What is it in statistics? What is statistics, and what is its importance in modern society? Statistics is a general theoretical science that studies quantitative changes in phenomena and processes

1. General concept statistics. Subject of statistics.

Statistics refers to systematic and systematic accounting carried out nationwide by state statistics bodies, headed by the State Committee of the Russian Federation on Statistics.

Statistics - digital data published in special reference books and the media.

Statistics is a special scientific discipline.

Subject and content of statistical science for a long time were controversial. In order to resolve these issues in 1954 and 1968. special meetings were held with the participation of wide range scientists and practitioners, not only statisticians, but also specialists in related science. In addition, until the mid-70s. there was a discussion about the subject of statistics in specialized literature. During the discussions it emerged 3 main points of view on the subject of statistics:

1. Statistics is a universal science that studies mass phenomena of nature and society.

2. Statistics is a methodological science that does not have its own subject of knowledge, but is a doctrine of the method used by the social sciences.

3. Statistics is a social science that has its own subject, methodology and research quantitative patterns social development.

As a result of meetings and discussions in statistical science, the first two points of view were rejected by the majority of scientists and practitioners, and the third was largely accepted, supplemented and clarified.

The subject of statistics is the quantitative side of mass socio-economic phenomena, inextricable connections with their qualitative side, specific conditions, place and time. From this definition follow main features of the subject of statistical science:

1. Statistics is a social science.

2. Unlike other social sciences, statistics studies the quantitative side social phenomena.

3. Statistics studies a mass phenomenon.

4. Statistics studies the quantitative side of phenomena in unbreakable connection with the quantitative side and this is embodied in the existence of the system statistical indicators.

5. Statistics studies the quantitative side of phenomena in specific conditions of place and time.

2. Method of statistics and statistical methodology.

Statistical methodology is understood as a system of principles and methods for their implementation aimed at studying quantitative patterns manifested in the structure of relationships and dynamics of socio-economic phenomena. The most important components methods of statistics and statistical methodology are mass statistical observation, summary and grouping, as well as the use of generalizing statistical indicators and their analysis.

The essence of the first element of statistical methodology compiles the collection of primary data about the object being studied. For example: during the census of a country, data is collected on every person living on its territory, which is entered into a special form.

Second element: summary and grouping represents the division of the totality of data obtained at the observation stage into homogeneous groups according to one or more characteristics. For example, as a result of grouping census materials, the population is divided into groups (by gender, age, population, education, etc.).

The essence of the third element of statistical methodology consists in the calculation and socio-economic interpretation of general statistical indicators:

1. Absolute

2. Relative

3. Medium

4. Variation indicators

5. Speakers

The three basic elements of statistical methodology also constitute the three stages of any statistical study.

3. The law of large numbers and statistical regularity.

The law of large numbers is important for statistical methodology. In its most general form, it can be formulated as follows:

The law of large numbers is a general principle by virtue of which cumulative actions large number random factors leads, under certain general conditions, to a result almost independent of chance.

The law of large numbers is generated by the special properties of mass phenomena. Mass phenomena, in turn, on the one hand, due to their individuality, differ from each other, and on the other hand, they have something in common that determines their belonging to a certain class.

Single occurrence in to a greater extent subject to the influence of random and unimportant factors than the mass of phenomena as a whole. Under certain conditions, the value of a characteristic of an individual unit can be considered as a random variable, taking into account that it is subject not only to general pattern, but is also formed under the influence of conditions independent of this pattern. It is for this reason that statistics widely use average indicators, which characterize the entire population with one number. Only with a large number of observations are random deviations from the main direction of development balanced, cancelled, and the statistical pattern appears more clearly. Thus, essence of the law of large numbers lies in the fact that in the numbers summarizing the results of mass statistical observation, the pattern of development of socio-economic phenomena is revealed more clearly than in a small-scale statistical study.

4. Branches of statistics.

In progress historical development As part of statistics as a unified science, the following branches emerged and received a certain independence:

1. General theory of statistics, which develops the concept of categories and methods for measuring quantitative patterns of social life.

2. Economic statistics studying the quantitative patterns of reproduction processes at various levels.

3. Social statistics, which studies the quantitative side of the development of the social infrastructure of society (statistics of health care, education, culture, moral, judicial, etc.).

4. Industry statistics (industry statistics, agro-industrial complex, transport, communications, etc.).

All branches of statistics, by developing and improving their methodology, contribute to the development of statistical science as a whole.

5. Basic concepts and categories of statistical science in general.

A statistical population is a set of elements of the same type that are similar to each other in some ways and different in others. For example: this is a set of economic sectors, a set of universities, a set of cooperation between design bureaus, etc.

The individual elements of a statistical population are called its units. In the examples discussed above, the units of the population are, respectively, industries, a university (one) and an employee.

Units of a population usually have many characteristics.

A characteristic is a property of units of a population that expresses their essence and has the ability to vary, i.e. change. Characteristics that take on a single value in individual units of the population are called varying, and the values ​​themselves are called variants.

Variable characteristics are divided into attributive or qualitative. A feature is called attributive or qualitative if its individual meaning (variants) are expressed in the form of a state or properties inherent in the phenomenon. Variants of attribute characteristics are expressed in verbal form. Examples of such signs include economic.

A characteristic is called quantitative if its individual value is expressed in the form of numbers. For example: wages, scholarship, age, PF size.

According to the nature of variation, quantitative characteristics are divided into discrete and continuous.

Discrete are such quantitative characteristics that can only take on a very specific, usually integer, value.

Continuous are those signs that within certain limits can take on both integer and fractional values. For example: country's GNP, etc.

There are also differences between primary and secondary signs.

