Download presentation on statistics. Presentations on the subject of statistics. System of National Accounts

Nikiforov
Sergey
Alexeyevich
46 100

INTRODUCTION

Statistics is the study of social phenomena
point of view of two categories:
QUANTITY AND QUALITY.
From any data set, the researcher in
according to the task must choose two
TYPES of collections you need
determined in terms of quality and
quantitative categories, and then
explore for the whole
a number of indicators.
2

INDICATORS

TOTAL is a quantitative
manifestation of animate or
inanimate objects in the study
areas. For example: workers, factories, machines.
OPTION (variation) - (X) - quality
manifestation of the object under study. In the variant
you can always select RANGES of quality
(max - min).
FREQUENCY (weight) - (f) - number option,
quantitative manifestation of a trait
object under study.
3

A TASK

Work shops were subjected to inspection at
the subject of detection of the TARIFF DISCHARGE,
AGE, SALARY. According to the data received
required.
1. Construct distribution series.
2. Give a graphic representation of the series.
3. Calculate the indicators of the distribution center.
4. Calculate the variation indicators.
5. Calculate the indicators of the distribution form.
6. Build a pie chart.
4

THEORETICAL TRAINING

1. Select aggregates from the data array.
These are the aggregates:
workers,
salaries,
ages
tariff ranks.
2. Define populations as variants and frequencies.
Options: tariff category (lowest - highest),
age (young - old),
salary (low - high).
Frequencies: working (quantity).
5

THEORETICAL TRAINING

3. Identify options by row
distribution. Statistical
distributions can be of two types:
DISCRETE AND INTERVAL.
They are determined by the variant level. Any
research starts with building
discrete series, which is determined
option with the narrowest range
extensions. In this problem, the narrowest
y range tariff category, that's why.
we build a discrete series on this set
6

THEORETICAL TRAINING

4. Determine the required number of groups (n)
The key issue of the statistical
distribution is the definition
required number of groups. Theoretically,
the number is determined by the formula
STurgess:
n=1 + 3.322 logN.
But in discrete series, the number of groups
determined by the number of varieties
option.
7

INITIAL DATA

Tariff category options (x):
433635
456444
332242
542544
In this case, the notation should not be confused.
n=24 – (number of workers) – number of units
sample population. (chevs).
n=5 – (number of groups), because five
types of tariffs.
8

Build a statistical table.
Group
py
Diff
ovid
news
boil
ant
Hour
that
s
Produced
second option
to frequencies
x
f
(xf)
1
0
1
2
4
2 4= 8
2
3
5
3
4
4
5
Accumulated Frequencies
S
(plotz)
Linear deviation
d = x -х̄
ІdІf d²f
4 (1 -3)
2-3,792=-1,792
4
4
3 5=15
4+5= 9 (4 – 8)
3-3,792=-0,792
5
5
9
4 9=36
9+9=18 (9 – 7)
4-3,792=+0,208
9
9
5
4
5 4=20
18+4=22(18-21)
5-3,792=+1,208
4
4
6
2
6 2=12
22+2=24(22-24)
6-3,792=+2,208
2
2
7
0
-
24 91
Udeln
th weight
Degree
sectors
Y(%)
c
100
360
9

SOLUTION

1. Construct a discrete distribution series in
which to determine:
Required number of groups, options, frequencies,
accumulated frequencies to distribute with
using the RULES OF THE LEFT MADE NUMBER
(PLOC): The left digit in the range belongs to
given group, the right digit in the range
belongs to the next group. Rule no
extends to the last group.
S - accumulated (cumulative) frequency -
determined by successive summation
frequencies from the first row to the last.
10

SOLUTION

The discrete series is distributed over five
groups, so we enter five
varieties option. frequencies,
entered in the table according to
the number of options owned
certain type:
The first group - 2 2 2 2 - 4.
The second group - 3 3 3 3 3 - 5.
11

SOLUTION

The third group - 4 4 4 4 4 4 4 4 4 - 9.
The fourth group - 5 5 5 5 - 4.
Fifth group - 6 6 - 2.
Finally, you need to calculate
total score: 4+5+9+4+2 = 24.
In doing so, you can use the following
rule: n \u003d f \u003d S \u003d 24
12

