Rates of growth− is the ratio of the levels of a series of one period to another.

Growth rates can be calculated as base rates when all levels of the series refer to the level of the same period, taken as the base:

T R = y i /y 0 − base growth rate

and as chain ones, this is the ratio of each level of the series to the level of the previous period:

T R = y i /y i-1− chain growth rate.

Growth rates can be expressed as a ratio or percentage.

Basic growth rates characterize a continuous line of development, and chain rates characterize the intensity of development in each individual period, and the product of chain rates is equal to the base rate. And the quotient of dividing the base rates is equal to the intermediate chain rate.

8.3 Growth and growth rate. Absolute value of 1% increase.

There is a distinction between the concepts of absolute and relative growth. The absolute increase is calculated as the difference between the levels of the series and expressed in units of measurement of the indicators of the series.

If the previous level is subtracted from the subsequent level, then we have a chain absolute increase:

If the same level, the base one, is subtracted from each level, then this is the base absolute increase:

The following relationship exists between chain and basic absolute increases: the sum of successive chain increases is equal to the corresponding basic increase, which characterizes the total increase for the entire relevant period of time.

Relative score the values ​​of absolute growth compared to the initial level give indicators of the growth rate ( T ∆ i). It is defined in two ways:

As the ratio of absolute growth (chain) to the previous level:

This is a chain growth rate.

As the ratio of the base absolute increase to the base level:

This is the base growth rate.

2 As the difference between the growth rate and one, if the growth rate is expressed by a coefficient:

T ∆ = T R-1, or

T ∆ = T R- 100 if the growth rate is expressed as a percentage.

Rate of increase shows by what percentage the size of the phenomenon increased over the period under study. If the growth rate has a minus sign, then we talk about the rate of decline.

Absolute value of 1 percent increase equal to the ratio of absolute growth (chain) to the chain growth rate, expressed as a percentage:

A i= 0.01x U i ;

8.4 Calculation of average dynamics indicators

The average level of the series is called the chronological average.

Average chronological− this is the average value of indicators that change over time.

In an interval series with equal intervals the average level of the series is determined by the simple arithmetic average formula.

The average level of a series in an interval dynamics series requires that it be indicated for what period of time it was calculated (monthly average, annual average, etc.).

Example 1

Calculate the average monthly turnover for the first quarter.

Because We are given an interval series with equal intervals; we apply the simple arithmetic mean formula:

If the interval series has different intervals, then it first needs to be reduced to a series with equal intervals, and then it will be possible to use the simple arithmetic average formula.

Example 2 The following data on trade turnover are available, monetary units:

Since the indicators of moment series do not have the property of totality, the average cannot be calculated using the simple arithmetic average formula, due to the fact that the balances changed continuously throughout the month, and the data are given for a specific day.

Therefore, we will use an approximate method based on the assumption that the phenomenon under study changed uniformly throughout each month. The shorter the series interval, the less error will be made when using this assumption.

We get the formula:

This formula is used to calculate average level in moment series with equal intervals.

Example 3 There is data on the balances of building materials at the beginning of the month, den. units:

Determine the average balance for the 1st quarter.

.

If the intervals in the moment series are not equal, then the average level of the series is calculated using the formula:

where is the average level in the intervals between dates,

t- time period (series interval)

Example 4 There is data on the balances of raw materials and supplies, den. units

Find the average monthly balances of raw materials and materials for the first half of the year.

We apply the formula:

Average absolute increase calculated in two ways:

1 As the simple arithmetic average of annual (chain) increases, i.e.

2 As the quotient of base growth divided by the number of periods:

Calculation of the average absolute value of 1% increase over several years is produced using the simple arithmetic average formula:

When calculating the average annual growth rate You cannot use a simple arithmetic average, because the sum of the annual rates will not make sense. In this case, the geometric mean is used, i.e.:

Where Tr i− annual chain growth rates;

n− number of tempos.

Since the product of chain rates is equal to the base rate, the average growth rate can be calculated as follows:

Error: Reference source not found

When calculating using this formula, it is not necessary to know the annual growth rate. The average tempo will depend on the ratio of the initial and final levels of the series.

Example 5 The nominal wages of workers in the national economy of the Republic of Belarus are characterized by the data presented in Table 1.