The main features characterize the main content and essence of the phenomenon or process being studied.

Secondary signs give additional information and are directly related to the internal content of the phenomenon.

Depending on the goals of a particular study, the same signs in the same cases may be primary, and in others secondary.

Statistical indicator- this is a category reflecting the dimensions and quantitative relationships of signs of socio-economic phenomena and their qualitative certainty in specific conditions of place and time. It is necessary to distinguish between the content of a statistical indicator and its specific numeric expression. Contents, i.e. qualitative certainty lies in the fact that indicators always characterize socio-economic categories (population, economy, financial institutions etc.). Quantitative dimensions of statistical indicators, i.e. their numerical values ​​depend primarily on the time and place of the object that is subject to statistical research.

Socio-economic phenomena, as a rule, cannot be characterized by any one indicator, for example: the standard of living of the population. For a comprehensive comprehensive characterization of the phenomena under study, a scientifically based system of statistical indicators is required. This system is not permanent. It is constantly being improved based on the needs of social development.

6. Tasks of statistical science and practice in the conditions of development of a market economy.

The main tasks of statistics in the conditions of development of market relations in Russia are the following:

1. Improving accounting and reporting and reducing document flow on this basis.

2. Strengthening efforts to monitor the reliability of statistical information provided to enterprises, institutions and organizations of all sectors of the economy and forms of ownership.

3. Increasing the timeliness of statistical information both to the incoming statistical body and to the structures of state power and management they provide.

4. Recess analytical functions, developed statistical data, formation of subjects of statistical data in accordance with the current tasks of the socio-economic development of the country.

5. Further development and improvement of statistical methodology based on the increasingly widespread introduction of PC practice and... statistical analysis was not predicted.

Statistical summary is a method of scientific processing of statistical data collected during the observation process, in which information related to an individual unit is summarized and then characterized by analytical indicators and a system of tables. The summary produces statistical data characterizing the entire population. At this stage, a transition is made from individual characteristics of units of the population and a general indicator that characterizes the entire population.

There are summaries in the narrow and broad sense of the word. In the narrow sense of the word, a summary is understood as a technical operation for calculating the results. In the broad sense of the word, a summary consists of grouping the information obtained during the observation process, compiling systems of indicators to characterize typical groups, presenting these indicators in tables, as well as calculating general and group results.

2.1. General concept of groupings.

Groupings are a method of researching socio-economic phenomena, in which the statistical population is divided into homogeneous groups that reveal the state and development of the entire population.

Grouping is the most important stage statistical research, combining the collection of primary information about the scope of the study and the analysis of this information based on generalizing statistical indicators.

Grouping methods are varied. This diversity is due, on the one hand, to a huge variety of characteristics that are subject to statistical research, and on the other hand, to a variety of tasks that are solved on the basis of groupings.

2.2. The most important problem arising from grouping.

The most important problem when constructing a grouping is the choice of a grouped characteristic or the basis of the grouping.

Grouping sign- a varying characteristic by which units of the population are combined into groups.

According to the nature of variation, characteristics are divided, as is known, into: attributive and quantitative. This division determines the features of solving the second problem of groupings, namely, determining the number of allocated groups. When selecting some attribute characteristics as grouping characteristics, only a strictly defined number of groups can be identified. In particular, when grouping the population by gender, it can be distinguished...

When grouping enterprises by profit, 3 groups can be distinguished.

For many attribute characteristics, stable groupings called classifications are developed. For example: classification of economic sectors, classification of occupations of the population, etc.

When grouping according to quantitative criteria, the question of the number of group boundaries should be decided based on the essence of the socio-economic phenomenon being studied. In this case, one should take into account such an indicator as the range of variations. The greater the range of variation, the more groups are formed and vice versa. It is also necessary to take into account the number of units in the population on which the grouping is constructed. With a small population size, it is not advisable to form a large number of groups, because in this case, there will not be a sufficient number of units in the groups to identify statistical patterns.

An essential issue when grouping by quantitative criterion is the definition of intervals. The indicators of the number of groups and the size of intervals are inversely related. The larger the intervals, the fewer groups are required and vice versa.

An interval is the difference between its upper and lower boundaries.

Based on the size of the grouping characteristic, intervals are divided into equal and unequal. Equal intervals are used in cases where the change in the grouping characteristic within the population occurs evenly. The equal interval value is calculated using the formula:

k - number of groups

Xmax, Xmin - respectively the largest and smallest value a sign of the quality of the groups.

If the distribution of a grouping characteristic within a population is uneven, then unequal intervals are used. Unequal intervals can be progressively increasing or progressively decreasing. Often when grouping, so-called specialized intervals are used, i.e. those that are determined based on the purpose of the study and the essence of the phenomenon. For example: when grouping with the goal of characterizing the working-age population of a country, five-year age intervals of people are used.

The third problem in constructing groupings is the designation of interval boundaries. When identifying intervals based on discrete quantitative characteristics, their boundaries should be designated so that the lower boundary of the subsequent interval differs from the upper boundary of the previous one by one.

When grouping according to a continuous quantitative characteristic, the boundaries are designated so that the groups are clearly separated from one another. This is achieved by adding instructions to the numerical boundaries of the intervals about where a unit with a grouping characteristic should be placed in sizes that exactly coincide with the boundaries of the intervals. Usually, additional explanations for the numerical boundaries of intervals formed according to continuous quantitative principles are expressed by the words: “more”, “less”, “above”, etc.

2.3. Types of groups.

Depending on the tasks solved with the help of groupings, the following types are distinguished:

Typological

Structural

Analytical

The main task of the typology is to classify socio-economic phenomena by identifying groups that are homogeneous to qualitative relations.