SOLUTION

The accumulated frequency is counted
in the following way:
In the first group, the cumulative frequency is
the frequency of the corresponding series (4).
In the second group, the calculation is carried out according to
following scheme: 4+5=9.
Third group: 9+9=18.
Fourth group: 18+4=22.
Fifth group: 22+2=24.
13

SOLUTION

Distribution by rule (PLOC)
is carried out as follows:
First group (1 - 4), unit (left)
means belongs to the first group,
four (right) means belongs
the subsequent second group, i.e. total: (1 -
3).
14

SOLUTION

The second group (4 - 8).
The third group (9 - 17).
The fourth group (18 - 21).
Fifth group (22 - 24), because rule on
the last group is not covered.
15

SOLUTION

2. Give a graphic
discrete row. Graphic
the image of a discrete series are:
frequency polygon, histogram, cumulate.
Before plotting, you need to
carry out the process of expanding the borders
Varieties option, according to
following rule:
16

SOLUTION

step back from the left edge to the left by one
option and from the right edge to the right by one
option. Left edge of distribution 2.
Step left one option - 1. This is the left
extension. Right edge 6 - 7, this is the right
extension. At the same time, it is necessary
understand that the frequencies in the options
extensions are 0.
the values ​​are entered into the table.
17

SOLUTION

Polygon. Built in rectangular
coordinate systems. Along the abscissa

version with expansion, along the axis
ordinates are the frequency values.
The axes must be calibrated: axis (0 - x)
– (0 – 7), i.e.
18

SOLUTION

from origin to right
expansion varieties variant, axis
(0 - y) - (0 - 9), i.e. from the origin to
maximum frequency. Then, in
according to the data in the table, apply
on the point chart. Received points
connect in series from left to right.
19

SOLUTION

Polygon
10
9
8
7
6
5
4
3
2
1
0
0
1
2
3
4
5
6
7
8
20

SOLUTION

Bar chart. This is the system
rectangles whose heights are equal
the frequencies of the corresponding groups, and
bases are located on
varieties of variant
corresponding retreat to the left and
to the right by 0.5 from each option. AT
histogram coordinate axes coincide
with polygon axes.
21

bar chart

10
9
8
7
6
5
4
3
2
1
0
0
1
2
3
4
5
6
7
22

SOLUTION

Cumulate. Built in a rectangular
coordinate system, abscissa
values ​​of varieties are postponed
option (no right value
extensions), along the y-axis of the value
accumulated frequencies. Graduation: axis (0 -
x) - (0 - 6), axis (0 - y) - (0 - 24), i.e. from
origin to the value of the last
groups.
23

SOLUTION

When drawing dots,
use the following rule:
left extension border
varieties option is
starting point, in it
cumulative frequencies are 0, all
rest
24

SOLUTION

options are equal to values
accumulated frequencies of the corresponding
groups. Received points
connected in series
straight lines from left to right.
Right added border option
in scheduling participation
accepts.
25

CUMULATE

26

SOLUTION

and the arithmetic weighted average:
(Xf) 91
X
3,792
f
24
27

SOLUTION

Fashion (Mo) is an option that is more often
of all occurs in the distribution,
determined by the maximum frequency.
Mo = 4, because f(max) = 9.
28

SOLUTION

The median (Me) is the variant that
divides the distribution series in half,
determined by the number of the median in
column of accumulated frequencies, taking into account plots.
Me = 4, because
N(Me)
n 1 24 1
12.5S (9 17) X 4 Me 4
2
2
The coincidence of mode and median is random.
29

SOLUTION

3. Calculate center indicators
distributions, which include FASHION,
MEDIAN, ARITHMETIC AVERAGE.
The average is denoted
a horizontal bar above the symbol.
Take the arithmetic mean
simple:
X
X
n
30

SOLUTION

4. Calculate the variation indicators, to
which include:
linear deviation d = x –х̄, which
calculated for each group,
31

SOLUTION

Average linear deviation
(/ x x / f) (/ d / f)
d
f
f
Standard deviation
(xx) f
f
2
(df)
f
2
32

SOLUTION

Dispersion
(x x) f (d f)
D
f
f
2
2
The coefficient of variation
V
x
100%
33

SOLUTION

Calculate Shape Measures
distribution (skewness coefficient)
x Mo
As
34

SOLUTION

Moreover, if As is greater than 0, then the asymmetry
right-handed, if As is less than 0, then
left side asymmetry. If a
asymmetry is greater than unity in absolute value,
then the asymmetry is significant if
asymmetry is less than unity in absolute value,
the asymmetry is negligible.
35