Table 1 – Nominal wages of workers in the national economy of the Republic of Belarus

To analyze the dynamics of wages, determine:

average annual salary for 8 years;

annual and basic absolute increases, growth rates and wage increases;

absolute value of 1% increase;

average annual absolute growth;

average annual growth rate and average annual growth rate;

average 1% increase.

Present the results in a table and draw conclusions.

Solution

1 We determine the average annual salary using the simple arithmetic average formula

2 Annual (chain) absolute growth () is determined by the formula

where , is the value of the indicator, respectively, in the th period and the period preceding it.

For example, for 2005, thousand rubles, i.e. wages in 2005 compared to 2004 increased by 64.1 thousand rubles; for 2006 thousand R. etc.

The basic absolute increase () is determined by the formula

where , is the value of the indicator in the th and base (2004) periods, respectively.

For example, for 2005, thousand rubles; for 2006 thousand rubles, i.e. wages in 2006 compared to 2004 increased by 130.3 thousand rubles. etc.

The chain growth rate is determined by the formula

For example, for 2005, i.e. wages in 2001 compared to 2004 increased by 108.8%; for 2006, etc.

The base growth rate is determined by the formula

For example, for 2001; for 2002, i.e. wages in 2002 compared to 2000 increased by 221.2%, etc.

We find the growth rate using the formula

So, the chain growth rate

for 2005: ;

for 2006: .

Base growth rate

for 2005: ;

for 2006: .

3 The absolute value of 1% growth () is found using the formula

This indicator can also be calculated as one hundredth of the previous level:

For example, for 2005, thousand rubles; for 2006 thousand R.

Calculations of indicators for points 1, 2, 3 will be presented in Table 2

Table 2 - Indicators of wage dynamics for 2004-2011.

	wages,	Absolute increase, thousand rubles			Growth rate, %			Growth rate, %			Absolute value of 1% increase, thousand rubles
			basic			basic			basic

Dynamics series- these are a series of statistical indicators characterizing the development of natural and social phenomena over time. Statistical collections published by the State Statistics Committee of Russia contain a large number of dynamics series in tabular form. Dynamic series make it possible to identify patterns of development of the phenomena being studied.

Dynamics series contain two types of indicators. Time indicators(years, quarters, months, etc.) or points in time (at the beginning of the year, at the beginning of each month, etc.). Row level indicators. Indicators of the levels of dynamics series can be expressed in absolute values ​​(product production in tons or rubles), relative values ​​(share of the urban population in %) and average values ​​(average wages of industry workers by year, etc.). A dynamics row contains two columns or two rows.

Correct construction of time series requires the fulfillment of a number of requirements:

1. all indicators of a series of dynamics must be scientifically based and reliable;
2. indicators of a series of dynamics must be comparable over time, i.e. must be calculated for the same periods of time or on the same dates;
3. indicators of a number of dynamics must be comparable across the territory;
4. indicators of a series of dynamics must be comparable in content, i.e. calculated according to a single methodology, in the same way;
5. indicators of a number of dynamics should be comparable across the range of farms taken into account. All indicators of a series of dynamics must be given in the same units of measurement.

Statistical indicators can characterize either the results of the process being studied over a period of time, or the state of the phenomenon being studied at a certain point in time, i.e. indicators can be interval (periodic) and momentary. Accordingly, initially the dynamics series can be either interval or moment. Moment dynamics series, in turn, can be with equal or unequal time intervals.

The original dynamics series can be transformed into a series of average values ​​and a series of relative values ​​(chain and basic). Such time series are called derived time series.

The methodology for calculating the average level in the dynamics series is different, depending on the type of the dynamics series. Using examples, we will consider the types of dynamics series and formulas for calculating the average level.

Interval time series

The levels of the interval series characterize the result of the process being studied over a period of time: production or sales of products (for a year, quarter, month, etc.), the number of people hired, the number of births, etc. The levels of an interval series can be summed up. At the same time, we get the same indicator over longer time intervals.

Average level in interval dynamics series() is calculated using the simple formula:

• y— series levels ( y 1 , y 2 ,...,y n),
• n— number of periods (number of levels of the series).

Let's consider the methodology for calculating the average level of an interval dynamics series using data on the sale of sugar in Russia as an example.

	Sugar sold, thousand tons

This is the average annual volume of sugar sales to the Russian population for 1994-1996. In just three years, 8137 thousand tons of sugar were sold.

Moment dynamics series

The levels of moment series of dynamics characterize the state of the phenomenon being studied at certain points in time. Each subsequent level includes, in whole or in part, the previous indicator. For example, the number of employees on April 1, 1999 fully or partially includes the number of employees on March 1.

