1.5.1. The following data is known for the construction enterprise of the city:

Table 1.6.

	Work experience, years	Production, rub.

Build a number of distribution of workers by eye, forming four groups with equal intervals. To study the dependence between the experience and the production of workers' partners, produce: 1) the grouping of workers in the face. Each group is characterized by: the number of workers, the average work experience, the production of products is only on average per worker;

2) A combination group on two signs: I experience the work and production of products per worker.

To build a series of distribution, it is necessary to calculate the magnitude of the range of the grouping feature (work experience):

wherex max and x min is a sign value; N is the number of groups formed.

For our example, the magnitude of the interval will be equal of the year.

Consequently, the first group of workers will be with an experience of 2-6 years, the second - 6-10, etc. For each group, we calculate the number of workers and issuing in Table. 1.7.

Table 1.7.

Distribution of workers on experience

Group number	Groups workers by experience, years	Number of workers person.	Number of workers in% to the outcome
	2–6		30,0
	6–10		30,0

In a number of distribution, for clarity, the studied feature is calculated as a percentage. The results of the primary group showed that 60.0% of workers have an experience of up to 10 years, and equally from 2-6 years - 30% and from 6-10 years - 30%, and 40% of workers have experience from 10 to 18 years.

To study the dependence between work experience and the development, it is necessary to build an analytical group. Based on it, take the same groups that in a number of distribution. The results of the group will be submitted in Table. 1.8.

Table 1.8.

Grouping workers on experience

№ Groups	Groups Workers by experience, years	Number workers, people	Middle Work experience, years	Production, rub.
					per slave.
	2 –6		3,25	1335,0	222,5
	6 –10		7,26	1613,0	268,8

To fill in Table. 1.8 It is necessary to make a working table. 1.9.

Table 1.9.

	Groups workers by experience, years	Worker number		Developing in rubles.
		1, 2, 3, 4, 7, 10	2,0; 2,3; 3,0; 5,0; 4,5; 2,7	205, 200, 205, 250, 225, 250
Total in group:
		5, 6, 8, 13, 17, 19	6,2; 8,0; 6,9; 7,0; 9,0; 6,5	208, 290, 270, 250, 270, 253
Total in group
		9, 12, 15, 16, 18	12,5; 13,0; 11,0; 10,5; 12,8	230, 300, 287, 276, 258
Total in group
Total in group

Dividing graphs (4: 3); (5: 3) Table. 1.9, we obtain the appropriate data to fill in Table. 1.8. And so on in all groups. Filled in Table. 1.8, we get an analytical table.

Having calculated the working table, we carry out the final results of the table with the given conditions of the task, they must coincide. Thus, in addition to building groups, finding average values, we will carry out more arithmetic control.

Analyzing Analytical Table 1.8, it can be concluded that the studied signs (indicators) depend on each other. With an increase in the experience of the work, the production of products per worker is constantly increasing. Developing the working fourth group by 99.1 rubles. higher than the first or 44.5%. M s reviewed an example of grouping on one basis. But in some cases, this grouping is insufficient for solving the tasks. In such cases, go to the group on two or more signs, that is, a combination. We will be secondary grouping of data on the average production production. To build a secondary analytical group on the average production production within the initially created groups, we define the interval of the secondary group, allocating three groups, i.e. one less than in the initial grouping.

Then rub.

There is no sense more groups, there will be a very small interval, less - it is possible. The total data on the group is calculated as the sum of the experience of the group, for example, by the first 19.5 years, it is divided into the number of workers - 6 people, we received 3.25 years.

Each group is characterized by the number of workers, medium work experience, the average production is only one worker. P Askheta is presented in Table. 1.10.

Table 1.10

Grouping workers on the experience and moderate production

No. p / p	Groups workers		Number slave person.	Environments experience slave years	Middle Production Prod., Rub.
	by experience	on media. Cut. Prod. in rubles.			total	per slave.
		200,0–250,0 250,0–300,0 300,0–350,0		2,5 4,75 -	835,0 500,0 -	208,75 250,0 -
Total in group
		200,0–250,0 250,0–300,0 300,0–350,0		- 7,26 -	- 1613,0 -	- 268,8 -
		200,0–250,0 250,0–300,0 300,0–350,0		12,5 11,43 13,0	230,0 821,0 300,0	230,0 273,6 300,0
Total group2
		200,0–250,0 250,0–300,0 300,0–350		- 16,0 16,75	- 295,0 670,0	- 295,0 335,0
Total in group
Total groups		200,0–250,0 250,0–300,0 300,0–350,0	5 12 3	3,0 9,86 14,87	1065,0 3229,0 970	213,0 269,0 323

Table data show that product production is directly dependent on experience.

Sometimes the initial group does not allow to clearly identify the nature of the distribution of units of aggregate, or to bring to a comparable type of groupings, with the aim of holding a comparative analysis, it is necessary to change the existing group to change somewhat: combine previously selected relatively small groups into a small number of larger typical groups or change the boundaries of previous groups In order to make a grouping comparable to others.

1.5.2. There are data from two branches of enterprises about the cost of fixed assets:

Table 1.11

1 industry		2 Industry
Groups of enterprises at the cost of the main Foundations in million rubles.	Specific weight in %	Groups of enterprises at the cost of the main Foundations in million rubles.	Specific weight in %
To 10 10–12 12–15 15–20 20–30 Over 30.	10 10 20 30 22 8	To 10 10–15 15–25 25–30 Over 30.	5 20 40 25 10

Compare the structure of enterprises at the cost of fixed assets.

As part of the educational program of the university, it is unlikely to meet a separate discipline with the name "Mathematical Statistics", however mathematical statistics Often studied together with probability theory, but only after studying the main course of probability theory.

Mathematical statistics: General information

Mathematical statistics are a section of mathematics, which develops the methods of registration, descriptions and analysis of these observations and experiments, the purpose of which is to build probabilistic models of mass random phenomena.

Mathematical statistics as science emerged in the XVII century. And developed by a parallel course with probability theory. A great contribution to the development of science was made in the XIX-XX centuries. Chebyshev P.L., Gauss K., Kolmogorov A.N. and etc.

The overall task of mathematical statistics is to create methods for collecting and processing statistical data to obtain scientific and practical conclusions.

The main sections of mathematical statistics are:

• selective method (familiarization with the concept of sampling, methods of collecting and processing data, etc.);
• statistical assessment of sampling parameters (estimates, confidence intervals, etc.);
• payment summary characteristics samples (calculation option, moments, etc.);
• correlation theory (regression equations, etc.);
• statistical test hypotheses;
• single-factor dispersion analysis.

TO the most common The objectives of mathematical statistics, which are studied at the university and are often found in practice, belong:

• tasks of determining the estimates of the sampling parameters;
• tasks for testing statistical hypotheses;
• tasks for determining the type of distribution law on statistical data.

Tasks for determining the estimates of the sampling parameters

The study of mathematical statistics begins with the definition of such concepts as "sample", "frequency", "relative frequency", "empirical function", "Polygon", "Cumulat", "Histogram", etc. Next is the study of the concepts of estimates (shifted and unstable): selective medium, dispersion, corrected dispersion, etc.

A task

Measuring the growth of children of the younger group kindergarten Presented by the sample:
92, 96, 95, 96, 94, 97, 98, 94, 95, 96.
We find some characteristics of this sample.

Decision

Sample size (number of measurements; N.): 10.
The smallest sample value: 92. The largest value of the sample: 98.
Sampling scope: 98 - 92 \u003d 6.
We write the ranked row (options in ascending order):
92, 94, 94, 95, 95, 96, 96, 96, 97, 98.
Grouped a row and write to the table (I will put the number of its appearances in accordance with each version):

x I.	92	94	95	96	97	98	N.
n I.	1	2	2	3	1	1	10

We calculate the relative frequencies and accumulated frequencies, the result will write to the table:

x I.	92	94	95	96	97	98	TOTAL
n I.	1	2	2	3	1	1	10
	0,1	0,2	0,2	0,3	0,1	0,1	1
Accumulated frequencies	1	3	5	8	1	10

We construct a polygon of the sampling frequency (note on the chart options along the axis oh, frequencies along the Oy axis, connect the line of the line).

Selective average and dispersion calculated by formulas (respectively):

You can find other characteristics of the sample, but for the general presentation, quite found characteristics are quite sufficient.

Tasks for checking statistical hypotheses

Tasks related to this type, higher tasks Previous type and their solution is often more volume and time consuming. Before you begin to solve problems, the concepts of statistical hypothesis, zero and competing hypothesis, etc. are being studied first.

Consider the simplest task This type.

A task

Two independent samples of volume 11 and 14 were given, extracted from normal sets X, Y. Also, corrected dispersions are also known equal to 0.75 and 0.4. It is necessary to check the zero hypothesis about the equality of the general dispersions in the level of significance γ \u003d 0.05. Competing hypothesis choose at will.

Decision

Zero hypothesis for our problem is written as follows:

As a competing hypothesis, consider the following:

We calculate the ratio of greater corrected dispersion to the smaller and obtain the observed value of the criterion:

Since competing hypothesis, which we chose, has the form, the critical area is right-hand.
According to the table for the level of significance 0.05 and the number of freedoms of freedom equal to 10 (11 - 1 \u003d 10) and 13 (14 - 1 \u003d 13), respectively, we will find the critical point:

Since the observed value of the criterion is less than the critical value (1,875<2,67), то нет оснований отвергнуть гипотезу о равенстве генеральных дисперсий. Таким образом, исправленные дисперсии различаются между собой незначимо.

The considered task of not easy at first glance, but it is quite standard and is solved on the template. Other tasks are different from each other, as a rule, the values \u200b\u200bof the criteria and the critical area.

More time-consuming (since they contain many calculations, some of which are reduced to the table) are tasks for testing the hypothesis about the type of distribution of the general population. When solving such tasks, various criteria are used, for example, Pearson's criterion.

Tasks for determining the type of distribution law on statistical data

This type of task refers to the section that studies the elements of the correlation theory. If we consider the dependencies of Y from x, then you could remember the method of least squares to determine the type of dependence. However, in mathematical statistics, everything is much more complicated and two-dimensional values \u200b\u200bare considered in the correlation theory, the values \u200b\u200bof which are usually specified in the form of tables.

	x 1	x 1	…	x N.	n y.
y 1.	n 11.	n 21.	…	n N1.
y 1.	n 12.	n 22.	…	n N2.
…	…	…	…	…	…
y M	n 1m.	n 2m.	…	n nm.
n X.			…		N.

We give the formulation of one of the tasks of this section.

A task

Determine the selective equation of the straight line of regression Y to X. The data are shown in the correlation table.

Y.	X.				n y.
	10	20	30	40
5	1	3			4
6		2	1		3
7			3	2	5
8				1	1
n X.	1	5	4	3	N.=13

Conclusion

In conclusion, we note that the level of complexity of tasks in mathematical statistics will be very much in the transition from one type to another. The tasks of the first type are quite simple and do not require a special understanding of the theory, you can simply write up the formulas and solve almost any task. The tasks of the second and third type are a bit more complicated and for their successful solution requires a certain "luggage of knowledge" for this discipline.

We give a list of just two books, but it is these books for the author of the article have long been the desktop.