SOLUTION

22,26
d
0,928
24
36

SOLUTION

31,958
D
1,332
24
37

SOLUTION

31,958
1,332 1,154
24
38

SOLUTION

1,154
V
100% 4,8%
4
39

SOLUTION

3,79 4
As
0,182
1,154
40

SOLUTION

Build a pie chart. It's a circle
divided by radii into separate
sectors. To build a chart
frequencies from absolute indicators
convert to relative, i.e. calculate
specific gravity Y(%), and then using
formulas to calculate the degree of the sector.
360 at %
FROM
100%
0
41

SOLUTION

Pie chart. Despite,
that the calculations were made
frequencies, and as a result
percentages and degrees, but sectors
marked with variant values.
42

Pie chart Despite the fact that the calculations were made by frequencies, and as a result, percentages and degrees were obtained, but the sectors are marked

Pie chart
Although the calculations were made
by frequencies, and as a result, interest was obtained and
degrees, but sectors are labeled with values
option
43

RESULTS

That. as a result of solving the problem,
following results:
Mo
Me
X
4
4
3,792
d̄
G
V
As
44

RESULTS

x
f
(xf)
S
1
0
1 2
4
2 4=8
4 (1 – 3)
2-3,792=-1,792
2 3
5
3 5=15
4+5= 9 (4 – 8)
3-3,792=-0,792
3 4
9
4 9=36
9+9=18 (9–17)
4-3,792=+0,208
4 5
4
5 4=20
18+4=22 (18–21)
5-3,792=+1,208
5 6
2
6 2=12
22+2=24 (22–24)
6-3,792=+2,208
7
0
-
24
-
-
-
91
(plotz)
d = x - x̄
/d/ d²f
f
Y(%)
c
100
360
45

test number 1 1. Build the distribution series. 2. Give a graphic representation of the series. 3. Calculate the indicators of the distribution center. four.

test №1
1. Construct distribution series.
2. Give a graphic representation of the series.
3. Calculate the indicators of the distribution center.
4. Calculate the variation indicators.
5. Calculate the indicators of the distribution form.
6. Build a pie chart.
OPTIONS (X)
FREQUENCY (f)
HB + 10
HB + 30
HB + 20
HB + 40
HB + 30
HB + 80
HB + 40
HB + 20
HB+ 50
HB + 10
46

TASK #2

INTERVAL SERIES.
In the second part of the problem solution
it is necessary to study the age of the workers, but
because age range over range
tariff category, then it is considered with
using statistical intervals, i.e.
so-called interval boundaries
option. In this case, the sequence
problem solution is saved.
47

THEORETICAL TRAINING

1. At the first stage, it is necessary to calculate
distribution interval using
INTERVAL RULE: upon receipt
fractional values ​​are rounded to integers
big side. For example: 2.1 = 3!
X max X min
i
n
48

2. At the second stage, it is necessary to calculate
distribution centers or intervals
distribution of each group:
X max X min
X
2
49

INITIAL DATA

Worker age options (X) :
24 42 36 18 22 21 43 38 19 25 34 40
31 26 28 35 18 42 23 29 27 33 22 40
n= 24 (chevs) - the number of workers.
n = 5 (number of groups), because in the first part
tasks were considered five groups, then
interval series is necessary
divided into five groups.
50

INTERVAL

43 18
i
5
5
51

SOLUTION

1. Build an interval distribution series in
which to define: boundary intervals
options, interval midpoints, frequencies,
cumulative frequencies distributed over
rule (plots).
First group. (18 - 23). Xmin = 18 - left
border of the first interval to get
the right border must be added to Xmin
interval value: 18+5=23 – right border
first interval.
52

SOLUTION

Second group. (23-28). Beginning of the second group
is the right boundary of the first group, i.e. (23) -
left border of the second interval. Right border
calculated according to the standard scheme: 23+5=28.
Third group. (28 - 33).
Fourth group. (33 - 38).
Fifth group. (38 - 43).
With correctly composed intervals Xmax
must be less than or equal to the right border
last interval.
53

SOLUTION

Interval series as well as discrete
needs to be expanded. At
this in interval series expansion
carried out on the amount received
interval, i.e. for 5 units. From left
interval to the left, from the right interval
to the right by the interval. THEN. left
the additional interval will be (13-18),
and the right one is additional (43-48).
54