If we add up these indicators, we get a repeat count of those workers who worked throughout the month. The resulting amount has no economic content; it is a calculated figure.

In moment series of dynamics with equal time intervals, the average level of the series calculated by the formula:

• y-moment series levels;
• n-number of moments (series levels);
• n - 1— number of time periods (years, quarters, months).

Let's consider the methodology for such calculation using the following data on the payroll number of employees of the enterprise for the 1st quarter.

It is necessary to calculate the average level of a series of dynamics, in this example - an enterprise:

The calculation was made using the average chronological formula. The average number of employees of the enterprise for the 1st quarter was 155 people. The denominator is 3 months in a quarter, and the numerator (465) is a calculated number that has no economic content. In the vast majority of economic calculations, months, regardless of the number of calendar days, are considered equal.

In moment series of dynamics with unequal time intervals, the average level of the series is calculated using the weighted arithmetic mean formula. The length of time (t-days, months) is taken as the average weight. Let's perform the calculation using this formula.

The list of employees of the enterprise for October is as follows: on October 1 - 200 people, on October 7, 15 people were hired, on October 12, 1 person was fired, on October 21, 10 people were hired, and until the end of the month there were no hiring or dismissal of workers. This information can be presented as follows:

When determining the average level of a series, it is necessary to take into account the duration of the periods between dates, i.e. apply:

In this formula, the numerator () has economic content. In the example given, the numerator (6665 person-days) is the company’s employees in October. The denominator (31 days) is the calendar number of days in a month.

In cases where we have a moment series of dynamics with unequal time intervals, and the specific dates of change in the indicator are unknown to the researcher, then first we need to calculate the average value () for each time interval using the simple arithmetic average formula, and then calculate the average level for the entire series of dynamics, by weighing the calculated average values ​​over the duration of the corresponding time interval. The formulas are as follows:

The dynamics series discussed above consist of absolute indicators obtained as a result of statistical observations. The initially constructed series of dynamics of absolute indicators can be transformed into derivative series: series of average values ​​and series of relative values. Series of relative values ​​can be chain (in % of the previous period) and basic (in % of the initial period taken as the basis of comparison - 100%). The calculation of the average level in the derivative time series is performed using other formulas.

A series of averages

First, we transform the above moment series of dynamics with equal time intervals into a series of average values. To do this, we calculate the average number of employees of the enterprise for each month, as the average of the indicators at the beginning and end of the month (): for January (150+145): 2 = 147.5; for February (145+162): 2 = 153.5; for March (162+166): 2 = 164.

Let's present this in tabular form.

Average level in derivative series average values ​​are calculated by the formula:

Note that the average payroll number of employees of the enterprise for the 1st quarter, calculated using the chronological average formula based on the database on the 1st day of each month and the arithmetic average - according to the derived series - are equal to each other, i.e. 155 people. A comparison of the calculations allows us to understand why in the average chronological formula the initial and final levels of the series are taken in half size, and all intermediate levels are taken in full size.

Series of average values ​​derived from moment or interval series of dynamics should not be confused with series of dynamics in which levels are expressed by an average value. For example, the average wheat yield by year, the average salary, etc.

Series of relative quantities

In economic practice, series are widely used. Almost any initial series of dynamics can be converted into a series of relative values. In essence, transformation means replacing the absolute indicators of a series with relative values ​​of dynamics.

The average level of the series in relative dynamics series is called the average annual growth rate. Methods for its calculation and analysis are discussed below.

Analysis of time series

For a reasonable assessment of the development of phenomena over time, it is necessary to calculate analytical indicators: absolute growth, growth coefficient, growth rate, growth rate, absolute value of one percent of growth.

The table shows a numerical example, and below are calculation formulas and economic interpretation of the indicators.

Analysis of the dynamics of production of product "A" by the enterprise for 1994-1998.

	Produced thousand tons	Absolute gains,		Growth rates		Pace growth, %		Growth rate, %		Value of 1% increase, thousand tons.
			basic		basic		basic		basic
		3	4	5	6	7	8	9	10	11

Absolute increases (Δy) show how many units the subsequent level of the series has changed compared to the previous one (gr. 3. - chain absolute increases) or compared to the initial level (gr. 4. - basic absolute increases). The calculation formulas can be written as follows:

When the absolute values ​​of the series decrease, there will be a “decrease” or “decrease”, respectively.