1. Gmurman V.E. Probability Theory and Mathematical Statistics: Tutorial. - 12th ed., Pererab. - M.: Eid Yuratt, 2010. - 479 p.
2. Gmurman V.E. Guide to solving problems on probability theory and mathematical statistics. - M.: Higher School, 2005. - 404 p.

Solution of mathematical statistics to order

We wish you good luck in the development of mathematical statistics. There will be problems - contact. We will be happy to help!

Moscow Department of Education

GBOU SPO city of Moscow "Moscow State College of Book Business and Information Technologies"

for specialty: 080114ECONOMICS AND ACCOUNTING

Considered at the meeting

Subject (cyclo) commission

accounting

and economic disciplines

year 2012

Explanatory note

The development of the discipline "Statistics" offers a practical understanding of its sections and those in practical classes that should contribute to the formation of the student general and professional competencies, the acquisition of the necessary skills, consolidation and deepening of theoretical knowledge.

The development of discipline is part of the development of the main type of professional activity and the relevant general (OK) and professional competencies (PC):

OK 1. Understand the essence and social significance of your future profession, to show sustainable interest.

OK 2. Organize your own activities, identify methods and methods for performing professional tasks, evaluate their efficiency and quality.

OK 3. Solve problems, evaluate the risks and make decisions in non-standard situations.

OK 4. To search, analyze and evaluate the information necessary for setting and solving professional tasks, professional and personal development.

OK 5. Use information and communication technologies to improve professional activities.

OK 6. Work in the team and team, to ensure its cohesion, effectively communicate with colleagues, management, consumers.

OK 7. Set goals, motivate the activities of subordinates, organize and control their work with the adoption of responsibility for the result of the tasks.

OK 8. Independently identify the tasks of professional and personal development, to engage in self-education, consciously plan to plan advanced training.

OK 9. Being ready for changing technology in professional activities.

PC 1.1. Processing primary accounting documents.

PC 1.3. Conduct money accounting, make money and cash documents.

PC 2.2. Conduct preparations for inventory and verifying the actual compliance of actual data inventory data.

PC 4.1. Reflect the growing outcome on accounting accounts Property and financial position of the organization, identify the results of economic activities during the reporting period.

PC 4.4. Conduct control and analysis of property information and financial position of the organization, its solvency and profitability.

PC 5.1. Organize tax accounting.

As a result of the development of educational discipline, the student must:

Be able to:

1. collect and register statistical information;
2. carry out primary processing and monitoring of observation materials;
3. perform calculations of statistical indicators and formulate the main conclusions;
4. implement a comprehensive analysis of the underlying socio-economic phenomena and processes, including using computing equipment.

In the curriculum on practical classes, 20 audit hours are provided, students must fulfill 10 practical work.

. To organize independent extracurricular work Approximate procedure for practical work

1. Repetition of the theoretical foundations on the topic of practical work

2. issuance of individual tasks and guidelines for their implementation.

3. Instructing the teacher in the order of execution and design of practical work.

5. Independent audit work of students to fulfill the task

6. Control of the teacher for the completion of the task.

7. Counseling on emerging issues to fulfill the task.

8. Check the correctness of the implementation and design of practical work.

Criteria for assessing practical work

Rating "5" - It is raised if the student demonstrates knowledge of theoretical and practical material on the topic of practical work, determines the relationship between the indicators of the problem, gives the correct algorithm of the solution, formulates the conclusions, determines the interdisciplinary relations under the condition of the task, shows the assimilation of the relationship of the basic concepts used in the work, was able to respond to all clarifying and additional questions.

Evaluation "4" - It is raised if the student demonstrates knowledge of theoretical and practical material on the topic of practical work, allowing minor inaccuracies in solving problems, formulates conclusions, having an incomplete understanding of interdisciplinary relations with the right choice of a task decision algorithm, was able to respond almost to all the questions specified and clarifying questions.

Rating "3" - It is raised if the student is difficult with the correct assessment of the proposed task, the choice of an algorithm for solving the problem is possible with the leadership of the teacher, it is hampered in the formulation of conclusions, answered not to all clarifying teacher's questions.

Rating "2" - It is raised if the student gives an incorrect assessment of the situation, incorrectly chooses the actions algorithm, cannot respond to clarifying questions, leadership and assistance from the teacher and well-trained students are ineffective due to poor student training.

A student who received the "2" rating should be prepared and perform work in extracurricular time.

List of practical work

Topic Name	Practical work	Number of hours (full-time learning)
	room	Name
		"Calculation of absolute and relative indicators of variation"
		"Calculation of structural averages"
Topic 3.2. Rows of speakers
		"Calculation of individual and aggregate indices"
		"Calculation of medium indices"
		"Drawing up a selective observation plan"
Topic 3.5 Statistical study of links between phenomena
TOTAL

Topic 2.2. Summary and grouping statistical data

Practical work number 1

"Performing a summary and grouping of statistical data"

Purpose: - Learn to make a summary, grouping and regrouping of statistical data.

be able to:

Perform a simple summary, structural, analytical, combined grouping and rearrangement of data;

know:

Principles of building statistical groups.

The main part of the practical work with students is to build structural and analytical groups based on a predetermined teacher of the matrix of source data containing individual data on a relatively small number of units (10) of the totality and two to three indicators in statics.

During the implementation of practical work, ways to determine the required number of groups and the width of the interval, the construction of structural and analytical groups are enshrined.

Methodical instructions

Building a grouping begins with determining the composition of grouping signs.

Grouped sign It is called a sign that the units of aggregate are divided into separate groups.

After the basis of the grouping is determined, the question of the number of groups to which the aggregate must be broken should be solved.

The definition of the number of groups can be made mathematically using the Formula of the Strocess:

where n is the number of groups;

N - The number of units of aggregate.

When the number of groups is defined, then the grouping intervals should be determined.

Interval - This is the value of the varying feature lying in certain boundaries. Each interval has its own magnitude, upper and lower boundaries or at least one of them.Lower border The interval is called the smallest sign in the interval, andupper border - The greatest sign is in the interval. The magnitude of the interval is the difference between the upper and lower boundaries of the interval.

Intervals of grouping depending on their magnitude are equal and unequal.

The magnitude of the equal interval is determined by the following formula:

where xmax, and x min - the maximum and minimum values \u200b\u200bof the totality in the aggregate;

p - number of groups.

Rules for rounding the chart of interval

If the magnitude of the interval has one sign to the comma, then the values \u200b\u200bobtained are advisable to round up to the tenths.

If the calculated size of the interval has two significant digits to a comma and several decimal places, then this value must be rounded to an integer

If the calculated value of the interval is a three-digit, four-digit and so on, the number should be rounded to the nearest number, multiple 100 or 50.

Grouping intervals can be closed and open.

Closed The intervals that have upper and lower boundaries are called. W.open The intervals indicated only one border: the upper one - at the first, lower - in the latter.

When the boundaries denote the boundaries, a question may be included in which group to include units of the object, the characteristic values \u200b\u200bof which coincide with the interval boundaries. It is recommended to be guided by the principle:

the lower limit is "inclusive", and the upper is "exclusively".

We will analyze 10 enterprises using the grouping method.

1. We construct a structural grouping.

As a group of signs, we take the authorized capital.

Forming four groups of banks with equal intervals.

The size of the interval is determined by the formula

Denote by the boundaries of groups:

Group border

1-J.

2nd

3rd

4th

By distributing enterprises by groups, we calculate the number of enterprises in each of them. Calculation technique is as follows: It is necessary to make a sample of enterprises in magnitude, for example, authorized capital and distribute them for groups obtained above. At the same time, each vertical wand will correspond to one unit of the aggregate, i.e. one enterprise.

Groups of enterprises Number of enterprises

by the magnitude of the statutory

capital, billion rubles.

After a grouping feature is defined - the authorized capital is given by the number of groups - 4 and the groups themselves are formed, it is necessary to select indicators that characterize groups, and determine their surrounding indicators for each group. Indicators characterizing enterprises are distributed under the specified groups, and calculate the results by groups in the developing table. Then the group results are entered into a consolidated table.

Group number		enterprise number	Indicator	Indicator
	TOTAL
	TOTAL
	TOTAL
	TOTAL
	Total

The consolidated table has the same number of graph, but only the final lines are transferred. Count number of the enterprise will be called the number of enterprises.

2. We construct an analytical group. As a factor (grouping) feature, we will take the authorized capital, and the effective feature is working assets.

The procedure will be similar. The final table will be

Group number	Group of Inquiry Capital	number enterprises	Indicator
			total	on average, 1 enterprise
	Total

Practical work number 2

"Construction of distribution series and their graphic image"

Purpose: - learn how to build rows of distribution and depict them graphically.

Providing practical work:

Tasks for performing work.

As a result of this work, a student must form general and professional competencies.

As a result of the execution of this work, the student must

be able to:

Build rows of distribution and depict them graphically;

know:

Principles for constructing distribution series.

Methodical instructions

Recall the basic concepts related to this topic:

Row of distribution

Elements of a series of distribution (options and frequency, frequency)

Attribute rows of distribution

Variation rows of distribution

Discrete and interval variational series

Accumulated frequencies

Types of graphs used for the image of variational series (distribution polygon, histogram, cumulating, rogue).

Algorithm for constructing a discrete variational series

1. Select from the available data all numeric variants of the trait learned and place them in ascending order.

2. Consider how many times each option is found.

3. Consider the share of each option in the total compatibility

4. Consider the accumulated frequencies

5. Results Substitute in the form of a statistical table

6. Build a distribution polygon: in the rectangular coordinate system construction of the points, the abscissions of which are options, and the ordinates - frequencies, and then connect their segments direct, having received a broken line.

7. Build a cumulant: In the rectangular coordinate system, build a point, the abscissions of which are options, and the orders are accumulated frequencies, and then connect them to the straight line, obtaining a broken line.

8. Make conclusions.

Algorithm for building interval variational series

The principles of constructing interval rates of distribution are similar to the principles of building statistical groups!

1. Select a grouping feature.

2. Determine the variation variation.

3. Determine the number of groups.

4. Determine the step (value) of the grouping interval.

5. Build the grouping intervals.

6. Distribute the available options for the studies of groups and calculate the number of options in each group.

7. Consider the share of each option in the total total of aggregate.

8. Consider the accumulated frequencies

9. Results Substitute in the form of a statistical table

10. Build a histogram: in a rectangular coordinate system building columns with bases equal to the width of intervals, and a height corresponding to the frequency.

11. Build a cumulat: In the rectangular coordinate system along the abscissa axis, options are postponed, and the accumulated frequencies that are applied to the graph in the form of perpendicular to the abscissa axis in the upper boundaries of the interval.

12. Build the OGIV, changing the axis of the abscissa and ordinate.

13. Make conclusions.

Topic 3.1. Statistical indicators

Practical work number 3

Calculation of absolute and relative indicators of variation

Purpose: - learn how to calculate the absolute and relative indicators of variations on non-major and grouped data.

Providing practical work:

As a result of this work, a student must form general and professional competencies.

As a result of the execution of this work, the student must

be able to:

Calculate and analyze the absolute and relative indicators of variation in grouped and non-maternal data;

know:

Methods for calculating absolute and relative parameters of variation.

The main part of the practical work with students is to calculate the absolute and relative indicators of variation on the basis of the initial information prepared by the teacher containing individual data.

Methodical instructions

When studying socio-economic phenomena and processes, statistics occurs with a variety ofvariation Signs characterizing certain units of aggregate.