MIDDLE INTERVALS

23 18
X (1)
20,5
2
55

SOLUTION

Interval midpoints are determined
in the following way:
First group: 20.5
Second group:
25,5
Third group:
30,5
Fourth group: 35.5
Fifth group:
40,5
56

SOLUTION

Frequencies are calculated as follows
way. Each group owns
options that, by their meanings
fit into the boundaries of the intervals, with
condition for the operation of the rule (plots).
For example, for the first group, options with
value 23 do not belong to the first
group, and the subsequent - the second. That. in
options remain for the first group: 18 22
21 19 22 18, i.e. only 6 frequencies.
57

SOLUTION

In the second group, the options are: 24 25 26 23 27, i.e. 5
frequencies. Option 28 belongs to the third group.
Third group: 28 29 31, i.e. 3 frequencies.
Fourth group: 36 33 35 34 i.e. 4 frequencies.
Fifth group: 42 38 40 40 42 43, 6 frequencies, with
this option 43 belongs to the fifth group, because
rule (plots) on the last group is not
spreads and Xmax = 43 coincides with
the value of the right boundary of the last group.
58

SOLUTION

Values ​​are plotted along the y-axis
frequencies, i.e. from 0 to 6 (maximum
values.
In this case, the points are plotted on the graph according to
table values: the middle of the interval -
frequency, so on the axis (o - x), in addition to
intervals it is necessary to note the values
the middle of the intervals.
59

SOLUTION

The accumulated frequencies are determined by
standard scheme.
First group:
6
Second group:
6 + 5 = 11
Third group:
11 + 3 = 14
Fourth group: 14 + 4 = 18
Fifth group:
18 + 6 = 24
60

SOLUTION

Distribution of cumulative frequencies over
rule (plots).
First group:
(1 – 5)
Second group:
(6 – 10)
Third group:
(11 – 13)
Fourth group: (14 - 17)
Fifth group:
(18 – 24)
Enter the received data into the standard
statistical table.
61

SOLUTION

X
X
f
x΄f
13-18
15,5
0
0
1
18-23
20,5
6
2
23-28
25,5
3
28-33
4
5
∑
S (plots)
d
/d/f
d²f
123
6 (1-5)
-9,8
58,8
5
127,5
11(6-19)
-4,8
30,5
3
91,5
14(11-13)
33-38
35,5
4
142
38-43
40,5
6
243
43-48
45,5
0
0
24
727
d⁴f
Y%
С⁰
576,24
25
90
24
115,2
20,6
74
+0,2
0,6
0,12
12,5
45
18(14-17)
+5,2
20,8
108,16
16,6
60
24(18-24)
+10,2
61,2
624,24
25
90
1423,96
100
360
62

SOLUTION

2. Give a graphic representation of the interval
row. Graphically interval series
distribution can be represented
polygon, histogram, cumulative.
Polygon. Built in rectangular system

values ​​of the boundaries of the intervals option, taking into account
expansion intervals, i.e. from (13-18) to (43-48).
63

POLYGON

7
6
5
4
3
2
1
0
10,5
15,5
20,5
25,5
30,5
35,5
40,5
45,5
50,5
64

SOLUTION

Bar chart. Coordinate axes
match the polygon. However, in
interval row rectangles
histograms are constructed according to a different principle.
The heights of the rectangles are equal to the frequencies
corresponding groups, and the bases
rectangles are located on
intervals borders option.
65

BAR CHART

7
6
5
4
3
2
1
0
13
18
23
28
33
38
43
48
53
66

SOLUTION

With a histogram, you can
determine the value of the graphic mode.
For this you need to do
following procedure. right vertex

the right top of the previous
rectangle. left vertex
modal rectangle connect with
the left top of the next
rectangle.
67

SOLUTION

The question arises. What rectangle
is modal? Modal is
rectangle corresponding to
interval with the maximum frequency (6), i.e.
tallest rectangle. In this
problem two intervals with maximum
frequency (6), i.e. given distribution
BIMODAL, which means that the solution will have
two mods.
68

SOLUTION

From the point of intersection of the obtained segments
drop the perpendicular to the abscissa axis, this is
and will be an approximate value
graphic fashion.
The first modal interval (18 - 23), and
first mode Mo(1)(graph) = 22.5
The second modal interval (38 - 43), and
second mode Mo(2)(graph) = 39
69

Cumulate. Built in rectangular systems
coordinates. On the abscissa axis are plotted
values ​​of the boundaries of the intervals option, and without
extension intervals. Y-axis
the accumulated frequencies are plotted, i.e.
from 0 to 24. When drawing dots, use
next rule. Left border of the first
interval is the starting point, i.e. in
its accumulated frequencies are equal to zero. Rights
the values ​​of all other intervals are equal
values ​​of the accumulated frequencies of the corresponding
rows.

