of distances, empirical and theoretical averages are determined, the laws of large numbers are proved, nonparametric estimates of the probability distribution density are constructed, diagnostic problems and cluster analysis are solved, etc. (see).

Applied research uses various types of statistical data. This is due, in particular, to the methods of obtaining them. For example, if testing of some technical devices continues until a certain point in time, then we get the so-called. censored data consisting of a set of numbers - the duration of operation of a number of devices before failure, and information that the remaining devices continued to operate at the end of the test. Censored data is often used in assessing and monitoring the reliability of technical devices.

Typically, statistical methods for analyzing data of the first three types are considered separately. This limitation is caused by the fact noted above that the mathematical apparatus for analyzing data of a non-numerical nature is significantly different than for data in the form of numbers, vectors and functions.

Probabilistic-statistical modeling

When applying statistical methods in specific fields of knowledge and sectors of the national economy, we obtain scientific and practical disciplines such as “statistical methods in industry”, “statistical methods in medicine”, etc. From this point of view, econometrics is “statistical methods in economics”. These disciplines of group b) are usually based on probabilistic-statistical models built in accordance with the characteristics of the field of application. It is very instructive to compare probabilistic-statistical models used in various fields, to discover their similarities and at the same time to note some differences. Thus, one can see the similarity of problem statements and statistical methods used to solve them in such areas as scientific medical research, specific sociological research and marketing research, or, in short, in medicine, sociology and marketing. These are often grouped together under the name "sample studies".

The difference between sample studies and expert studies is manifested, first of all, in the number of objects or subjects surveyed - in sample studies we are usually talking about hundreds, and in expert studies - about tens. But the technology of expert research is much more sophisticated. The specificity is even more pronounced in demographic or logistic models, when processing narrative (text, chronicle) information or when studying the mutual influence of factors.

Issues of reliability and safety of technical devices and technologies, queuing theory are discussed in detail in a large number of scientific works.

Statistical analysis of specific data

The application of statistical methods and models for statistical analysis of specific data is closely tied to the problems of the relevant field. The results of the third of the identified types of scientific and applied activities are at the intersection of disciplines. They can be considered as examples of the practical application of statistical methods. But there are no less reasons to attribute them to the corresponding field of human activity.

For example, the results of a survey of instant coffee consumers are naturally attributed to marketing (which is what they do when giving lectures on marketing research). The study of the dynamics of price growth using inflation indices calculated from independently collected information is of interest primarily from the point of view of economics and management of the national economy (both at the macro level and at the level of individual organizations).

Development prospects

The theory of statistical methods is aimed at solving real problems. Therefore, new formulations of mathematical problems for the analysis of statistical data constantly arise in it, and new methods are developed and justified. Justification is often carried out by mathematical means, that is, by proving theorems. A major role is played by the methodological component - how exactly to set problems, what assumptions to accept for the purpose of further mathematical study. The role of modern information technologies, in particular, a computer experiment.

An urgent task is to analyze the history of statistical methods in order to identify development trends and apply them for forecasting.

Literature

2. Naylor T. Machine simulation experiments with models of economic systems. - M.: Mir, 1975. - 500 p.

3. Kramer G. Mathematical methods of statistics. - M.: Mir, 1948 (1st ed.), 1975 (2nd ed.). - 648 p.

4. Bolshev L. N., Smirnov N. V. Tables of mathematical statistics. - M.: Nauka, 1965 (1st ed.), 1968 (2nd ed.), 1983 (3rd ed.).

5. Smirnov N. V., Dunin-Barkovsky I. V. Course in probability theory and mathematical statistics for technical applications. Ed. 3rd, stereotypical. - M.: Nauka, 1969. - 512 p.

6. Norman Draper, Harry Smith Applied regression analysis. Multiple Regression = Applied Regression Analysis. - 3rd ed. - M.: “Dialectics”, 2007. - P. 912. - ISBN 0-471-17082-8