Absolute and relative characteristics are used to measure and evaluate the variation.

The most advanced scattering assessment (variations) according to these distribution series is determined byr.which shows how large the difference between the units of aggregate having the smallest and greatest value of the sign.

Medium linear deviation A is a generalizing measure of variation of individual signs of a feature from an average arithmetic value. It gives the absolute measure of variation.

If the data is not grouped, then the calculation of the average linear deviation is carried out according to the principle of an unbelievable average, i.e.

If these variations are represented by variational rows of distribution, then the calculation is made according to the principle of a weighted average, i.e.

Dispersion Σ 2. - This is the average square of deviations of individual values \u200b\u200bof the feature from the average value. Dispersion is used not only to evaluate variation, but also when measuring interconnections, to verify statistical hypotheses.

It is calculated by the formulas:

However, due to the summation of the squares of deviations, the dispersion gives a distorted idea of \u200b\u200bdeviations, measuring them in square units. Therefore, on the basis of the dispersion, two more characteristics are introduced: the average quadratic deviation and the coefficient of variation.

Average quadratic deviationσ it is the root of the second degree from the middle square of deviations of the individual values \u200b\u200bof the feature from their average, i.e. It is calculated by extracting a square root from the dispersion and is measured in the same units as a variating feature.

The average quadratic deviation, as well as the average linear deviation, shows how on average specific options for the feature from its average value are deflected.

For the purposes of comparing the amounts of different signs in the same totality, or when comparing the amounts of the same character, in several sets are calculatedrelative variation indicators. The database for comparison is the average arithmetic. These indicators are calculated as the ratio of the scope, or the average linear deviation, or the average quadratic deviation to the middle arithmetic. Most often, they are expressed in percentage and characterize not only a comparative estimate of the variation, but also give a characteristic of the uniformity of the totality. A combination is considered homogeneous if the coefficient of variation does not exceed 33% (for distributions close to normal). Distinguish the following relative parameters of variation(V):

Practical work number 4

Calculation of structural mean values

Purpose: - To learn how to calculate the structural averages on non-major and grouped data.

Providing practical work:

Task for performing work.

As a result of this work, a student must form general and professional competencies.

As a result of the execution of this work, the student must

be able to:

Calculate and analyze the structural averages according to grouped and non-maternal data;

know:

Methods of structural averages.

The main part of the practical work with students is the calculation of the structural average variational range of distribution based on a predetermined teacher of source information containing individual data.

Methodical instructions

Recall the structural average variations of the distribution include fashion and median. The average value characterizes the typical level of the sign in the aggregate.

Fashion (MO) - the value of the attribute most common in the total totality, i.e. This is one of the feature of the feature that has the highest frequency (frequency).

In the discrete row of the mode is determined visually at maximum frequency or frequency.

In the interval row at the highest frequency, the modal interval is determined, and the specific mode of fashion in the interval is calculated by the formula:

Mediana (Me) - The value of the feature (option) coming to the middle of the ranked (ordered) totality, i.e. This is a variant that divides a number of distribution into two equal in volume.

Median, like fashion, does not depend on the extreme values \u200b\u200bof the options, therefore it is used to characterize the center in a number of distribution with uncertain borders.

To determine the median in a ranked row, you must first findmedian number:

In the discrete row of the median distribution is located directly at the accumulated frequency corresponding to the median number.

In the case of an interval variational range of distribution, the specific value of the median is calculated by the formula

where x 0 and i - accordingly the lower boundary and the magnitude of the median interval;

f ME. - the frequency of the median interval;

S ME-I - The accumulated frequency of the premedicated interval.

In symmetric rows of distribution, the modes and medians coincide with the average value (x \u003d me \u003d MO), and in moderately asymmetric they relate in this way:

The considered generalizing indicators of the distribution center do not open the nature of the sequential change in the frequency, therefore, in the analysis of the patterns of distribution, rank (ordinal) indicators are used: quarters and deciles.

Topic 3.2. Rows of speakers

Practical work number 5

"Analysis of the dynamics of studied phenomena"

Purpose: - learn to count absolute, relative and average indicators of rows of speakers.

Providing practical work:

Task for performing work.

As a result of this work, a student must form general and professional competencies.

As a result of the execution of this work, the student must

be able to:

- calculate the speakers;

know:

Methods for calculating speakers.

The main part of the practical work with students is the consolidation of methods for calculating indicators based on a predetermined teacher of source information containing individual data.

When studying this topic, it is necessary to pay special attention to the calculation of the average chronological suspended number of rows, the average growth rate and increase using the series for which the speakers were calculated.

Methodical instructions

To identify the specifics of the development of studied phenomena during certain periods of time, the absolute and relative indicators of the change in the dynamics of absolute increases are determined, the absolute value of one percent of the increase, the growth rate and increase. Clarification of the entity is a necessary condition for the assimilation of this topic.

Considering these indicators, it is necessary to properly choose the comparison base, which depends on the purpose of the study.

When comparing each level of the row with the previous onechain indicators; When comparing each level with the same level (base) is obtainedbase indicators.

To express the absolute growth rate (reduction) of a number of speakers, the statistical indicator is calculated -absolute increase (Δ). Its value is defined as the difference between two compared levels. It is calculated by the formula

where. Ii - the level of the i-year;

0. - Basic year level.

The intensity of changes in the levels of dynamics is estimated by the ratio of the current level to the previous or basic, which is always a positive number. This indicator is calledgrowth rate (TR). It is expressed as a percentage, i.e.

Growth rates can be expressed in the formcoefficient (Kr). In this case, it shows how many times this level of a series of more than the level of the base year or which part it is.

To express the change in the magnitude of the absolute increase in the levels of a series of dynamics in relative values, the rate of growth (TPR) is determined, which is calculated as the ratio of absolute increase in the previous or base level, i.e.

The growth rate can also be calculated by subtracting 100% from the growth rates, i.e. Tpr \u003d TP - 100.

Indicator absolute value of one percent of growth|%| it is defined as the result of dividing the absolute increase in the corresponding growth rate, expressed as a percentage, i.e.

The calculation of this indicator makes sense only on a chain basis.

Special attention should be paid to calculation methodsaverage indicators Rows of speakers that are a generalizing characteristic of its absolute levels. Methods of calculationmedium level A number of speakers depend on its type and methods for obtaining statistical data.

IN interval row Dynamics S. equifiable levels In time, the calculation of the average level of the row (y) is made according to the middle arithmetic formula:

If a interval series speakers has unequal levelsthen the average level of the series is calculated by the formula

where I is the number of periods of time during which the level does not change.

For a torque with equifiable levels The average chronological is calculated by the formula

where n is the number of row levels.

Medium chronological forunequal levels of torque series The speakers are calculated by the formula

The definition of the average absolute increase is made by the formula

Or

Average annual growth rate It is calculated using the middle geometric formula:

where M is the number of growth coefficients.

Average annual growth rate We will get a deduction from the average growth rate of 100%.

Practical work number 6

"Analysis of the main trend of a number of speakers"

Purpose: - learn to identify and analyze the main trend in the ranks of the dynamics.

Providing practical work:

Task for performing work.

As a result of the execution of this work, the student must

As a result of this work, a student must form general and professional competencies.

be able to:

- identify and analyze the main tendency in the ranks of the dynamics by smoothing the direct equation;

know:

Methods for analyzing the main trend in the ranks of the speaker.

The main part of the practical work with students is the consolidation of techniques and methods of studying in the ranks of the dynamics of the main trend in the development of the phenomenon on the basis of the initial information prepared by the teacher containing individual data.

Methodical instructions

The most effective way to identify the main development trend is the analytical alignment. In this case, the levels of a number of speakers are expressed as a function of time.

Analytical alignment can be carried out according to any rational polynomial. The choice of function is based on the analysis of the nature of the patterns of the dynamics of this phenomenon.

Equation is used to align the speakers in a straight line

in T \u003d a 0 + a 1 t.

The method of smallest squares gives a system of two normal equations to find the parameters A0 and a 1

where y is the initial level of radical dynamics;

n is the number of members of the series;

t is the time indicator that is indicated by sequence numbers, ranging from the lower.

The solution of the system of equations allows you to obtain an expression for parameters a0 and a 1

In the ranks of the dynamics, the technique of calculating the parameters of the equation can be simplified. For this purpose, such values \u200b\u200bgive such values \u200b\u200bso that their sum is zero

In this case, the system equations will take the following form:

from

As a result, the equation of the main trend is obtained. Substituting into the equation taken designations T, calculate the levelly levels of a number of speakers:

At the end of the calculation of the main trend, it is advisable to build a graph on which the initial data and theoretical values \u200b\u200bof the row levels should be depicted.

The main trend (trend) shows how to develop systematic factors to a number of speakers, and levels of levels about the trend serves as a measure of the impact of residual factors. It can be measured by the formula

average quadratic deviation.

The relative measure of the oscillating is the coefficient of variation, which is calculated by the formula

Practical work number 7

"Calculation of individual and aggregate indices

Purpose: learn

Calculate individual and aggregate indices;

Product a factor analysis based on the index method.

Providing practical work:

Task for performing work.

As a result of this work, a student must form general and professional competencies.

As a result of the execution of this work, the student must

be able to:

Calculate individual and general indices and conduct factor analysis based on the index method.

know:

The main part of the practical work with students is the consolidation of the methods for building individual and consolidated indices based on a predetermined teacher of source information containing individual data.

Methodical instructions

Recall that Economic index - This is a relative value that characterizes the change in the studied phenomenon in time, space or compared to some standard.

The simplest indicator used in the index analysis is an individual index that characterizes a change in time (or in space) of individual elements of a particular set. So,individual price index Reads by formula

where p 1. the price of goods in the current period;

P 0 - price of goods in the basic period.

Estimate the change in sales of goods in natural measurement units allowsindividual index of physical sales:

where q 1 - the amount of goods implemented in the current period;

Q 0 - the amount of goods implemented in the base period.

Changing the amount of sales of goods in value expression reflectsindividual turnover index:

Individual indices, in essence, are relative indicators of the speakers or growth rates and according to several periods of time can be calculated in chain or basic forms.

Composite index - This is a complex relative indicator that characterizes the average change in the socio-economic phenomenon consisting of directly incommensurable elements. The source form of the consolidated index is an aggregate.

When calculating the aggregate index for heterogeneous aggregate, such a general indicator is found in which all its elements can be combined. Prices of various goods implemented in retail trade are unlawful, but from an economic point of view, it is quite acceptable to summarize the turnover on these goods. If we compare the turnover in the current period with its value in the base period, then we getcomplete Index Turnover:

The value of this index is influenced by changing both prices for goods and the volumes of their implementation. In order to estimate the change in price only (indexed value), the number of goods sold (index weights) is required at a constant level. In the study of the dynamics of such indicators as the price, the cost, labor productivity, the yield quantitative indicator is usually fixed at the level of the current period. This way is obtainedconsolidated price index (by the method of PAASH)

The numerator of this index contains the actual turnover of the current period. The denominator is a conditional magnitude showing how the turnover would be in the current period, subject to the preservation of prices at the basic level. Therefore, the ratio of these two categories and reflects the price change that took place.

It should be noted thatconsolidated price index It is possible to obtain the Laspeyres method, fixing the number of sold goods sold at the baseline:

The third index in this index system iscomplement index of physical sales. It characterizes the change in the number of goods sold not in cash, but in physical units of measurement:

Weighs in this index are the prices that are fixed at the basic level.