Socio-economic statistics

Subject, method, tasks of SES

Socio-economic statistics (SES) are:

The branch of knowledge is a science that is a complex and branched system of scientific disciplines that have certain specifics and study the quantitative side of mass phenomena and processes in close connection with their quantitative side;

Industry practical activities- collection, processing, analysis and publication of mass data on the phenomena and processes of public life;

• a set of digital information characterizing the state of mass phenomena and processes of social life or their totality.

Subject of study

The subject of SES study is the quantitative side of mass socio-economic phenomena in close connection with their qualitative side.

Object of study

The object of study of SES are mass socio-economic phenomena and processes. This connects SES with other sciences that study society and the patterns of its development (macro- and microeconomics, sociology, demography). Socio-economic statistics is closely related to the theory of statistics, statisticians of individual industries.

The task of socio-economic statistics is the preparation of complete and up-to-date information that provides a quantitative and qualitative description of the state and development national economy .

AT modern conditions the central task of socio-economic statistics is to create a model of state statistics adapted to the conditions for the development of market relations on the basis of modern systems indicators that comply with international standards of accounting and statistics.

Tasks of SES

The tasks of socio-economic statistics in the conditions market economy are a systematic description and analysis of the following economic phenomena and social processes:

- the number and structure of the population of the country, the most important indicators its reproduction;

- employment and unemployment of the population;

- standards of living;

- distribution of income;

- development social sphere, education, healthcare;

- economic resources bodies;

Main results economic process and production results in the main sectors of the national economy;

- investment process;

- inflation;

- functioning of the financial and banking system; - foreign economic relations; - development of science and technology

SES Methods

The methodology of socio-economic statistics is based on:

general methods of statistics -

• observation;
• summary and grouping of statistical materials;
• absolute, relative and average values;
• indicators of variation of signs and statistical distributions;
• analysis of time series;
• correlation-regression analysis;
• indices;
• - special methods for studying socio-economic phenomena and processes - sectoral classification of the economy; system of national accounts, tables, balances.

SES scorecard

The system of indicators of SES consists of three groups:

1. Statistics of the economic potential of society population , labor resources, labor market

national wealth

2. Statistics of results economic activity production and use of the national product, the market for goods and services, the cost of producing goods and services, finance, the efficiency of economic activity

3. Statistics of the standard of living of the population, incomes of the population,

consumption of goods and services by the population, the state and development of industries serving the population

The totality of indicators characterizes the state and development of the national economy as a whole.

System of National Accounts

System of National Accounts

The development of standards in the field of national accounting is carried out by international organizations . Currently current standard is the 1993 SNA approved by the Statistical Commission UN .

The introduction of the SNA into statistical practice is a long process, which is carried out in stages through the transition from the BNC to the SNA. The final stage of the transition period will be the organization of national accounting, coordinated with the introduction international standards in Accounting .

Statistics. Tasks in statistics. The theory of statistics. Math statistics. Statistical research. Statistical observation. population statistics. Statistical indicators. Least square method. Theory of mathematical statistics. Total stats. Information transformation. Enterprise statistics. federal Service state statistics.

Statistical characteristics. Medical statistics. Statistical research methods. Descriptive statistics. International statistics. General theory of statistics. Statistical testing of statistical hypotheses. Elements of statistics. Population standard of living statistics. labor market statistics. Statistical data processing.

Median as a statistical characteristic. Statistical tables. Business finance statistics. Socio-economic statistics. Population and employment statistics. Summary and grouping of statistical data. Statistics is the design of information. Elements of mathematical statistics. Statistical summary and grouping of data.

Population-statistical method. Statistical Information Systems. Statistical methods in psychology. Subject and method of the problem of statistics. Statistics for decision making. State budget statistics. Stock market statistics. Classification of statistical methods. Methods of statistical data processing.