Indicators of absolute growth indicate that, for example, in 1998, the production of product “A” increased by 4 thousand tons compared to 1997, and by 34 thousand tons compared to 1994; for other years, see table. 11.5 gr. 3 and 4.

Growth rate shows how many times the level of the series has changed compared to the previous one (gr. 5 - chain coefficients of growth or decline) or compared to the initial level (gr. 6 - basic coefficients of growth or decline). The calculation formulas can be written as follows:

Rates of growth show what percentage the next level of the series is compared to the previous one (gr. 7 - chain growth rates) or compared to the initial level (gr. 8 - basic growth rates). The calculation formulas can be written as follows:

So, for example, in 1997, the production volume of product “A” compared to 1996 was 105.5% (

Growth rate show by what percentage the level of the reporting period increased compared to the previous one (column 9 - chain growth rates) or compared to the initial level (column 10 - basic growth rates). The calculation formulas can be written as follows:

T pr = T r - 100% or T pr = absolute growth / level of the previous period * 100%

So, for example, in 1996, compared to 1995, product “A” was produced by 3.8% (103.8% - 100%) or (8:210)x100% more, and compared to 1994 - by 9% (109% - 100%).

If the absolute levels in the series decrease, then the rate will be less than 100% and, accordingly, there will be a rate of decline (the rate of increase with a minus sign).

Absolute value of 1% increase(column 11) shows how many units must be produced in a given period so that the level of the previous period increases by 1%. In our example, in 1995 it was necessary to produce 2.0 thousand tons, and in 1998 - 2.3 thousand tons, i.e. much bigger.

The absolute value of 1% growth can be determined in two ways:

• divide the level of the previous period by 100;
• chain absolute increases are divided by the corresponding chain growth rates.

Absolute value of 1% increase =

In dynamics, especially over a long period, a joint analysis of the growth rate with the content of each percentage increase or decrease is important.

Note that the considered methodology for analyzing time series is applicable both for time series, the levels of which are expressed in absolute values ​​(t, thousand rubles, number of employees, etc.), and for time series, the levels of which are expressed in relative indicators (% of defects , % ash content of coal, etc.) or average values ​​(average yield in c/ha, average wage, etc.).

Along with the considered analytical indicators, calculated for each year in comparison with the previous or initial level, when analyzing dynamics series, it is necessary to calculate the average analytical indicators for the period: the average level of the series, the average annual absolute increase (decrease) and the average annual growth rate and growth rate.

Methods for calculating the average level of a series of dynamics were discussed above. In the interval dynamics series we are considering, the average level of the series is calculated using a simple formula:

Average annual production volume of the product for 1994-1998. amounted to 218.4 thousand tons.

The average annual absolute growth is also calculated using the simple arithmetic average formula:

Annual absolute increases varied over the years from 4 to 12 thousand tons (see column 3), and the average annual increase in production for the period 1995 - 1998. amounted to 8.5 thousand tons.

Methods for calculating the average growth rate and average growth rate require more detailed consideration. Let us consider them using the example of the annual series level indicators given in the table.

Average annual growth rate and average annual growth rate

First of all, we note that the growth rates shown in the table (columns 7 and 8) are series of dynamics of relative values ​​- derivatives of the interval series of dynamics (column 2). Annual growth rates (column 7) vary from year to year (105%; 103.8%; 105.5%; 101.7%). How to calculate the average from annual growth rates? This value is called the average annual growth rate.

The average annual growth rate is calculated in the following sequence:

The average annual growth rate ( is determined by subtracting 100% from the growth rate.

The average annual growth (decrease) coefficient using geometric mean formulas can be calculated in two ways:

1) based on the absolute indicators of the dynamics series according to the formula:

• n— number of levels;
• n - 1- number of years in the period;

2) based on annual growth rates according to the formula

• m— number of coefficients.

The calculation results using the formulas are equal, since in both formulas the exponent is the number of years in the period during which the change occurred. And the radical expression is the growth rate of the indicator for the entire period of time (see Table 11.5, column 6, line for 1998).

The average annual growth rate is

The average annual growth rate is determined by subtracting 100% from the average annual growth rate. In our example, the average annual growth rate is

Consequently, for the period 1995 - 1998. The production volume of product "A" increased by 4.0% on average per year. Annual growth rates ranged from 1.7% in 1998 to 5.5% in 1997 (for each year’s growth rates, see Table 11.5, group 9).