Qualitative homogeneity is understood in the sense that, with respect to the property being studied, all units of the population obey the same law of development. For example: grouping enterprises of economic sectors.

Absolute and relative values.

An absolute value is an indicator that expresses the size of a socio-economic phenomenon.

In statistics, a relative value is an indicator that expresses the quantitative relationship between phenomena. It is obtained by dividing one absolute value by another absolute value. The value with which we make comparisons is called the basis or base of comparison.

Absolute quantities are always named quantities.

Relative values ​​are expressed in coefficients, percentages, ppm, etc.

The relative value shows how many times, or what percentage, the compared value is greater or less than the comparison base.

In statistics, there are 8 types of relative quantities:

1. The essence and meaning of average values.

Averages are one of the most common summary statistics. They aim to characterize with one number a statistical population consisting of a minority of units. Averages are closely related to the law of large numbers. The essence of this dependence is that with a large number of observations, random deviations from general statistics cancel each other out and, on average, the statistical pattern becomes more clearly evident.

Using the method of averages, the following main problems are solved:

1. Characteristics of the level of development of phenomena.

2. Comparison of two or more levels.

3. Study of the interrelations of socio-economic phenomena.

1. 4. Analysis of the location of socio-economic phenomena in space.

To solve these problems, statistical methodology has developed various types of averages.

2. Arithmetic mean.

To clarify the method for calculating the arithmetic mean, we use the following notation:

X - arithmetic sign

X (X1, X2, ... X3) - variants of a certain characteristic

n - number of population units

Average value of attribute

Depending on the source data, the arithmetic mean can be calculated in two ways:

1. If the statistical observation data are not grouped, or the grouped options have the same frequencies, then the simple arithmetic mean is calculated:

2. If the frequencies grouped in the data are different, then the weighted arithmetic mean is calculated:

Number (frequency) of options

Sum of frequencies

The arithmetic mean is calculated differently in discrete and interval variation series.

In discrete series, feature variants are multiplied by frequencies, these products are summed, and the resulting sum of products is divided by the sum of frequencies.

Let's consider an example of calculating the arithmetic mean in discrete series:

IN interval rows the value of a characteristic is given, as is known, in the form of intervals, therefore, before calculating the arithmetic mean, you need to move from an interval series to a discrete one.

The middle of the corresponding intervals is used as the Xi options. They are defined as half the sum of the lower and upper bounds.

If an interval does not have a lower limit, then its middle is determined as the difference between the upper limit and half the value of the following intervals. In the absence upper limits, the middle of the interval is defined as the sum of the lower limit and half the value of the previous interval. After the transition to a discrete series, further calculations occur according to the method discussed above.

If the weights fi are not specified in in absolute terms, and in relative terms, the formula for calculating the arithmetic mean will be as follows:

pi - relative values ​​of the structure, showing what percentage the frequencies of the variants are in the sum of all frequencies.

If the relative values ​​of the structure are specified not in percentages, but in shares, then the arithmetic mean will be calculated using the formula:

3. Harmonic mean.

The harmonic mean is a primitive form of the arithmetic mean. It is calculated in cases where the weights fi are not specified directly, but are included as a factor in one of the available indicators. Just like the arithmetic mean, the harmonic mean can be simple and weighted.

Harmonic mean unweighted:

Mean harmonic mixed:

Wi - product of options and frequencies

When calculating average values, it is necessary to remember that any intermediate calculations must be given both in the numerator and in the denominator and having economic sense indicators.

4. Structural average.

The structural average characterizes the composition of the statistical population according to one of the varying characteristics. These means include the mode and median.

Mode is the value of a varying characteristic that has the highest frequency in a given distribution series.

In discrete series of distributions, the mode is determined visually. First it is determined highest frequency, and according to it modal meaning sign. In interval series, the following formula is used to calculate the mode:

Xmo - lower limit of modality (interval of the series with the highest frequency)

Mo - interval value

fMo - modal interval frequency

fMo-1 - frequency of the interval preceding the modal

fMo+1 - frequency of the interval following the modal

The median is the value of a varying characteristic that divides the distribution series into two equal parts by volume of frequencies. The median is calculated differently in discrete and interval series.

1. If the distribution series is discrete and consists of an even number of terms, then the median is defined as the average value of the two middle values ​​of the ranked series of characteristics.

2. If in a discrete distribution series odd number levels, then the median will be the middle value of the ranked series of features.

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

The lower limit of the median interval (the interval for which the accumulated frequency first exceeds half the sum of frequencies)

Me - interval value

Sum of frequency series

Sum of accumulated frequencies preceding the median interval

Median interval frequency

1. General concept of variation.

Variation is the difference in the values ​​of a characteristic among individual units of a population.

The variation arises due to the fact that individual values characteristics are formed by the influence of a large number of interrelated factors. These factors often operate in opposite directions and their joint action forms the meaning of the characteristics of a specific unit of the population. The need to study variations is due to the fact that the average value, which summarizes statistical observation data, does not show how the individual value of a characteristic fluctuates around it. Variations are inherent in natural and social phenomena. At the same time, the revolution in society occurs faster than similar changes in nature. Objectively, there are also variations in space and time.

Variations in space show the difference in statistical indicators related to different administrative-territorial units.

Variations over time show the difference in indicators depending on the period or point in time to which they relate.

2. Measures of variation.

Examples of variations include the following indicators:

1. range of variations

2. average linear deviation

3. standard deviation

4. variance

5. coefficient

1. The range of variations is its simplest indicator. It is defined as the difference between the maximum and minimum value of the attribute. The disadvantage of this indicator is that it depends only on two extreme values characteristic (min, max) and does not characterize variability within the population. R=Xmax-Xmin.