Statistical methods of product quality control. Statistical characteristics in the lesson of algebra. Elements of statistics Grade 7. Dialogues about statistics. Innovation statistics in Russia. Statistical distributions and their main characteristics. Assessment of the quality of statistical indicators.

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Slides captions:

Statistical indicators

Definition A statistical indicator (SP) is quantitative characteristic socio-economic phenomenon and process in terms of qualitative certainty Qualitative certainty - shows that the indicator is directly related to the internal content of the phenomenon or process under study. The system of statistical indicators (SCS) is an interconnected set of indicators aimed at solving a specific problem

Unlike a sign, a statistical indicator, most often, is obtained by calculation. There are: given time Indicator-category (P-K) - reflects the general distinctive properties of the KSP without specifying the place and time

PI - characterize a separate object or unit of the population SVP - characterize a group of units of the population OP - are obtained by adding the values ​​of the attribute of individual units of the population RP - are calculated by formulas and serve to solve statistical problems OP - an indicator presented as a quotient of two absolute indicators AP - indicators, reflecting the volume (size) of the phenomenon under study

Absolute statistical indicators (ASP) This is a summary generalizing indicator that characterizes the size of the phenomena under study in specific conditions of place and time. This is the initial, primary, largest form of expressing the SP; numbers taken from tables without conversions These are named quantities expressed in terms of GDP units, cash income population, volume industrial production, output volume various kinds products, population, turnover retail etc.

IASP - characterizes the size of the sign of individual units of the population (the size of the salary individual worker, deposit in the bank of a particular person) SASP - characterizes the final value of the attribute for a separate set (the sum of the company's distribution costs, the number of sales and operational employees of the store

Units of measurement (UI) ASP Types of MU Name Natural, simple tons; PCS; m; m 3; l Natural, compound Cargo turnover t/km; Electricity volume KW/h Conventional natural Conditional fuel; conditional monetary units (cu) Value Rub; currency Labor Labor costs (person/hour; persons/days)

Relative Statistical Indicators (RSI) These are quantities that express a measure of the quantitative relationships inherent in specific phenomena or statistical objects RSI allows comparison of various indicators and makes such comparison visual These are secondary, calculated data

Relative values ​​are calculated as the ratio of two numbers The numerator is called the compared (current) value The denominator is called the base of the relative comparison (previous value) RSE the compared value is the base of the relative comparison

OSP are measured: In coefficients In percent In ppm (tenth of a percent) In prodecemille (hundredth of a percent) In named numbers (km, kg, ha ...) The choice of the form of OSP is determined by the tasks of statistical research

Types of OSP by content: Planned target and plan implementation Dynamics Structure Coordination Intensity Comparison

Relative indicators of the planned target (RPP) Used for planning activities, as well as for comparing the results achieved with previously planned ones Characterize the ratio of the planned level of the indicator to the actually achieved level of the period compared to which the increase or decrease of the indicator is planned Usually expressed as a percentage

An example of calculating the OPPP In January of the reporting year, the company's gross income amounted to 1,500 thousand rubles; in February, a turnover of 1,800 thousand rubles is planned. Define OPPP. THEN. in February, it is planned to increase the planned gross income of the company by 20%

Relative Plan Completion Rates (RPIs) Used to monitor the progress of plans. Show the ratio between the actual and planned levels of the indicator Usually expressed as a percentage

An example of calculating the OPVP The gross income of the company, in February of the reporting year, amounted to 2055.5 thousand rubles. with a plan of 1800 thousand rubles. Determine the degree of implementation of the plan for the gross income of the company in February of the current year. THEN. the plan for gross income was fulfilled by 114.2%, i.е. overfulfillment of the plan is 14.2%

Relative indicators of dynamics (RDI) - growth rates Characterize the change in the magnitude of social phenomena over time Used in planning, analysis and statistics Usually expressed in coefficients or percentages

Types of periods when calculating growth rates Base growth rates Calculated with respect to one constant base of comparison, i. to initial level Chain growth rates Calculated in relation to the variable base of comparison, ie. in each period in relation to the previous one

An example of calculating the GRP Calculate the chain and basic relative values ​​​​of the dynamics of the number of employees commercial enterprise for 2007-2010 Dynamics of the number of employees of the enterprise for 2007-2010 2007 2008 2009 2010 Number of employees, pers. 1285 1857 3345 3530