The average annual growth rate (growth) allows you to compare the dynamics of development of interrelated phenomena over a long period of time (for example, the average annual growth rate of the number of workers in sectors of the economy, the volume of production, etc.), to compare the dynamics of a phenomenon in different countries, to study the dynamics of some or phenomena according to periods of historical development of the country.

Seasonal analysis

The study of seasonal fluctuations is carried out in order to identify regularly recurring differences in the level of time series depending on the time of year. For example, the sale of sugar to the population in the summer increases significantly due to the canning of fruits and berries. The need for labor in agricultural production varies depending on the time of year. The task of statistics is to measure seasonal differences in the level of indicators, and in order for the identified seasonal differences to be natural (and not random), it is necessary to build an analysis on the basis of data for several years, at least for at least three years. In table 11.6 shows the initial data and methodology for analyzing seasonal fluctuations using the simple arithmetic average method.

The average value for each month is calculated using the simple arithmetic average formula. For example, for January 2202 = (2106 +2252 +2249):3.

Seasonality index(Table 11.5, column 7.) is calculated by dividing the average values ​​for each month by the total average monthly value, taken as 100%. The average monthly for the entire period can be calculated by dividing the total fuel consumption for three years by 36 months (1188082 tons: 36 = 3280 tons) or by dividing the average monthly sum by 12, i.e. total total for gr. 6 (2022 + 2157 + 2464, etc. + 2870) : 12.

Table 11.6 Seasonal fluctuations in fuel consumption in agricultural enterprises in the region for 3 years

	Fuel consumption, tons			Amount for 3 years, t (2+3+4)	Average monthly for 3 years, t	Seasonality index,
September

Rice. 11.1. Seasonal fluctuations in fuel consumption in agricultural enterprises over 3 years.

For clarity, a seasonal wave graph is constructed based on seasonality indices (Fig. 11.1). Months are located on the abscissa axis, and seasonality indices in percentage are located on the ordinate axis (Table 11.6, group 7). The overall average monthly for all years is located at the 100% level, and the average monthly seasonality indices in the form of points are plotted on the graph field in accordance with the accepted scale along the ordinate axis.

The points are connected by a smooth broken line.

In the example given, the annual fuel consumption differs slightly. If, in the dynamics series, along with seasonal fluctuations, there is a pronounced tendency of growth (decrease), i.e. levels in each subsequent year systematically significantly increase (decrease) compared to the levels of the previous year, then we obtain more reliable data on the extent of seasonality as follows:

1. for each year we calculate the average monthly value;
2. Let's calculate the seasonality indices for each year by dividing the data for each month by the average monthly value for that year and multiplying by 100%;
3. for the entire period, we calculate the average seasonality indices using the simple arithmetic average formula from the monthly seasonality indices calculated for each year. So, for example, for January we will obtain the average seasonality index if we add up the January values ​​of seasonality indices for all years (let’s say for three years) and divide by the number of years, i.e. on three. Similarly, we calculate the average seasonality indices for each month.

The transition for each year from absolute monthly values ​​of indicators to seasonality indices makes it possible to eliminate the tendency of growth (decrease) in the dynamics series and more accurately measure seasonal fluctuations.

In market conditions, when concluding contracts for the supply of various products (raw materials, materials, electricity, goods), it is necessary to have information about the seasonal needs for means of production, about the population’s demand for certain types of goods. The results of the study of seasonal fluctuations are important for the effective management of economic processes.

Reducing dynamics series to the same base

In economic practice, there is often a need to compare several series of dynamics (for example, indicators of the dynamics of electricity production, grain production, passenger car sales, etc.). To do this, you need to transform the absolute indicators of the compared time series into derived series of relative basic values, taking the indicators of any one year as one or 100%. Such a transformation of several time series is called bringing them to the same base. Theoretically, the absolute level of any year can be taken as the basis of comparison, but in economic research, for the basis of comparison it is necessary to choose a period that has a certain economic or historical significance in the development of phenomena. At present, it is advisable to take, for example, the 1990 level as a basis for comparison.