2. Average linear deviation is the average value absolute values deviations from the arithmetic mean. It is determined by the formula:

Simple

Deviations are taken modulo, because otherwise, due to mathematical properties average value, they would always be equal to zero.

4. Dispersion (the average square of deviations) is most widely used in statistics as an indicator of the measure of variability.

The variance is determined by the formulas:

example: page 36

Variance is a named measure. It is measured in units corresponding to the square of the units of measurement of the characteristic being studied. IN in this case it shows that the average deviation of profit for 50 enterprises from the average profit is 1.48.

The variance can also be determined by the formula:

3. Standard deviation is defined as the root of the variance.

According to the initial data given above, the standard deviation is equal to:

5. Coefficient of variation is defined as the ratio of the average square deviation to the average value of the characteristic, expressed as a percentage:

It characterizes the quantitative homogeneity of a statistical population. If this coefficient < 50%, то это говорит об однородности статистической совокупности. Если же совокупность не однородна, то любые статистические исследования можно проводить только внутри выделенных однородных групп.

3. Variance of an alternative characteristic.

Alternative are 2 mutually exclusive characteristics. Those are the characteristics that each individual unit of the population either possesses or does not possess. The presence of an alternative characteristic is usually denoted by one, and the absence by 0. The proportion of units possessing this characteristic is denoted by p (n), and the proportion of units possessing this characteristic is denoted by q. In this case p+q=1.

The variance of an alternative characteristic is determined by the formula:

4. Types of variances. I grafted on their build.

If the statistical population under study is divided into a group, then for each of them it is possible to determine group means and variances. These variances will characterize the variability of the studied trait for each individual group. On this basis, it is possible to determine the average from within the group variances.

ni=fi - number of units in separate groups

This dispersion characterizes the random variation of a trait, depending on the factor underlying the grouping.

Intergroup variance is also calculated.

and ni=fi, respectively, averages and numbers for individual groups.

This dispersion characterizes the variation in the influence of the grouping characteristic. The sum of the average from within group and intergroup variance allows you to determine the overall variance.

This equality is called the rule for adding variances.

; , i.e. There is a close relationship between the production of parts and other indicators.

If the values ​​of the characteristic under study are expressed in shares or coefficients, then the rule for adding variances is expressed by the following formulas:

ni - number of units in separate groups

pi - the proportion of the studied characteristic in the entire population

average of within-group variances for proportions of traits

1. Types and forms of dependence between socio-economic phenomena.

The variety of relationships in which socio-economic phenomena are located gives rise to the need for their classification.

By type, functional and correlation dependence are distinguished.

Functional is a dependence in which one value of the factor characteristic X corresponds to one strictly defined value of the resultant characteristic Y.

In contrast to functional dependence, correlational dependence expresses such a connection between socio-economic phenomena in which one value of the factor characteristic X can correspond to several values ​​of the resultant characteristic Y.

In terms of direction, a distinction is made between direct and inverse dependence.

A direct relationship is one in which the value of the factor attribute X and the resultant attribute Y change in the same direction. That. As the X value increases, the Y values ​​increase on average, and as X decreases, Y decreases.

An inverse relationship between factor and resultant characteristics if they change in opposite directions.

2. Statistical methods for studying relationships.

The following methods occupy an important place in the statistical study of relationships:

1. Parallel data reduction method.

2. Method of analytical groupings.

3. Graphic method.

4. Balance sheet method.

6. Correlation-regression.

1. Essence parallel data reduction method is as follows:

The initial data for characteristic X are arranged in ascending or descending order, and for characteristic Y the corresponding indicators are recorded. By comparing the values ​​of X and Y, a conclusion is made about the presence and direction of the dependence.

3. Essence graphic method provides a visual representation of the presence and direction of relationships between characteristics. To do this, the value of the factor characteristic X is located on the abscissa axis, and the value of the resultant characteristic along the ordinate axis. Based on the joint arrangement of points on the graph, a conclusion is drawn about the direction and presence of a relationship. The following options are possible:

a\, b/ (up), c\ (down).

If the points on the graph are located randomly (a), then there is no relationship between the characteristics being studied.

If the points on the graph are concentrated around the straight line (b)/, the relationship between the characteristics is direct.

If the points are concentrated around the line (c)\, then this indicates the presence of an inverse relationship.

Based on the parallel data method and the graphical method, indicators can be calculated that characterize the degree of closeness of the correlation dependence.

The most multiple of them is the Fechner sign coefficient. It is calculated by the formula:

C is the sum of coinciding signs of deviations of individual values ​​of a characteristic from the average.

H - sum of mismatches

This coefficient varies within (-1;1).

The value of KF=0 indicates the absence of dependence between the studied characteristics.

If KF=±1, then this indicates the presence of a functional direct (+) and inverse (-) relationship. With a value of KF>½0.6½, it is concluded that there is a strong direct (inverse) relationship between the characteristics. In addition, based on the initial data on the factor and resultant characteristics, the Spearman rank correlation coefficient can be calculated, which is determined by the formula:

Rank difference squares

(R2-R1), n ​​- number of pairs of ranks

This coefficient, like the previous one, varies within the same limits and has the same economic interpretation as KF.