Basic and chain indicators of the dynamics of the number of employees of the enterprise Year Number of employees, pers. GPI (growth rate), % basic chain calculation Total, % Growth rate, % Calculation Total, % Growth rate, % 2007 1285 1285/1285*100 100.0 0.0 1285/1285*100 100.0 0.0 2008 1857 1857/1285*100 144.5 44.5 1857/1285*100 144.5 44.5 2009 3345 3345/1285*100 260.3 160.3 3345/1857*100 180.1 80.1 2010 3530 /1285*100 274.4 174.4 3530/3345*100 105.5 5.5 Data analysis shows that in the period from 2007 to 2010 there was a gradual increase in the number of employees of the enterprise

Relative structure indicators (RPS) Characterize the constituent parts of the population under study Used in the study of complex phenomena that fall into a number of groups or parts, to characterize specific gravity of each group in the total Usually expressed as a percentage

An example of calculating the GPV There is the following grouping of stores in the city of ___ by the size of the turnover. Calculate relative performance structure of the Group of stores by turnover, billion rubles. Number of stores, pcs. Actual trade turnover, billion rubles up to 20 7 78.3 20 - 50 8 246.8 From 50 and over 5 322.3 Total: 20 674

Groups of stores by turnover, billion rubles Number of stores, pcs. Actual trade turnover, billion rubles Calculation Percentage of total, % up to 20 7 78.3 78.3/674.4*100 12.1 20 - 50 8 246.8 246.8/674.4*100 38.1 From 50 and above 5 322, 3,322.3/674.4*100 49.8 Total: 20,674.4 - 100.0 Data analysis shows that largest share in the actual turnover of stores belongs to stores from the group "from 50 and above"

Relative Comparison Indicators (RCC) Obtained as a result of dividing absolute values ​​of the same name corresponding to the same period or point in time, but related to different objects or territories Usually expressed as a percentage or multiple ratios

An example of calculation of the OPSR The population of the Russian Federation in 2002 amounted to 145.2 million people, including: urban - 106.4 million people, rural - 38.7 million people. Compare the urban and rural population of the country. OPSr=106.4: 38.7 = 2.7 In 2002, the urban population exceeded the rural population by 2.7 times

Summary In the statistical study of social phenomena, absolute and relative indicators complement each other ASP - characterize the statics of NSP phenomena - allow us to study the degree, dynamics, intensity of development of phenomena

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

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Types of statistics Economic studies changes in prices, supply and demand for goods, predicts the growth and decline in production and consumption. Medical studies the effectiveness of various drugs and treatments, the likelihood of a certain disease, predicts the occurrence of epidemics.

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Demographic studies the birth rate, population size, its composition (age, national, professional) Financial Tax Biological Meteorological, etc.

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"There are three types of lies: simple lies, blatant lies and statistics" B. Disraeli Mathematical statistics is a science based on the laws of probability theory. The main method of statistics is the sampling method.

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Example In one of the Russian regions, they decided to find out what the level of knowledge of ninth-graders in mathematics is. For this, a special control work was made. We made a sample of 9th grade students. The sample must be representative (representative). Let the sample include 50 students and control work 6 tasks.

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It turned out a series of numbers, each of which is in the range from 0 to 6 (the number of correctly solved problems by each student) Unranked series 4, 2, 0, 6, 2, 3, 4, 3, 3, 0, 1, 5, 2, 6, 4, 3, 3, 2, 3, 1, 3, 3, 2, 6, 2, 2, 4, 3, 3, 6, 4, 2, 0, 3, 3, 5, 2, 1, 4, 4, 3, 4, 5, 3, 2, 3, 1, 6, 2, 2. Ranked series 0, 0, 0 1, 1, 1, 1 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 3, 3, 3, 3, 3, 3, 3, 3, 3 4, 4, 4, 4, 4, 4, 4, 4 5, 5, 5 6, 6, 6, 6, 6

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Let's present the results in the table Number of correctly solved problems 0 1 2 3 4 5 6 Absolute frequency 3 4 12 15 8 3 5 Relative frequency 0.06 0.08 0.24 0.3 0.16 0.06 0.1

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Frequency polygon To construct a frequency polygon, the results of a random experiment (the number of correctly solved problems) are marked on the horizontal axis, and the relative frequencies corresponding to them are marked on the vertical axis. Then the marked points are sequentially connected by segments. It turns out broken. It is called the frequency range.