There is the following relationship between the calculated indexes:

When analyzing the results of industrial enterprise's production activities, the above summary indices are respectively called the index of the cost of products, the index of wholesale prices and the index of the physical volume of products.

Practical work number 8

"Calculation of medium indices"

Purpose: learn

Settle medium indices;

Providing practical work:

Task for performing work.

As a result of this work, a student must form general and professional competencies.

As a result of the execution of this work, the student must

be able to:

Calculate the average arithmetic and harmonic indices.

know:

Methods for calculating indexes;

The main part of the practical work with students is to consolidate the methods for the construction of medium indices based on a predetermined basis by the teacher of source information containing individual data.

Methodical instructions

Recall that ophimo aggregate indexes in statistics Another form is used - weighted average indices. They are resorted to their calculation when the information available does not allow you to calculate the overall aggregate index. So, if there are no price data, but there is information about the cost of products in the current period and the individual price indexes are known for each product, it is impossible to determine the general price indexas aggregate, but it is possible to calculate it as an average of individual. In the same way, if the number of products produced produced, but are known individual indexes and the cost of products of the baseline period, one can determine the general index of the physical volume of products as a weighted average value.

Middle Index - This is an index calculated as the average value from individual indices.

When calculating medium indices, two forms of medium are used: arithmetic and harmonic.

The average arithmetic index is identical to the aggregate index, if the weights of individual indexes will be the components of the aggregate index. Only in this case the magnitude of the index calculated by the middle arithmetic formula will be equal to the aggregate index.

The average arithmetic index of the physical volume of products is calculated by the formula

The average arithmetic productivity index is determined as follows:

Since IF x T-i \u003d TO, then the formula of this index can be converted to an aggregate index complexity of products. Weighsare the total cost of time for the production of products in the current period.

Average arithmetic indexes are most often applied in practice to calculate the summary indices of quantitative indicators.

The indices of other qualitative indicators (prices, cost, etc.) are determined by the formula of a medium harmonic suspended value.

The average harmonic index is identical to the aggregate, if individual indexes are weighted using the alignment of the numerator of the aggregate index. For example, the cost index can be calculated so:

a price index:

Thus, weighs in determining the average harmonic index of the cost are the costs of production of the current period, and the price index is the cost of production of this period.

Topic 3.4 Selective observation

Practical work number 9

"Drawing up a selective observation plan"

Purpose: - Learn to make a plan of selective observation.

Providing practical work:

Task for performing work.

As a result of this work, a student must form general and professional competencies.

As a result of the execution of this work, the student must

Be able to:

Compile a plan of selective observation;

Know:

Main indicators and practice of using selective observation

Methods for the formation of a selective set and methods for determining the required sampling.

The main part of the practical work with students is to prepare a plan of selective statistical observation.

Methodical instructions

According to the coverage of the units of the aggregate studied, statistical observation is divided into solid and unpaid. Dispose of the observation, in which not all is subject to accounting, but only a part of the units of the common aggregate, but some of this should be sufficiently mass to ensure that summoning statistical indicators.

Selective observation is the main form of unbleached observation.

The combination of units from which the selection is selected is called general. The number of units selected from the general population for selective observation is a selective set.

According to the method of selection of units to the selective set of sample, the sample is re-both reputive. A sample is re-called, in which each selected unit is returned to the general set for the subsequent selection and can re-enter the sample. At the same time, the number of general aggregate remains unchanged. Typically, selective observation is carried out by the method of a non-remote selection, in which the unit that fell into the sample does not return to the general population and further selection is made without previously selected units. At the same time, the number of general aggregate decreases by the magnitude of the sampling.

Selective Observation Plan Stages:

1. Purpose of observation- obtaining reliable information to identify the patterns of development of phenomena and processes.

2. Object of observation -some statistical aggregate in which the studied socio-economic phenomena and processes occur. To determine the object of statistical observation, it is necessary to establish the boundaries of the aggregate under study. To do this, specify the most important signs that distinguish it from other similar objects.

3. Unit of observation - Composite element of an object that is a carrier of signs to be registered.

4. Program Static observation is a list of signs.

5. The method and form of selection of units into the selective set.

Practical work number 10

"Construction of a linear regression equation"

Purpose: - Learn to calculate the parameters of the linear regression equation.

Security:

Task for performing work, statistical data for calculating the leveling parameters.

As a result of this work, a student must form general and professional competencies.

As a result of the execution of this work, the student must

be able to:

Calculate the parameters of the linear regression equation and build the equation.

know:

Methods for estimating communication using the linear regression equation.

The main part of the practical work with students is to consolidate the receptions and methods for studying the tightness of communication on the basis of a predetermined source information by the teacher containing individual data.

Methodical instructions

Recall that for the quantitative description of the relationship between economic variables, the statistics uses regression and correlation methods.

Regression is a value that expresses the dependence of the average value of the random variable from the values \u200b\u200bof the random variable x.

The regression equation expresses the average value of the same feature as a function of another.

Regression line is a graph of the function y \u003d f (x).

Linear - regression used in statistics in the form of a clear economic interpretation of its parameters: y \u003d a + b * x + e;

Pair regression - regression between two variables y and x, i.e. model of the form: y \u003d f (x) + e, where the dependent variable (the result is a result); X is an independent, explaining the variable (factor sign); E- indignation, or stochastic variable, including the effect of unaccounted factors in the model. In the case of a pair linear dependence, a regression model is built according to the linear regression equation. The parameters of this equation are evaluated using the procedures, the least squares method received the greatest distribution.

The method of least squares (MNC) is the method of evaluating linear regression parameters, minimizing the sum of the squares of the observation deviations of the dependent variable from the desired linear function.

Economic meaning of the parameters of the equation of linear steam regression. Parameter B shows the average change in the result of the factor x per unit. That is, MNK is to determine a and a, so that the sum of the squares of the difference between the actual y and y. The calculated values \u200b\u200bof A0 and A1 were minimal:

The method of smallest squares gives a system of two normal equations for finding parameters A0 and 1:

The solution of the system of equations allows you to obtain expressions for parameters A0 and 1:

Transcript.

1 Ministry of Agriculture of the Russian Federation Federal State Budgetary Educational Institution of Higher Professional Education "Orenburg State Agricultural University" Customs College PCC economically disciplines K.V. Ramemetova, N.A. Troenko Collection of tasks according to statistics Educational and methodological manual for discipline for students of students on the program of secondary vocational education 86 Finance (by industry) Electronic publication Orenburg Publishing Center 22

2 BBC 6.6 UDC 3 P 27 Recommended for the publication of the Editorial Publishing Council of the FGBOU VPO "Orenburg State Agrarian University" (Chairman of the Council Professor V.V. Karakulev). Considered and approved at a meeting of PCC economically disciplines on June 24, 22. Protocol. Considered and recommended for the publication of the Methodological Commission of the Customs College on June 29, 22. Protocol. Reviewer: T.V. Timofeeva Cand. ECON. science, st. PCC teacher of economically disciplines of the Customs College FGOU VPO OGAU R 27 Ramemetova, K.V. Collection of tasks according to statistics: a teaching and methodological manual for discipline for students of the student under the program of secondary vocational education 86 Finance (by industry): [Electronic resource], 2 MB / K.V. Ramemetova, N.A. Troenko Orenburg: OGAU Publishing Center, p. Systems Requirements: PC not lower than class Pentium II; 52 MB RAM; Windows XP / VISTA / 7; Adobe Acrobat Reader 7. And above. Certificate of registration of e-learning aids 48-e. The collection of tasks is drawn up taking into account the profile of the specialty, the practice of teaching on average professional institutions and is based on the requirements of the State Educational Standard of the specialty of the SPO, the Federal State Educational Standard and Operations on Discipline. The educational and methodological manual contributes to the acquisition by students, the skills and skills in solving problems are not necessary. To this end, it contains guidelines for the calculation of statistically indicators, as well as the tasks themselves with order and execution. An educational and methodological manual is intended for academic work on the "Statistics" discipline with students of the specialty SPO 86 Finance (by industry). Signed to use the order 48-e. OGAU Publishing Center. 464, Orenburg, ul. Chelyuskintsev, 8. Tel.: (3532) UDC 3 BBK 6.6 Ramemetova K.V., Troenko N.A., 22 OGAU Publishing Center, 22 2

3 Introduction Currently, marketplace relations cannot be managed by complex social and economic systems, without having operational, reliable and full statistical information. Statistical data are used by social sciences to substantiate the laws of public life, for the accomplishment and actions in specific conditions of place and time. With the help of statistics, plans of the country's economic and social development are being developed, and the implementation is also being analyzed, the needs and resources of the country are taken into account, unused reserves are revealed. The functioning of enterprises in the conditions of the market relationship requires a deeper analysis of economically processes, origin to enterprises. Such an analysis needs extensive statistical information, which can be obtained both on the basis of primary accounting, leading in the enterprise, and additionally, specially special surveys. Each economist should skillfully use statistical data, be able to process and analyze and, see in each digit it economic content. Such skills and decrease can be purchased in the process of solving problems. Training discipline "Statistics" is a general professional discipline that establishes basic knowledge to obtain professional skills. Its goal is to form theoretically theoretically knowledge and practically skills in the field of general theory of statistical science, the procedure for holding statistically research, the use of statistically methods for assessing, analyzing and predicting the state and development of different subjects. The tasks of the discipline are to assist students of the methods of organizing the collection statistically data, processing materials of statistical observation, the essence of generalizing statistically indicators for use and when processing and analyzing accounting and economic information, it becomes possible to obtain comprehensive accommodations of the object under consideration, whether it is the whole national economy or individual Eto industry, enterprises and and divisions. In accordance with the requirements of the requirements for the study of the discipline "Statistics", a student must: have an idea: the general principle of the principle and method of organizing statistically research and observations; know: essence, principles, methods for organizing the collection statistically data; essentially absolute, relative and average values; 3.