In cases where the value of X or Y is expressed the same indicators, the rank correlation coefficient is calculated using the following formula:

tj - the same number of ranks in the j - row

If the relationship between three or more mathematical characteristics is studied, then the concordance coefficient is used to study it, determined by the formula:

m - number of factors

n - number of observations

S - deviation of the sum of squares of ranks from the average of squares of ranks

3. Study of the relationship between quantitative characteristics.

To study the relationship between qualitative alternative characteristics that take only 2 mutually exclusive values, the coefficient is used associations and contingents. When calculating these coefficients, the so-called table of 4 stones, and the coefficients themselves are calculated using the formula:

If the association coefficient is ³ 0.5, and the contingent coefficient is ³ 0.3, then we can conclude that there is a significant relationship between the characteristics being studied.

If the characteristics have 3 or more gradations, then the Piersen and Chuprov coefficients are used to study the relationships. They are calculated using the formulas:

C - Pearson coefficient

K - Chuprov coefficient

j - mutual conjugacy indicator

K - number of values ​​(groups) of the first characteristic

K1 - number of values ​​(groups) of the second characteristic

fij - frequencies of the corresponding table cells

mi - table columns

nj - strings

To calculate the Piersen and Chuprov coefficients, an auxiliary table is compiled:

When ranking qualitative features in order to study their relationship, the Kendall correlation coefficient is used.

n - number of observations

S is the sum of the differences between the number of sequences and the number of inversions according to the second criterion.

P - the sum of rank values ​​following the data and exceeding its value

Q - the sum of rank values ​​following the data and less than its value (counted with a “-” sign).

If there are related ranks, the Kendall coefficient formula will be:

Vx and Vy are determined separately for ranks X and Y using the formula:

5. Methods for identifying the main trend of time series.

The levels of a number of dynamics are formed under the attention of 3 groups of factors:

1. Factors determining the main direction, i.e. development trend of the phenomenon being studied.

2. Factors acting periodically, i.e. directional oscillations by week of the month, month of the year, etc.

3. Factors acting in different, sometimes opposite directions and not having a significant impact on the level of a given series of dynamics.

The main task of the statistical study of danamics is to identify trends.

The main methods for identifying trends in time series are:

Interval enlargement method

Moving average method

Analytical alignment method

1. Essence interval enlargement method is as follows:

The original series of dynamics is transformed and replaced by others consisting of other levels related to enlarged periods or points in time.

For example: a series of dynamics of the profit of a small enterprise for 1997 by quarter of the same year. In this case, the levels of the series for enlarged periods or points in time can represent either total or average indicators. However, in any case, the series levels calculated in this way more clearly reveal trends, since seasonal and random fluctuations, when summing up or determining averages, cancel out and balance.

2. Moving average method, like the previous one, assumes a transformation of the original dynamics series. To identify a trend, an interval is formed consisting of the same number levels. In this case, each subsequent interval is obtained by shifting by 1 level from the initial one. From the intervals formed in this way, the sum is determined first, and then the average. Technically, it is more convenient to determine moving averages for an odd interval. In this case, the calculated average value will relate to a specific level of the dynamics series, i.e. to the middle of the sliding interval.

When determining a moving average over an even interval, the calculated value of the average refers to the interval between two levels, and thus loses economic meaning. This makes necessary additional calculations related to centering using the simple arithmetic formula of two adjacent non-centered averages.

Question 2.

Statistics show that every year about 70% of emergency situations occurring in the Russian Federation are man-made in nature. More than 72 million people in the Russian Federation live in areas where emergencies may occur. In Russia, the risk of mortality from an emergency is 100 times higher than in developed countries.

Currently, there are more than 3,000 chemically hazardous facilities operating on the territory of the Russian Federation. The total stock of SDYV in these facilities is 1 million tons and 10 12 fatal toxoses. The number of accidents per year reaches 1000, and the consequences of accidents are felt by more than 200,000 people.

The area of ​​chemical contamination is divided as follows:

1. Extremely dangerous contamination zone, i.e. with a lethal concentration of hazardous substances.

2. Danger zone, i.e. zone with a damaging concentration.

The degree of damage to toxic chemicals is characterized by a damaging toxodose, which is defined as the product of a damaging concentration by the exposure time, during which a person receives a lethal dose while in a contaminated area.

D=C*T, (mg*min)/m 3

When forecasting, the worst case scenario is taken into account.

Assessment of the chemical situation includes determining the possibility of an object entering the contaminated zone and the time of approach of the contaminated cloud to the object.

Measures to reduce accident factors:

· Creation and maintenance of a warning system in constant readiness.

· Providing working PPE.

· Special equipment technical means for setting up water curtains.

Currently, the following ROOs operate in the Russian Federation:

2. 29 nuclear power units

3. 235 nuclear icebreakers and cruisers.

4. B Leningrad region 250 facilities use radioactive isotopes in production.

Subject: "Infectious diseases".

Biologically harmful factors are microorganisms contained in preparations and pathogenic microorganisms present in the environment and products.

The microorganism penetrates through:

1. Gastrointestinal tract (internal)

2. Upper respiratory tract through skin contact.

3. Sexual method.

Depending on the location of the microorganism, all infectious diseases are divided into:

1. Infections respiratory tract

2. Roofing

3. Intestinal

4. External integument

To infections respiratory pathways include: ARVI, smallpox, diphtheria, tuberculosis, etc.

TO blood include: typhus, malaria, HIV infection, plague.

Intestinal: dysentery, typhoid fever, cholera, brucellosis, botulism, salmonellosis.

Brucellosis is caused by human infection through meat, wool, fluff, and milk. The incubation period of the acute form ranges from 7 to 60 days, after which the body temperature rises to 39-40°C, chills, sweating, pain in muscles and joints appear, headache, enlarged lymph nodes, in men inflammatory processes appear in the reproductive system.

The chronic form develops after 5-6 months. If left untreated, the disease lasts a very long time.