4 Essence of dynamics indicators; Economic and statistical methods for processing accounting and economic information; Basics of analysis are statistically data; Be able: calculate the main statistical indicators; use basic methods and techniques of statistics to solve practically tasks; Analyze statistical data and formulate conclusions arising from and analyzing. Obtaining skills and skills contribute to the solution offered in the Collection of Tasks. Objectives are accompanied by methodological instructions of software and decision. Fixing the mastered material is carried out using tasks tests, presented in the collection. four

5 topic Subject and statistics method. Tasks of statistics and sources of statistical information Methodical instructions for solving problems: When solving, the tasks should be familiar with such concepts as a totality, a unit of aggregate, signs, patterns, etc. The term statistics is used in several values, as synonymous with the words data, as a knowledge branch and as a branch of the practical activity of people. It can be defined as collecting mass data, and generalization, performance, analysis and interpretation. The subject of statistics are sets of many single-quality varying phenomena. The aggregate consists of separate units with quantitative and high-quality signs. Task Indicate which combinedness can be allocated in the field of education. Task 2 Indicate which aggregates can be allocated when studying the country's population. Task 3 Indicate which aggregates can be allocated in the field of finance. Task 4 Indicate which combinedness can be allocated in the field of health. Task 5 Indicate which combinedness can be allocated to the frame of one enterprise. Task 6 Indicate which combinedness can be allocated when studying space. Task 7 Name the aggregate in which Digesheva Antonina Grigorievna drives, often an ARVI and currently arriving in the clinical urban hospital 6 Task 8 Increase the aggregate in which the student leads from his native city to Moscow to go to the goal of learning in Moscow State University The pattern of elevated incidence of the ages of the ARZ in the spring-autumn period? Is it possible to consider the relationship between smoking and cancer is easy for example of statistical patterns? Explain why? five

6 Topic 2 Summary and grouping statistically Data Methodical instructions for solving tasks: When solving, tasks are provided for the execution of an analytical group. At the same time, it is important to understand the essence of groups, namely analytical grouping, with which the relationships are studied are studied. Under the grouping it is necessary to understand the distribution of units of aggregate in groups, in which the difference between units attributed to one group is less than between units related to different groups. When grouping, there is a homogeneity of data and a generalization, representation in a convenient form. The grouping creates the basis of the subsequent summary and analysis of the data. The rules for conducting the grouping include: Definition of grouping signs; Definition of values, distinguishing groups Definition of grouping intervals. Types of groupings: Grouping is made on the basis of one grouping simple feature; complex on the basis of two, tr grouping signs; Multidimensional based on the calculated, integral indicator, which is called a multidimensional average. Groupings differ in purpose: typological, structural, analytical. The typological is used to allocate socio-economically types. Sequence of actions during typological grouping:. Are called the types of phenomena that can be allocated; 2. The definition of a group of signs; 3. It comes to the establishment of interval boundaries; 4. Registration of grouping in a table. Structural grouping is accomplished by the structure of the totality on the basis. It can be built according to quality and quantitative features. Analytical grouping is intended to identify the relationship between the features, from which one is productive, and the other as a factor. Analytical grouping allows you to establish the presence and direction of the relationship between factor and effective features in the limit of a homogeneous aggregate. Grouping units of aggregate is made by factor. To compile an analytical group, it is required to determine the amount of the interval by the formula: 6

7 I MA N MIN, where Ma is the maximum value of a factor in the aggregate, MIN minimal value of a factor assembly in a set, n number of groups. The number of groups can be set (based on the experience of previous surveys). In the event that the question of the number of groups can decide on their own, can be used to determine the optimal number of groups: k \u003d + 3,322 lg n, where N the number of units in the aggregate. The resulting value should be rounded to facilitate the calculations. The rounding procedure when calculating the interval is always carried out. The trinatic, four or greater number is rounded to the nearest number, multiple 5 or. If the number has two signs to the comma and several decimal places, it is rounded to the whole, if one sign is up to the comma and several signs after the comma to tenth, etc. Then the number of units in each of the groups are formed, as well as the volume of the characteristics of the signs in the limit are created by groups and are calculated by the average dimensions of the indicator (feature) for each group. The results of the group are made in the form of a group analytical table. Analysis of the distribution rows is based on and graphic image. To do this, build graphs polygon and histogram. The polygon is used in the image are discrete variations. The discrete variationaries account for the distribution of units of aggregate on a discrete sign that takes only integer values. The histogram is used for the image of the interval variation range. The construction of the interval variations are appropriate, first of all, with continuous variation of the feature, as well as if the discrete variation is manifested in a wide limit, i.e. The number of interrupted options is large enough. In conclusion it is necessary to give an economic analysis of the indicators of the group table and draw conclusions. 7.

8 The task is available data of 25 enterprises in one of the sectors of the economy: the average annual cost is mainly mainly manufactured by the funds, thousand rubles. The cost of produced products, thousand rubles for the purpose of studying the dependence between the average value of the cost of funds and the volume of products are maintained at the average annual value. Production of funds, forming three groups of enterprises with equal intervals. For each group and the totality of enterprises as a whole, count :) Number of enterprises; 2) the average annual cost of the funds are mainly produced - only on average for one enterprise; 3) the cost of products is only on average for one enterprise; 4) Product size per ruble is mainly mainly manufactured by funds (FDOODOTIC). Perform the calculation results as a group table. Make conclusions. eight

9 Task 2 For the studied period, the following data on the work of small enterprises of the industry are available: P / P produced products, thousand tons The cost of production costs, thousand rubles. 3 ,,69 4, 8 6 6, 45 8.5 696 To study the relationship between the volume of products manufactured and the cost of its production, make a grouping of enterprises in terms of products manufactured by forming three groups with equal intervals. For each group and on the totality of enterprises as a whole, calculate :) the number of enterprises; 2) the volume of manufactured products is only on average per enterprise; 3) the amount of costs for the production of products in just one enterprise. Replace the results as a group table and draw conclusions. nine

10 Task 3 There are the following data on 25 enterprises of one of the industries: P / p equipment age, overhaul costs, million rubles. 5,6 6.7 2 6.8 23, 3,6 24.2 4 3,9 2, 5 7, 2, 6 8.4 4.8 7 8, 27, 8 5.8 6,9 9 6 , 4, 8,5 5, 3,9 9.3 2 5.2 3, 3 7.5 6.7 4 4, 8, 5 3.5 9,5 6.2 24.5 7 6.2 4 , 8 4,3,9 9 3.5 9, 2 6, 2 6,2,2 22 3, 8, 23 8.9 2.6 24 9, 4, 25 4, 5, to study the relationship between the age of equipment And the costs of major repairs are subject to a grouping of enterprises in the age of equipment, forming three groups with equal intervals. For each group and for the aggregate of the factories as a whole, count :) the number of plants; 2) the age of the equipment is only on average per enterprise; 3) sums up the cost of overhaul and on average for one enterprise. Present the results of calculations in the table. Make conclusions.

11 Task 4 During the reporting period, there are the following data on the sale of goods and the cost of access to enterprises of trade in the area, million rubles. Retail turnover The sum of the cost of circulation of P / P 5.3 2 5,6,34 3 7.46 4 4,6,3 5 3,3,5 6 \u200b\u200b3,925 7 6,4,42 8 4,4, 26 9 5.6 4,2,34 5,37 2 4,2,28 3 2,8 4 6,6,39 5 6,5,36 6,2,36 7 3,8,25 8 5, 5.38 9 7,5,444 2 6,6,37 2 4,5,6,4,44,4,24 to identify the relationship between the volume of retail turnover and circulation costs, the enterprises in terms of retail turnover equal intervals. For each group and the totality of enterprises as a whole, count :) Number of enterprises; 2) the volume of trade is only on average for one enterprise; 3) the sum of the costs of appeal all and on average per enterprise; 4) the relative level of costs of circulation (the percentage of the sum of the cost of accessing the volume of retail turnover). Perform the results of the calculation as a group of table. Write brief conclusions.

12 Task 5 There are data 25 enterprises of one of the industries: the average annual value is the main profit, thousand rubles. P / P production Funds, thousand rubles, 3 7 66, 3 4 5, 7, in order to study the dependence between the average annual value, the funds are mainly maintained and the amount of profit is made by grouping plants at the average annual value of the fundamental funds, forming three groups with equal intervals. For each group and the set of factories as a whole, calculate :) the number of plants; 2) the average annual value of the funds are mainly carried out on average for one plant; 3) Profit total and average for one factory; 4) Profit size on rub. The fundamental funds are main. Perform the calculation results as a group table. Write brief conclusions. 2.

13 Task 6 There are the following sample data on the 22nd enterprises of one of the industries (sample%, Mehanic): P / p. The number of industrialized personnel, people. Product release, million rubles, 8 9, 39 83, 22 55, 3 23, 9 29, in order to study the dependence between the number of industrialized personnel and production, manufacture enterprises in the number of industrial and production personnel, forming three groups with equal intervals. For each group and the totality of enterprises as a whole, count :) Number of enterprises; 2) the average number of industrial and production personnel and on average per enterprise; 3) production of products in total and on average per enterprise; 4) Product production per employee. Perform the calculation results as a group table. Write brief conclusions. 3.

14 Task 7 During the studied period, the following data on the work of small enterprises of the industry are: Product release, thousand rubles. Profit, thousand rubles. P / P 65 5.6 8 8.5 92 2, to study the relationship between the volume of products manufactured and the profit of the enterprise, make a grouping of enterprises in terms of products manufactured by forming three groups with equal intervals. For each group and on the totality of enterprises as a whole, calculate :) the number of enterprises; 2) the volume of production is only on average per enterprise; 3) the magnitude of the profit is just one enterprise. Replace the results as a group table and draw conclusions. four

15 Task 8 There are data on 2 banks of one of the regions. Names of banks share capital, million rubles. 4.8 7, 2 5,6 6.9 3 4.6 4.9 4 3.6 3,9 5.7 7.9 6.2 5.7 7.9 5.5 8 2.4 9, 5 9 7,4,9 3,3,21,2,7 2, 2 4,6 6,9 3 2.9 3.2 4 4.5 5.2 5 3,3 4, 6 2.9 4 , 4 7 2.7 3.2 8 9.4 9.9 9 8,97 2.3 2.4 Working assets, million rubles. In order to study the dependence between the size of the assets and the authorized capital, we are grouping banks in the size of the authorized capital, forming four groups with equal intervals. For each group and the totality of banks, count :) the number of banks; 2) the size of the authorized capital is only on average for one bank; 3) the size of the assets is only on average for one bank. Perform the results of calculations as a group table, make brief conclusions. five

16 Task 9 During the studied period, the following data on the cost of apartments in the city are available in P / n Square, M 2 Apartment price, million rubles. 33.2 3 5.2 5 33, 7 36.82 8 6.2 2.2 43.95 6 2, 3 3, 4 36,9 5 6.2 2,9 8 36,6,26 to study dependence Between the apartment area and it costs to group the size of the square, forming five groups with equal intervals. For each group and on the totality of apartments as a whole, count :) the number of apartments; 2) the total size of the area and the average size of one apartment; 3) the total cost of the group's apartments and one apartment. Replace the results as a group table and draw conclusions. 6.

17 Task 2 There are data on the value of land plots for individual development in Orenburg P / p Square, M 2 Plot price, million rubles. 6.25 2 8.72 3 2,88 4 2.6 5 6,64 6 7.87 7 5.68 8 7.9 9 2.5 2 4.7 2, 3 7 4,4 4 8.5 5 8, 2 3.5 24 9.3 To study the dependence between the size of the site and its value, produce a group by the size of the area of \u200b\u200bthe plots by forming five groups with equal intervals. For each group and in the totality of the plots as a whole, count :) the number of areas; 2) the total area of \u200b\u200bthe plots and the average size of one section; 3) the total price of the plots and the price of one site. Replace the results as a group table and draw conclusions. 7.