Tuberculosis is transmitted not only from people, but also from sick animals. Characteristic symptoms in the early stages: increased fatigue, general weakness, weight loss, low-grade fever, sweating, dry or with sputum, cough.

HIV infection (AIDS).

The source of the disease is sick people. The virus was found in the blood breast milk, in saliva. Transmission of infection can occur through damaged skin during medical procedures. Incubation period - 2 weeks - 3 months. Symptoms: swollen lymph nodes, rash, possible fever.

Stage 2 occurs after 3-5 years; the patient notices a strong enlargement of the lymph nodes.

Stage 3: weight loss, fever, infectious diseases of the ears, lungs, skin.

Stage 4: the height of these diseases or death.

Smallpox is an acute, highly contagious disease of a viral nature, which is characterized by severe intoxication of the body, fever, and the appearance of a blistering rash on the skin and mucous membranes, leaving scars. Pathogen: virus, has significant resistance to physical and chemical factors. The virus multiplies from respiratory system and gets into the blood. From there it again enters the skin and mucous membranes. Source of infection: sick person. The greatest infectivity is on days 6-10. Incubation period: 15-19 days. The onset of the disease is acute, with a rapid rise in temperature to 40° and above, lower back pain, frequent nausea and vomiting.

On the 4th day, with the appearance of a rash, the temperature decreases. The rash first appears on the face --> torso --> limbs. Initially, pale pink spots appear, which turn into dark red bubbles. After three to four days, vesicles filled with serous fluid appear in their center.

On the 7-8th day, the patient’s condition worsens again, the temperature again reaches 40° and the rash suppurates. The condition is severe, consciousness is confused, and by 10-14 days the blisters dry up and leave whitish scars for life.

Plague is an acute infectious disease characterized by intoxication, fever, damage to the lymph nodes and lungs.

The causative agent of the plague is a bacterium that does not form spores, is sensitive to environmental factors, and dies at a temperature of 50°-55° within 15 minutes. The main source of infections: rodents, fleas. A person becomes infected through a bite. A possible route of infection is when hunters process the carcasses of killed animals. The incubation period is usually from 3 to 6 days. There are localized and generalized forms of plague. The plague usually begins suddenly, the temperature rises to 39 and above, symptoms of intoxication quickly increase, consciousness is impaired, and delirium may occur.

The bubonic form of plague is characterized by the appearance of a sensitive bubo, i.e. This is an enlargement of the lymph nodes up to 10 cm. In 70% of patients they are localized in the groin area. The skin over the bubo becomes purple-red and shiny.

The lymph nodes of the primary lesion undergo softening. Then gradual healing occurs.

The bubonic form can lead to the development of a generalized form as a result of the pathogen entering the blood. A number of antibiotics are recommended for the treatment of plague: dixocycline, tetracycline, gentamicin, streptomycin.

Botulism is an acute infectious disease resulting from poisoning by toxins of batulism bacteria. Characterized by damage to the central nervous system and autonomic nervous system. The causative agent of batulism is widespread in nature. Batulism bacteria are anaerobic and multiply in the absence of oxygen. Vegetative forms die 2-3 minutes after boiling, spores die after 5 hours.

Botulinum toxin is a lethal biological poison, lethal dose - 0.003 mg/kg. There are 7 known antigenic variants of batulic microbes (A, B, C, 0, E, P, 6).

The most dangerous for people are A, B, E. The reservoir of infection in nature is warm-blooded animals, less often - cold-blooded animals. The incubation period for botulism ranges from several hours to 2-3 days. The more severe the disease, the shorter the incubation period. The clinical picture of batulism consists of 3 symptoms: paralysis, general toxicity, gastrointoxication.

The cause of death in patients is acute respiratory failure. People with botulism should go to the hospital immediately. You should rinse the stomach with a 2-3% soda solution and immediately administer anti-botulinum serum.

Subject: “Providing first aid for the main types of injuries”.

1. Medical supplies personal protection. Basic first aid measures.

2. First medical care for wounds and bleeding.

3. First aid for fractures and dislocations.

4. First aid for burns and poisoning.

The relevance of the topic lies in the fact that statistical concepts are the most important component of the intellectual luggage of a modern person. They are needed in everyday life, since elections and referendums, bank loans and insurance policies, employment tables and charts of sociological surveys have powerfully entered our lives; they are also needed for continuing education in such areas as sociology, economics, law, medicine, demography and others.

Tables and diagrams are widely used in reference literature and in the media. Government and business entities regularly collect extensive information about society and the environment. This data is published in the form of tables and charts.

Society begins to study itself more deeply and strives to make predictions about itself and about natural phenomena that require ideas about probability. Every person must be well versed in the flow of information.

We must learn to live in a probable situation. And this means extracting, analyzing and processing information, making informed decisions in a variety of situations with random outcomes.

Our class was chosen as the object of the study.

Subject of research :

• use of statistical methods
• public opinion poll
• statistical characteristics: arithmetic mean, median, range;
• interpretation of statistical characteristics;
• visual presentation of information.

Purpose of the study:

• become familiar with the types and methods of statistical observation; - find out how statistical data is collected and grouped, how statistical information can be visually presented.

Research objectives:

1. Study the literature on this topic.

2. Collect information to confirm statistical characteristics.

3. Process this information.

4. Interpret the results of statistical studies.

5. Visually present the information received.

Research methods :

Stages of work :

Work (research) plan:

1. Analysis of educational and additional literature on this issue.

2. Conducting a survey among students in grade 9A.

3. Processing the received data, constructing graphs and diagrams.

4. Analysis, generalization and comparison of the results obtained.

Methods and materials.