18 Topic 3: Middle values \u200b\u200band indicators of variation in statistics Methodical instructions for solving tasks: The main value of the average values \u200b\u200bis in and a generalizing function. For the generalization of the set different, the individual values \u200b\u200bof the feature separately the set of aggregate is calculated and the average value is calculated, which is accelerating the entire totality. The average value is a generalizing aractericure of a set of individual values \u200b\u200bof some quantitative feature. If the average value summarizes the qualitatively homogeneous values \u200b\u200bof the feature, it is the typical accomplishment of signs of a given population. For example, the level of salary of employees of the trading company, the average production in the brigade of the Tokarei, the average profitability of the fluked enterprises and so on. System medium can accomplish as spatial or object systems, existing one-time (state, industry, region, the world as a whole, and so on) and dynamic systems extended in time (year, decade, season, and so on). Examples of systemic system are the average grain yield, the average cost of the construction of awards. Meter housing, the average level of milk consumption and dairy products per capita and so on. The average, being the function of the set individual values, is one value of the entire set and reflects that in common, which is inherent to all its units. The statistics use different types (forms) of average values. The most commonly used the following averages: average arithmetic; average harmonic; medium geometric; Middle quadratic. The specified averages relate to the Class of Power Middle. They can be calculated, or when each embodiment (i) in this set occurs only once, while the average is called simple or unbalanced, or when the options are repeated for a different number of times, and the number of repetitions is called the frequency (I) or statistical weight, And the average, calculated taking into account the weights, mean weighted. We introduce the conventional designation M III and consider the formula for calculating the power of the average (table). eight

19 Table Types of Middle and Formula and Calculation of the formula Middle Middle Calculation Type Arithmetic I Geometric Simple N Simple Arithmetic II Geometric Weighted Weighted Harmonic Harmonic Harmonic Weighted Iin Quadratic Simple MI Quadratic MI MI Weigneled Calculation Formula N 2 ... NN PI II 2 IN 2 III P I The choice of the form of the average is based on the isode ratio of the average (logical formula). This ratio is a ratio of 2- economically categories that lead to the ISOD-based medium indicator. For each average, it is possible to make only one basic ratio, regardless of the form of the representation of the ISODD, the data: the total value or the volume of the averaged-to-know the number of units or the amount of the set is available if there are a number of data on two interconnected indicators, for one of which needs to be calculated averaged value, and at the same time The numerical values \u200b\u200bof the denominator of the logical formula are known, and the numerator is unknown, but can be found as a product of these indicators, the average is calculated by the formula of arithmetic weighted. 2 If the numerical values \u200b\u200bof the logical formula numerator are known, and the values \u200b\u200bof the denominator are unknown, but can be found as a private from dividing one indicator on the other, the average is calculated by the formula of harmonic weighted. 3 If there are numerical values \u200b\u200bof the numerator and denominator of the logical formula, the average is calculated directly on this formula. In statistics, in addition to the power of the average, the use and structural medium mods, median, quartile, declines, percenteled .. Fashion is the value of the sign (option), the most frequently repeated in the studied aggregate. For discrete, the modular distribution rows will be the value of the options with the highest frequency. For interval, the distribution rows with equal intervals of the Fashion is determined by the formula: 9

20 Mo Mo I MO * MO MO MO MO MO MO, where Mo the initial value of the interval containing the fashion; I Mo the magnitude of the modal interval; Mo frequency of the modal interval; Mo the frequency of the interval preceding the modal; The frequency of the interval following modal. Mo Median is an option located in the middle of the variational series. If the distribution range is discrete and has an odd number of members, then the median will be an option that appears in the middle of an ordered row (ordered series is the arrangement of the units of the set in an increasing or descending order). If an ordered series consists of an even number of members, then the median will be the average arithmetic of two options, located in the middle of the row. To determine the median it is necessary to calculate the amount accumulated frequencies of the row. Building the result continues until the accumulated frequency amount exceeds half. If the sum accumulated against one of the option is equal to exactly half the sum of the frequency, the median is defined as the average arithmetic of this options and the subsequent. The median of the interval variational range of distribution is determined by the ME ME I ME formula, 5 S ME where ME is the initial value of the interval containing median; i ME The value of the median interval; The sum of the frequency of the series; S ME sum accumulated frequencies preceding the median interval; ME The frequency of the median interval. The dispersion calculation is made according to the formula: 2 I i 2 i. The average quadratic deviation is the root of the second degree from the mid-square of deviations separately the values \u200b\u200bof the feature from and medium, i.e. it is calculated by extracting square root and measuring- 2

21sts in the same unit as a varientizing sign. The average quadratic deviation shows: how many on average specific options are deflected from its average value. The calculation formula is as follows: I i 2 i. The variation coefficient is calculated by the formula: v%. The percentage is expressed and give the accuracy of the uniformity of the aggregate. A set is considered homogeneous if the coefficient of variation does not exceed 33%. Further, the ranks of the distribution portray graphically and make conclusions on the calculations produced. In this task, the interval variational distribution series are presented, which it is necessary to convert into discrete calculation of the mean value, dispersion, the average quadratic deviation and variation coefficient. Task 2 In order to study the level of remuneration, the workers of the enterprise conducted an% mehanic sample, as a result of which the following distribution of workers were obtained by average wages: average wages, rub. Number of workers, people Less than 6 7 total on the basis of these data will calculate :) average salary of one worker; 2) fashion and median 3) secondary quadratic deviation; 4) coefficient of variation; 5) with probability, 954 possible borders, in which the average salary in the enterprise is expected; 2.

22 Task 22 In order to study the level of remuneration, the workers of the enterprise conducted an interactive mehanic sample, as a result of which the following distribution of operating wages were received: average wages, rub. Number of workers, people Less than 2 times based on this data will calculate :) average salary of one worker; 2) fashion and median 3) secondary quadratic deviation; 4) coefficient of variation; 5) with probability, 954 possible borders, in which the average salary in the enterprise is expected; Task 23 in the goal of studying the norms of raw materials during the manufacture of products at the factory, a 5% self-random sample was carried out, as a result of which the following distribution of product products was obtained: product weight, g number of products, pcs. up to over 26 5 total on the basis of these data Calculate :) The average weight of the product; 2) fashion and median 3) secondary quadratic deviation; 4) coefficient of variation; 5) with probability, 997 possible borders, in which the average weight of the product of the entire batch is expected; Make conclusions. 22.

23 Task 24 For accommodation of the size of the balance profit. The company was carried out by the% self-random sample, as a result of which the following distribution of profit firms were obtained: Balance Profit, Mlow. RUB. The number of banks over 5 2 TOT 25 on the basis of the given data determine :) Middle profit on the totality of firms; 2) fashion and median; 3) secondary quadratic deviation; 4) coefficient of variation; 5) with probability, 954 possible borders, in which the average profit in the bank is expected in the region; Task 25 In order to study the norms of raw materials to produce a unit of products, an% mehanic sample was carried out, as a result of which the following distribution was obtained: raw materials, g. Number of products, pcs. Up to more than 32 Total on the basis of the present data Calculate :) Middle raw materials on one product; 2) fashion and median; 3) secondary quadratic deviation; 4) coefficient of variation; 5) with probability, 954 possible borders, in which the average raw materials are expected for the entire batch of products; 23.

24 Task 26 In order to study the cost of time for the manufacture of a unit of products at the enterprise, a 5% mehanic sample was carried out, as a result of which the following time distribution was obtained: time spent per unit number of units, pcs. products, min. Up to and more than 5th on the basis of these data Calculate :) The average time of time on the manufacture of a unit of products; 2) fashion and median; 3) secondary quadratic deviation; 4) coefficient of variation; 5) With a probability, 954 possible borders, in which the average time of time is expected to manufacture a unit of products Task 27 to the goal of studying the experience of workers of the factory, a 36-% mehanic sample was carried out, as a result of which the following distribution of workers' experience was obtained, number of years , people Less than 25 4 Total 8 on the basis of these data Calculate :) Average experience worker; 2) fashion and median 3) secondary quadratic deviation; 4) coefficient of variation; 5) With a probability, 997 possible borders, in which the average experience is expected to workers. 24.

25 Task 28 In order to study the cost of time for the manufacture of a unit of products at the enterprise, a 5% mehanic sample was held, as a result of which the following time distribution was obtained: time spent per unit of products, min. Number of units, pcs. Up to and more on the basis of these data, calculate :) The average time spent on the manufacture of a unit of products; 2) fashion and median; 3) secondary quadratic deviation; 4) coefficient of variation; 5) With a probability, 954 possible borders, in which the average time spent on the manufacture of a unit of products are expected. Task 29 According to selective observation, the distribution is the evaluation of companies in the number of orders for the period, which is accomplished by the following data: Groups are evaluated companies. The number of orders companies up to over 3 9 identify :) Average orders for one organization; 2) fashion and median; 3) secondary quadratic deviation; 4) Camefficient of variation. Build a histogram and distribution polygon evaluated companies by number of orders. According to the results of the calculations, draw conclusions. 25.

26 Task 3 In order to study the cost of time for the appraiser of measuring the land plot in the estimated company, a 5% mehanic sample was held, as a result of which the following time distribution was obtained: the cost of time for measurements, min. Number of measurements, pcs. Up to and more than 5th on the basis of these data will calculate :) The average time of time for measurements; 2) fashion and median; 3) secondary quadratic deviation; 4) coefficient of variation; Build a histogram and polygon distribution of measurements and duration. According to the results of the calculations, draw conclusions. 26.

27 Topic 4: Rows of dynamics and analysis Methodical instructions for solving tasks: A number of speakers This series is sequentially located statistically indicators (in a ronological order), the change of which shows the development of the phenomenon under study. A number of speakers consists of two elements: the moment (period) of the time and the corresponding statistical indicator, which is called the level of the row. The level of the row is accomplishing the size of the phenomenon as the point specified in it (period) of time. Distinguish the following types of speakers: torque and interval; rows equals equal and unequal levels in time; Stationary and nonstationary. The moment of the dynamics of the levels of which are accomplished by the studied phenomenon at a particular point in time, such rows are used to describe the values \u200b\u200bof the type of stock. The interval is a series of ct, the levels of which are accomplished by the accumulated result of changing phenomena for certain intervals. In a row with the equifiable levels, the registration and end date of the periods are presented through equal interest in each other. In a number with no equitrate levels, the principle of equality of periods of time is not respected. A number of speakers in a change in levels of which is not observed in general orientation is stationary, on the contrary, the non-stationary series is characterized by the presence of a general orientation in changing the levels of the studied indicator. The absolute change is accomplishing an increase in or reducing the level of a number during a certain period of time. The absolute increase in the variable base is called growth rate. Absolute increase (chain): y y y absolute increase (basic): y y c b i i i where y i level of the compared period; y i level of the preceding period; y The level of the base period. For the accuracy of intensity, i.e. The relative change in the level of dynamic series for any period of time is calculated growth rates (decrease). The intensity of the level change is estimated by the rating - y 27

28 IEC report level to basic. The indicator of the intensity of changes in the level of the row, expressed in the proportion of a unit is called the growth rate, and in the percentage of growth rate. These indicators of the intensity change differ only by units of measurement. Growth coefficient: chain y c i to r; Basis yi y b i to r. y The growth ratio (reduction) shows how many times the level compared to the level with which the comparison is made (if this coefficient is more than one) or which part of the level with which a comparison is made is a compared level (if it is smaller than one). The growth rate is always a positive number. The relative estimate of the rate of change in the level of the row per unit of time is given indicators of the growth rate (abbreviation). T to r. Growth rate: C yi b yi chain t p; Basic T y y i r. The growth rate (abbreviations) shows how much percent compared levels greater than or less than the level accepted beyond the comparison base and is calculated as the absolute gain ratio to the absolute level accepted beyond the comparison base. The growth rate can be positive, negative or equal to zero, it is expressed as a percentage and share of the unit (growth coefficients): growth rate: y C b yi chain TR; The basic T PR. Y Y y I The rate of growth (abbreviations) can be obtained from the growth rate expressed as a percentage if the% subtract out of it. The growth rate is obtained by subtracting a unit from the growth coefficient: T PR T R; To pr to r. Y C Y B between chain and basic speaker indicators There is a relationship. Chain and basic absolute gains are interconnected: 28

29 The product is sequential chains of growth coefficients equal to the basic growth ratio of the final: to the RCs to the RBN, from dividing the subsequent basis growth rate to the previous one equal to the corresponding chain growth rate: T T T RBi RBI T RCI. In order to correctly assess the value of the growth rate, consider it in comparison with an absolute increase. As a result, we obtain an absolute value (content) of one percent of the increase and calculate as an absolute increase ratio to the growth rate for the same period of time,%: Yu Yi Yi Yi A%, Yi. The T Yi y y y y y is for generalizing the speakers of the studied phenomenon to determine the average indicators: the average levels of the row and the average parameters of the row levels. The average level of the row is based on the middle arithmetic formula: where y, ..., yn absolute levels of the row; n number of row levels. The average absolute increase can be calculated by the basic and chain methods: the base: where n is the number of row levels. Chain: Y y y n y n, where n number of chains absolute gains. y n y c, y, n 29

30 a consolidated generalizing aspectuation of the intensity of the intensity of a number of speakers is the average coefficient (rate) of growth (reduction), showing how many times an average per unit of time changes the level of a number of speakers. bk n y y n; The average growth rate (abbreviations) is calculated based on the average growth rate, subtraction from the latter. Accordingly, when calculating the average growth factors from the values \u200b\u200bof growth coefficients, a unit is subtracted: if the levels of the speakers grow, the average growth rate will be greater than%, and the average growth rate of positive value. A negative growth rate is an average rate of abbreviation and aparthes the average relative rate reduction rate. T PR T PR; TO PR. The tasks are based on the calculation and analysis of analytically indicators of dynamically series, which are determined by the formulas (for convenience and clarity of ISOD, and the calculated indicators set out in tabular form, pre-name it. Task 3 Production of cement by enterprises of the Orenburg region is accomplished by the following data: years of issue, million PCS, 9 28 3, 29 34, 2 4.9 2 38.8 To analyze the dynamics of cement production for 25 2 years. Calculate: chain and basic absolute increases, growth rates and growth rates, the absolute content of one percentage of increment; obtained indicators Imagine in the table and build a schedule; 2. The average values \u200b\u200bof the dynamics of cement production; Make conclusions. 3

31 Task 32 Gross grain collection of agricultural enterprise is suitable for the following data: the years of gross grain collection, thousand tons 2.7 8.9 9, 8.3 6.4 25, to analyze the dynamics of grain production for 25 2 Gg. Calculate: chain and basic absolute increments, growth rates and growth rates, the absolute content of one percentage of growth; Replace the indicators in the table and build a schedule; 2 average grain production dynamics; Make conclusions. Task 33 The yield of grain crops in the agricultural enterprise is suitable for the following data: years yield, c / ha 25,76 26 2.8 27 6.4 28 9.8 29.3 2 9.9 2 3.2 for analyzing the yield crop yield for 25-2 years. Calculate:. chain and basic absolute gains, growth rates and growth rates, the absolute content of one percent of the increase; Replace the indicators in the table and build a schedule; 2. Average rates of crop grain yields; Make conclusions. 3.

32 Task 34 The dynamics of the number is large and medium of industrial enterprises in Orenburgia is accomplished by the following data: the number of enterprises for analyzing the dynamics of the size of the size and average industry enterprises for 25 2 years. Calculate:. chain and basic absolute gains, growth rates and growth rates, the absolute content of one percent of the increase; Replace the indicators in the table and build a schedule; 2. Average indicators of the dynamics of the number of enterprises; Make conclusions. Task 35 Dynamics of electrically equipment of labor at one of the industrial enterprises of the region is accomplished by the following data: Years Electricity, kWh / person. 25 3,7 29 3,88 2 4, 2 4.5 For analyzing the dynamics of electrically equipment of an industrial enterprise for 25 2 GG . Calculate :) Chain and basic absolute growths, growth rates and growth rates, the absolute content of one percentage of growth; Replace the indicators in the table and build a schedule; 2) average indicators of the dynamics of electrically equipped enterprises; Make conclusions. 32.

33 Task 36 Overdue wage arrears in January-June is as follows: Months January February March April May June Debt, 42, 52.2 64.3 5.4 54,6,52, million RUB. To analyze the dynamics of overdue debt, calculate :) chain and basic absolute increases, growth rates and growth rates, the absolute content of one percent of the increase; Replace the indicators in the table and build a schedule; 2) average indicators of the dynamics of overdue wage debt; Make conclusions. Task 37 The dynamics of the cost of chicken eggs in the Russian Federation is accomplished by the following data: the year price for the dec., Rub. 6.57 24.5 27.6 34.89 4.2 34.6 38,56 For analyzing the dynamics of the value of eggs, calculate :) Chain and basic absolute increases, growth rates and growth rates, the absolute content of one percent of the increase; Replace the indicators in the table and build a schedule; 2) average rates of the cost of eggs; Make conclusions. Task 38 Dynamics of the cost of butter in the Russian Federation is as follows: a year price per kg, rub. 69.2 2.42 9.7 55, 75.54 9.68 239.55 To analyze the dynamics of the cost of cream oil, calculate :) chain and basic absolute increases, growth rates and growth rates, the absolute content of one percentage of growth; Replace the indicators in the table and build a schedule; 2) average indicators of the dynamics of the cost of the cream oil; Make conclusions. 33.

34 Task 39 The dynamics of the cost of Saara sand in the Russian Federation is accomplished by the following data: year price per kg, rub. 5,62 9.69 22.7 2.63 23.7 33.2 4.62 To analyze the dynamics of the cost of Saara sand, calculate :) chain and basic absolute increases, growth rates and growth rates, the absolute content of one percentage of growth; Replace the indicators in the table and build a schedule; 2) Average indicators of the cost of the cost of sara-sand; Make conclusions. Task 4 Dynamics of the cost of sunflower oil in the Russian Federation is as follows: year price per liter, rub. 23.2 4.6 39.4 6.26 74.32 58.6 72.6. To analyze the dynamics of sunflower oil, calculate :) Chain and basic absolute growths, growth rates and growth rates, the absolute content of one percentage of growth; Replace the indicators in the table and build a schedule; 2) average rates of the cost of sunflower oil; Make conclusions. 34.

35 Topic 5: Indices in statistics Methodical instructions for solving problems: Statistical index This is a relative value that accepts the ratio of values \u200b\u200bof a certain indicator in time, space, as well as comparison is actually data with a plan or other standard. Individual indices are accomplishing the relative change in a separate single element of a complex set (for example, a change in the price of LEB, milk, a change in the volume of oil and gas production, etc.). General (aggregate) indices account for the relative change in the indexed value (indicator) as a whole in a complex combination, the individual elements of which are incommensurable in physically one (table). Table Types Aggregate indexes and formulas and calculation The value index (turnover, revenue) of the calculation formula I PQ \u003d QQPP Price index (PAIS) PI PI \u003d QQPP formula of the physical volume of products I Q \u003d QQPP Price (E. Laspeyres) Li P \u003d QQPP wages I \u003d TT prices (I. Fisher) F P PLI \u003d II PP Foundation for wage IT \u003d TT cost I Z \u003d QQZZ The difference between the numerator and denominator of the value of the value of the implementation (turnover) reflects the absolute change in the turnover due to the dynamics of the price of the price and physical volume of products. The difference between the numerator and denominator of the price index means the absolute increase in the turnover (sales revenues) as a result of the average price changes or savings (recreation) due to the average decline (increase) of prices. The difference between the numerator and denominator of the index of the physical volume of products reflects the change in commodity turnover under the influence of the dynamics of the physical volume of the products implemented. 35.

36 The relationship of indexes: i pq \u003d p i Q i; I T \u003d IT I. (26) Any aggregate index can be transformed into an average arithmetic of individual indexes. For this, the indexed value of the reporting period, which is in the numerator of the aggregate index, is replaced by the product of the individual index to the indexed value of the base period. Thus, the individual price index is: P I, P Location: P i p. Consequently, the transformation of the aggregate price index in the middle arithmetic is: i p \u003d q q p p \u003d q q p p i, therefore: similar to the cost index is И z \u003d q q z z \u003d q q z z i. Z i, from where z iz z is equal to the same way to the index of the physical volume of products (turnover) Q i, from where q q q, therefore: i p \u003d q q p \u003d q q p p i. When studying, the qualitative indicators can reason be considered a change in time or in the space of the average value of the indexed indicator for a certain homogeneous totality. Being a summary of the quality indicator, the average value is folded as 36

37 Influenced by the values \u200b\u200bof the indicator in individual elements (units), from which the object consists and under the influence of the relationship and scales ("structure" of the object). The variable composition index reflects the dynamics of the average (for a homogeneous set) by changing the indexed value of the individual elements (parts) of the whole) and by changing the scales on which individual values \u200b\u200bare weighted. I. Absolute change in the indexed value due to DV factors:. The fixed-line index reflects the dynamics of the average due to changes in the indexed value, when fixing weights at the level, as a rule, the reporting period: I F.S. ; (). The dynamics of the average due to changes in weights when fixing the indexed value at the base period level reflects the shifting structural index: i page; (). The relationship of indexes and absolute changes in the average value of the indexed indicator: I p.S. I F.S. I; p. () () In the task, general indices should be calculated, the absolute size of savings or recreation of money, the process of turnover. It is necessary to know the methodology for building an aggregate index, which provides for a response to three questions: 37

38 What value will be indexed; Through what composition is the heterogeneous elements of the phenomenon it is necessary to calculate the index; What will serve as weighing when calculating the index. When choosing weight should be guided by the following rule: if the quantitative indicator index is built (production, sales of goods, etc.), the weights are taken for the basic period; If the index of the qualitative indicator (cost, price, profit, etc.), will take weight during the reporting period. Task 4 Dynamics of price average prices and sales in the city market is accomplished by the following data: the name of the goods sold goods, kg June 2. July 2 G. Middle price per kg, rub. June July 2 G. 2. Market: Fresh cucumbers Fresh tomatoes Market 2: Fresh cucumbers for the market for two types of goods computiate: a) Common Travel Index; b) general price index; c) communities index of physical volume of turnover. Show the relationship between calculated indexes. Determine in the reporting period, the increase in turnover and decompose the factors (due to changes in prices and sales of goods). 2. For two markets together for fresh cucumbers, identify: a) the index of price of variable composition; b) constant price index; c) index structural shifts. Explain the difference between the values \u200b\u200bof the indexes of permanent and variable composition. Make conclusions. Task 42 Dynamics of the cost and production volume is accomplished by the data presented in the table. Based on the available data, calculate: 38

39. For the plant (for two types of products together): a) General index of production costs; b) general index cost of production; c) communities index of physical volume of production. Show the relationship between calculated indexes. Type of products produced products, thousand units basis reporting period Period costing unit products, rub. Base reporting period The period is plant A 5 5 B Factory 2 and determine in the reporting period a change in the cost of production costs and decompose by factors (due to changes in the cost and volume of products produced). 2. For two plants together (according to products a): a) the cost index of the variable composition; b) the cost index of constant composition; c) index structural shifts. Explain the difference between the values \u200b\u200bof the indexes of permanent and variable composition. Make conclusions. Task 43 The volume of implementation and prices for vegetable products of the city's markets are accomplished by the following data: Product type The basis is sold, kg reporting period Price per kg, rub. Basic Period Reporting Period Market Carrot Cabbage Market 2 Carrot Based on Available Data Calculate: For the market (for two types of vegetables together): a) Common Travel Index: 39