1. Drawing up questionnaires for public opinion polls.

2. Collection of material on the topic under study.

3. Analysis of the collected material.

4. Interpretation of statistical results.

5. Visual presentation of the results of statistical research.

Survey Questions:

1. Students' favorite subject.

2. Height and weight of students for 2013-2014, 2014-2015, 2015-2016.

3. Favorite TV shows of parents and students.

4. Students' favorite show.

5. Students' shoe sizes.

6. Students' favorite singer.

7. Student performance for the first half of the 2015-2016 academic year in core subjects.

2. Statistics

2.1. What are statistics

Statistics (from the Latin status) is the science that studies, processes and analyzes quantitative data about a wide variety of mass phenomena in life.

The term "statistics" appeared in the mid-18th century. Meant "government". It became widespread in monasteries. Gradually acquired a collective meaning. On the one hand, statistics are a set of numerical indicators that characterize social phenomena and processes (labor statistics, transport statistics).

On the other hand, statistics refers to the practical activities of collecting, processing, and analyzing data in various areas of public life.

On the third hand, statistics are the results of mass accounting published in various collections. Finally, in the natural sciences, statistics refers to methods and methods for assessing the correspondence of mass observation data to mathematical formulas. Thus, statistics is a social science that studies the quantitative side of mass social phenomena in inextricable connection with their qualitative side.

2.2. Types of statistics

Types of statistics: financial, biological, economic, medical, tax, meteorological, demographic. Mathematical statistics is a branch of mathematics that studies mathematical methods for processing and using statistical data for scientific and practical conclusions.

2.3. Statistical characteristics

The main statistical characteristics are the arithmetic mean, mode, range, median.

Average arithmetic series numbers is the quotient of dividing the sum of these numbers by their number.

The mode is usually the number in a series that occurs most frequently in that series. Mode is the value of a characteristic (variant) that is most often repeated in the population being studied.

Range is the difference between the largest and smallest values ​​of a data series.

The median of a series consisting of an odd number of numbers is the number in this series that will be in the middle if this series is ordered.

2.4. Information processing

Methods for collecting and processing numerical data in any specific areas of science are the subject of corresponding special statistics, for example physical, stellar, economic, medical, demographic, etc. The formal mathematical side of statistical methods of analysis, independent of the specifics of the objects being studied and the specific area knowledge constitutes the subject of mathematical statistics proper. Statistical observation is the collection of necessary data on phenomena and processes of social life. You can conduct a public opinion poll, find the central tendencies of a series of data: arithmetic mean, mode, median, range; give an interpretation to the results of statistical studies and visually present the information obtained.

But this is not just any collection of data, but only systematic, scientifically organized, systematic and aimed at recording features characteristic of the phenomena and processes being studied. The final results of the study depend on the quality of the data obtained at the first stage.

To study various social and socio-economic phenomena, as well as some processes occurring in nature, special statistical studies are carried out. Research methods : literature analysis, questionnaires, statistical survey, statistical processing of the data obtained, analysis, comparison of the results obtained.

Any statistical study begins with the targeted collection of information about the phenomenon or process being studied.

The statistics method involves the following sequence of actions:

• development statistical hypothesis,
• statistical observation,
• summary and grouping of statistical data,
• data analysis,
• interpretation of data.

The passage of each stage is associated with the use special methods explained by the content of the work performed.

Methods of statistical observation

The basis for recording facts can be either documents, or an opinion expressed, or timing data. In this regard, the observation is distinguished:

• direct (measure themselves),
• documented (from documents),
• survey (according to someone).

The following methods of collecting information are used in statistics:

• correspondent (staff of voluntary correspondents),
• forwarding (oral, specially trained workers)
• questionnaire (in the form of questionnaires),
• self-registration (filling out forms by respondents themselves),
• personal (marriages, children, divorces), etc.

2.5. Graphical representation of data

Modern science cannot be imagined without the use of graphs. They have become a means of scientific generalization.

The expressiveness, clarity, conciseness, versatility, and visibility of graphic images have made them indispensable in research work and in international comparisons of socio-economic phenomena.

A statistical graph is a drawing in which statistical aggregates, characterized by certain indicators, are described using conventional geometric images or signs. Presentation of table data in the form of a graph makes a stronger impression than numbers, allows you to better understand the results of statistical observation, interpret them correctly, greatly facilitates the understanding of statistical material, makes it visual and accessible. This, however, does not mean that the graphs are only illustrative. They provide new knowledge about the subject of research, being a method of summarizing the original information.

The importance of the graphical method in analyzing and summarizing data is great. A graphical representation, first of all, makes it possible to monitor the reliability of statistical indicators, since, presented on a graph, they more clearly show the existing inaccuracies associated either with the presence of observation errors or with the essence of the phenomenon being studied. Using a graphic image, it is possible to study the patterns of development of a phenomenon and establish existing relationships. A simple comparison of data does not always make it possible to grasp the presence of causal dependencies; at the same time, their graphical representation helps to identify causal connections, especially in the case of establishing initial hypotheses that are then subject to further development. Graphs are also widely used to study the structure of phenomena, their changes over time and location in space. They show the compared characteristics more clearly and clearly show the main development trends and relationships inherent in the phenomenon or process being studied.

When constructing a graphic image, the requirements must be observed. First of all, the graph must be quite visual, since the whole point of a graphical representation as a method of analysis is to clearly depict statistical indicators.

Methods graphical representation data: charts, histograms, graphs.

Diagrams are the most common way graphic images. These are graphs of quantitative relationships. The types and methods of their construction are varied. Diagrams are used for visual comparison in various aspects (spatial, temporal, etc.) of quantities independent from each other: territories, population, etc.