40 b) general price index; c) the general index of the physical volume of turnover. Show the relationship between calculated indexes. Determine the growth in turnover in the reporting period and decompose the factors (due to changes in prices and the volume of vegetables). 2. For two markets together (for carrots): a) the price index of variable composition; b) constant price index; d) index structural shifts. Explain the difference between the values \u200b\u200bof the indexes of permanent and variable composition. Make conclusions. Task 44 Dynamics of the cost and production volume is accomplished by the following data: the type of production is developed, thousands of units basis reporting period Period the cost of the unit of products, rub. The underlying reporting period The period factory A B plant 2 A based on the available data Calculate:. For the plant (for two types of products together): a) General index of production costs; b) general index cost of production; c) communities index of physical volume of production. Show the relationship between calculated indexes. Determine in the reporting period a change in the amount of costs for the production of products and decompose the factors (by changing the cost and volume of products produced). 2. For two plants together (according to products a): a) the cost index of the variable composition; b) the cost index of constant composition; c) index structural shifts. Explain the difference between the values \u200b\u200bof the indexes of permanent and variable composition. Make conclusions. four

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Option 6 task. Absorption 6 .. P / p Number of average score based on p / p Number of average scores missed all subjects missing for all mandatory classes, mandatory subjects. Classes, Part 8,8 6 4

3 Introduction Statistics is designed to ensure the collection, processing and presentation of information on the level and opportunities for the development of enterprises and the industry as a whole. Development of market relations in the country before statistics

11. Methodical instructions for learning discipline. Starting a study of discipline, the student needs to be carefully familiar with the thematic plan of classes, a list of recommended literature.

Ministry of Education and Science of Russia Federal State Budgetary Educational Institution of Higher Professional Education "Chelyabinsk State University" (FGBOU VPO "Chelju") Kostanay branch

Lecture 3. Main statistics categories. Summary and grouping of statistical data 3.1. The main categories of statistics of one of the most important categories of statistical science is a sign category. Exactly

Option 5 The task is to group stores ... on the basis of the number of sellers, forming 5 groups with equal intervals. The store number turnover (million rubles) costs of circulation (million.

Task for testing on the discipline "Statistics" for students of the second courses of training for 2013/2014 learning year The task for testing consists of two parts. The first part of the work

Luxury head. Department of Accounting, Analysis and Audit MK Ulthanova Protocol 2012 Polls on the discipline "Tatstika" for correspondence department 1. Subject, method and objectives of statistics 2. Organization of statistics

Task 1 There are the following reporting data 25 plants in one of the industries: factory number The average annual value of the main production facilities, billion rubles. Product volume in comparable

4 .. Index method 372. Task ((6)) ROF 3 ... - - preceding reporting. 373. Task ((57)) Larof 5 ... - preheated reporting. 374. Task ((92)) 347 total performance index

262 food. To solve the tasks of analyzing the dynamics of indicators characterizing heterogeneous totals, and the index is used. Statistical index is a relative comparison value of complex

Ministry of Education and Science of the Russian Federation Federal Agency for Education State Educational Institution of Higher Professional Education Orenburg State

1 2 Table of contents Annotation ... 4 1. Enterprise and grouping data 5 2. Statistical tables. 7 3. Graphic image of statistical data "...... 8 4. Rows of distribution. Medium values \u200b\u200band indicators of variations..8

Theme 3.4: absolute, relative, average values \u200b\u200band indicators of Variation 1. The effect of absolute, relative and average values. 2. Home types of relative and medium sizes. 3. Constitutional variation

Ministry of Education of the Russian Federation Kazan State Technical University. A.N. Tupolev branch "Vostok" OM SUSLOVA, D.S. Sattars Workshop on general statistical theory Educational and methodical

Tasks on statistics Task 1. Statistical groups. Grouping 25 enterprises at the cost of fixed assets, highlighting, five groups with equal intervals. : The interval was found according to the formula

Government License of St. Petersburg Committee on Education 0665 dated 03.09.2013 Program "Statistics" 1. Introduction 2. Item 1. Item, method and objectives of statistics Subject of statistics research. Mass

Large Russian encyclopedia indexes Authors: in Mnashkin indexes in statistics (from lat index pointer, indicator), indicators of relative change in this level of the investigated phenomenon compared

Podzors N.G. Bikeeva M.V. Statistics Tutorial Saransk 5 G. Ministry of Education and Science of Russia Federal State Budgetary Educational Institution of Higher Professional Education "Mordovsky

Methodical instructions for performing testing in the system of economic sciences Statistics is one of the fundamental disciplines that form a specialty economist its methods and indicators are used.

Moscow Humanitarian and Economic Institute Work Program Statistics Specialty: 40.0.01 Law and Organization of Social Security Stavropol, 015 g Working program of the academic discipline "Statistics"

Task for testing on the discipline "Statistics" for students of the second courses of training for 2010/2011 The academic year The task for testing consists of two parts. The first part of the work

Statistics 1. The goal and objectives of the discipline The purpose of studying the discipline "Statistics" is to familiarize students with the content of statistics as a scientific discipline, with its basic concepts, methodology and methods

Federal Agency Communication Agency of the State Federal Educational Institution of Higher Professional Education Volga State University of Telecommunications and Informatics Electronic

1. The passport of the working program of the academic discipline "Statistics" 1.1 The scope of the program The program of the educational discipline is part of the approximate main professional educational program

Ministry of Agriculture of the Russian Federation Federal State Budgetary Educational Institution of Higher Professional Education "Orenburg State Agrarian University" Faculty

Theoretical foundations of statistics Question 8 What is the general concept of statistical observation? The general concept of statistical observation can be formulated as follows: a planned, scientific and organized

Ministry of Education and Science of the Russian Federation South Russian State Polytechnic University (NPI) named after M.I. Platov Shakhtinsky Institute (branch) Yurgpu (NPI). M.I. Platov statistics

Nan Chow at the Academy of Marketing and Socio-Information Technologies IMSI, Krasnodar Abstract Direction of Training 38.03.04 "State and Municipal Management" Focus (profile)

Department of Economics and Management Statistics Educational and Methodical Complex for FSPO students, studying with the use of remote technologies Module 6 rows of dynamics Compiler: Art. Teacher E.N.

This page posted a large number of solved statistics problems - from simple to complex, with confusing conditions. These typical examples are designed for independent work of students of economic and management specialties of universities. Theme covers the entire course of the general theory of statistics, the main sections of the course of socio-economic statistics and statistics of the enterprise. Solutions contain explanations and conclusions.

Tasks with solutions for mathematical Statistics are in the site section of probability theory and mathematical statistics

About paid assistance to students with studies can be read on the page

A summary of the statistical summary and grouping, types of groups, as well as the Formula of Strocesssess are briefly considered. An example of solving the problem of grouping a statistical aggregate is given.

1. Relative indicators of the planned task and execution of the plan

Relative indicators of the planned task, the implementation of the plan, dynamics and their relationship between themselves are considered. Examples of calculation of the relative values \u200b\u200bunder consideration are given.

The page considers the calculation of the relative indicators of the structure (ABS) and coordination (HWC). Examples of calculation of the relative values \u200b\u200bunder consideration are given.

The page discusses the relative indicators of the dynamics (ATS) and intensity (WII). Examples of calculation of the relative values \u200b\u200bunder consideration are given.

Solved several tasks on statistics on the use of average values. Examples of calculations of the average arithmetic simple, medium arithmetic weighted, mean harmonic weighted are given. Solving tasks preceders a brief theory.

The concept of average chronological magnitude in the ranks of the dynamics, types of average chronological are considered. Examples of calculating the average chronological for moment and interval rows with equifiable and unequal intervals are given.

Description of structural medium discrete and interval series. At the examples of solving problems, the calculation of indicators - fashion, medians, quarters, deciles are shown.

In the problem above, the calculation of absolute and relative indicators of the variation of the interval row - the variation variation, the average linear deviation, dispersion, the variation coefficient is shown.

The page considers the problem for the rule of dispersions and the accompanying calculation of the average intragroup and intergroup dispersions.

Calculating the numeric characteristics of the sample. Specifications are calculated as selective medium, mod and median, the average square of deviations (dispersion), selective average quadratic deviation and variation coefficient. An example of calculating the marginal error of the sample medium and selective share, as well as the boundaries of the general average and specific gravity.

The page is a description of the methods of selective observation, formulas are presented to calculate the average and limit sampling errors. The information on the methods of the actual selection, mechanical sample, a typical (zoned) sample, serial sample are presented. A table with formulas is shown to determine the size of the sample with various selection methods.

A brief theory is given and an example of solving the problem of calculating the correlation coefficient of fechin signs is considered.

The formula and meaning of the linear correlation coefficient of Pearson, the significance of the linear correlation coefficient. The page contains a brief theory and a typical example of calculating the Pearson correlation coefficient and checking its importance.

There is a brief theory and an example of solving the problem of rank correlation. The concept of rank correlation is given, the calculation of the coefficient of rank correlation of the Spirmeal is shown.

The page addresses the use of rank correlation and the Kendalla rank correlation coefficient in statistics. A brief theory is given, as well as a task with an example of calculating the Kendalla coefficient with a test of a hypothesis about its importance.

The calculation of the empirical correlation ratio and the empirical coefficient of determination is considered, the example shows the calculation of the intragroup and intergroup dispersion.

A brief theory and the example of solving the problem shows the calculation of the coefficients of the association and contingentation.

2. The coefficients of mutual conjugacy of Chuprov and Pearson

The page contains information on the methods of studying the relationship between high-quality features using the mutual conjugacy coefficients of Chuprov and Pearson.

The page addressed the tasks on the ranks of the speakers. The calculation of chain, basic and average speakers, as well as the missing levels of dynamic series are shown. The formulas of chain, basic and medium absolute gains, growth rates and growth rates are given.

The page contains a sequential and systematic presentation of the proven practices of processing methods for processing dynamic series - method of moving average and method of enlarging intervals.

The basic methods of index analysis are presented. In solvable tasks, individual and general price indices, cost, physical volume, the cost of turnover and costs are calculated, and the expansion of absolute increase by factors is shown. The calculation of medium indices - indices of prices and the cost of variable and constant compositions, as well as the index of structural shifts. The decomposition of the absolute increase in the average price and cost of factors is shown.

An example of solving the problem for calculating the price indices of Paasha, Laspeyres, Fishera, as well as indices of the physical volume of Laspeyres and Paasha is given. The relationship between calculated indexes is shown.

The method of calculating the calendar, tablet and maximum possible work time funds, as well as their use coefficients is presented. Contains information on the preparation of working time balances in the enterprise. The workday use coefficients, working period, as well as an integral operation of working time use are considered.

Solved the task with the calculation of the level and dynamics of labor productivity. The indices of the average labor productivity are calculated - the index of variable composition, constant composition and structural shifts. The decomposition on product growth factors is shown, calculating the number of ever-free workers due to the growth of productivity.

In the task presented on the page, the indices of the average wage of the variable composition, direct composition, structural shifts, shows the decomposition on the factors of changes in the average wage and wage foundation.