A more common way of graphically depicting the structure of statistical populations is a pie chart, which is considered the main form of chart for this purpose. This is explained by the fact that the idea of ​​the whole is very well and clearly expressed by the circle, which represents the entirety. The share of each part of the population in a pie chart is characterized by the value of the central angle (the angle between the radii of the circle). The sum of all angles of a circle, equal to 360°, is equal to 100%, and therefore 1% is taken to be equal to 3.6°.

To visually depict phenomena in time series, charts are used: bar, strip, square, circular, linear, radial, etc. The choice of chart type depends mainly on the characteristics of the source data and the purpose of the study.

When the number of levels in a dynamics series is large, it is advisable to use linear diagrams that reproduce the continuity of the development process in the form of a continuous broken line. In addition, line diagrams are convenient to use: if the purpose of the study is to depict the general trend and nature of the development of a phenomenon; when it is necessary to display several time series on one chart for the purpose of comparing them; if the most significant is the comparison of growth rates, not levels. To build line graphs a rectangular coordinate system is used.

The polygon illustrates the dynamics of changes in statistical data over time, allows one to judge the values ​​of a quantity at certain points; it cannot be used to find the value of this quantity at intermediate points.

To display an interval series, a histogram is used - a stepped figure made up of closed rectangles. The base of each rectangle is equal to the length of the interval, and the height is equal to the frequency or relative frequency.

Practical part

Conclusion

While conducting my research, I was once again convinced that mathematics has firmly entered my daily life, and I no longer notice that I live according to its laws. In this academic year I started studying statistical characteristics and their visual presentation. During the research, I learned to systematize, visually present data, generalize and draw conclusions.

The role of statistics in life is so significant that people, often without thinking or realizing, constantly use elements of statistical methodology not only in work processes, but also in everyday life. Working and relaxing, shopping, meeting other people, making some decisions, a person uses a certain system of information available to him, established tastes and habits, facts, systematizes, compares these facts, analyzes them, draws conclusions and makes certain decisions, takes specific actions. Thus, every person contains elements of statistical thinking, which is the ability to analyze and synthesize information about the world around us.

But we must remember that people can interpret the same statistical information in different ways, and that if I want to see reliable information, it is better to find not one indicator, but two, and best of all, all four: the arithmetic mean, mode, median and range .

Literature

1. School Encyclopedia “Mathematics”. Edited by Nikolsky.
2. Algebra. 9th grade: educational. for general education institutions /Yu. N. Makarychev, N. G. Mindyuk, K. I. Neshkov, I. E. Feoktistov. – 7th ed., rev. and additional – M.: Mnemosyne.
3. Textbook “Mathematics-9.Arithmetic. Algebra. Data Analysis.” Edited by G. V. Dorofeev. Authors: G. V. Dorofeev, S. B. Suvorova, E. A. Bunimovich, L. V. Kuznetsova, S. S. Minaeva.
4. Computer Science and ICT. Basic course. Textbook for 9th grade. N.D. Ugrinovich.
5. Cool magazine.

IN modern society Statistics play an important role in the mechanism of economic management. She collects scientific processing, generalization and analysis of information characterizing the development of the country's economy, the standard of living of the population and other social phenomena and processes.

Statistics as a science

Statistics- these are series of numbers that characterize various aspects of the life of the state.

Statistics- this is the genus practical activities people whose purpose is to collect, process and analyze information.

Statistics is a science that develops statistical methodology i.e. a set of techniques and methods for collecting, processing and analyzing information.

Thus, Withstatistics is a general theoretical science (complex scientific disciplines), which studies the quantitative side of qualitatively defined mass socio-economic phenomena and processes, i.e. composition, distribution, placement in space, movement in time, identifying existing interdependencies and patterns in specific conditions of place and time.

Object studying statistics is society, processes occurring in it and patterns of development.

• General theory of statistics - develops the theory of statistical research, which is the methodological basis of other branches of statistics.
• (Macroeconomic statistics). Uses methods general theory statistics, studies the quantitative side of socio-economic phenomena and processes at the level of the national economy.
• Mathematical statistics and probability theory. Studying random variables, laws of their distribution.
• International statistics. The premise of international statistics is the quantitative side of phenomena and processes foreign countries And international organizations.
• Industry statistics. The subject of study is the quantitative side of activity various industries economics (Industrial and agricultural statistics).

The general theory of statistics opens the course of study of statistical disciplines. It is a fundamental discipline for the study of industry statistics and creates the foundation for the assimilation and application of statistical methods of analysis.

General theory of statistics is the science of the most general principles and methods of socio-economic phenomena and solves other social issues. She develops a system of categories, reviews statistical data.

General theory of statistics - methodological basis all industry statistics.

• the subject, methods and tasks of statistics and its connection with some other related disciplines;
• system of statistical indicators and classifications used in economic statistics, their content and scope, relationships between indicators and classifications of statistics;
• most important directions statistical analysis based on economic and financial data;
• main sources of primary data and the basis for the formation of a statistical base.

Subject of statistics- dimensions and quantitative relationships of qualitatively defined socio-economic phenomena, patterns of their connection and development in specific conditions of place and time.

• Mass social phenomena and their dynamics using statistical indicators. The requirement of mass character is due to the action of the law of large numbers - with a large number of observations, the effects of random characteristics cancel each other out. (population, number of products produced)
• Quantitative and qualitative phenomena(Digital coverage of community events).
• The quantitative side of social phenomena, inextricably linked with their qualitative content, is observed by the process of transition of quantitative changes into qualitative ones (patterns).
• Development of a phenomenon over time (dynamics)