Methods for aligning time series

To study the pattern (trend) of development of the phenomenon under study, data over a long period of time is required. The development trend of a particular phenomenon is determined by the main factor. But along with the action of the main factor in the economy, the development of the phenomenon is directly or indirectly influenced by many other factors, random, one-time or periodically recurring (years favorable for agriculture, drought years, etc.). Almost all series of dynamics of economic indicators on the graph have the shape of a curve, a broken line with ups and downs. In many cases, it is difficult to determine even the general trend of development from actual data from a series of dynamics and from a graph. But statistics must not only determine the general trend in the development of a phenomenon (growth or decline), but also provide quantitative (digital) characteristics of development.

Trends in the development of phenomena are studied by methods of aligning dynamics series:

• Interval enlargement method
• Moving average method

In table Table 11.7 (column 2) shows actual data on grain production in Russia for 1981-1992. (in all categories of farms, in weight after modification) and calculations for leveling this series using three methods.

Method of enlarging time intervals (column 3).

Considering that the dynamics series is small, three-year intervals were taken and the averages were calculated for each interval. The average annual volume of grain production for three-year periods is calculated using the simple arithmetic average formula and referred to the average year of the corresponding period. So, for example, for the first three years (1981 - 1983), the average was recorded against 1982: (73.8 + 98.0 + 104.3): 3 = 92.0 (million tons). Over the next three-year period (1984 - 1986), the average (85.1 +98.6+ 107.5): 3 = 97.1 million tons was recorded against 1985.

For other periods, the calculation results in gr. 3.

Given in gr. 3 indicators of the average annual volume of grain production in Russia indicate a natural increase in grain production in Russia for the period 1981 - 1992.

Moving average method

Moving average method(see groups 4 and 5) is also based on the calculation of average values ​​for aggregated periods of time. The goal is the same - to abstract from the influence of random factors, to cancel out their influence in individual years. But the calculation method is different.

In the example given, five-tier (over five-year periods) moving averages are calculated and assigned to the middle year in the corresponding five-year period. Thus, for the first five years (1981-1985), using the simple arithmetic average formula, the average annual volume of grain production was calculated and recorded in table. 11.7 versus 1983 (73.8+ 98.0+ 104.3+ 85.1+ 98.6): 5= 92.0 million tons; for the second five-year period (1982 - 1986) the result was recorded against 1984 (98.0 + 104.3 +85.1 + 98.6 + 107.5): 5 = 493.5: 5 = 98.7 million tons

For subsequent five-year periods, the calculation is made in a similar way by eliminating the initial year and adding the year following the five-year period and dividing the resulting amount by five. With this method, the ends of the row are left empty.

How long should the time periods be? Three, five, ten years? The researcher decides the question. In principle, the longer the period, the more smoothing occurs. But we must take into account the length of the dynamics series; do not forget that the moving average method leaves cut ends of the aligned series; take into account the stages of development, for example, in our country for many years, socio-economic development was planned and accordingly analyzed according to five-year plans.

Table 11.7 Alignment of data on grain production in Russia for 1981 - 1992

	Produced, million tons	Average for 3 years, million tons	5-year rolling total, million tons		Estimated indicators

Analytical alignment method

Analytical alignment method(gr. 6 - 9) is based on calculating the values ​​of the aligned series using the corresponding mathematical formulas. In table 11.7 shows calculations using the equation of a straight line:

To determine the parameters, it is necessary to solve the system of equations:

The necessary quantities for solving the system of equations have been calculated and given in the table (see groups 6 - 8), let’s substitute them into the equation:

As a result of the calculations we get: α= 87.96; b = 1.555.

Let's substitute the values ​​of the parameters and get the equation of the straight line:

For each year we substitute the value t and get the levels of the aligned series (see column 9):

Rice. 11.2. Grain production in Russia for 1981-1982.

In the leveled series, there is a uniform increase in series levels on average per year by 1.555 million tons (the value of the “b” parameter). The method is based on abstracting the influence of all other factors except the main one.

Phenomena can develop in dynamics evenly (increase or decrease). In these cases, the straight line equation is most often suitable. If the development is uneven, for example, at first very slow growth, and from a certain moment a sharp increase, or, conversely, first a sharp decrease, and then a slowdown in the rate of decline, then the leveling must be performed using other formulas (equation of a parabola, hyperbola, etc.). If necessary, one should turn to textbooks on statistics or special monographs, where the issues of choosing a formula to adequately reflect the actual trend of the dynamics series being studied are described in more detail.

For clarity, we will plot the indicators of the levels of the actual dynamics series and the aligned series on a graph (Fig. 11.2). The actual data is represented by a broken black line, indicating increases and decreases in the volume of grain production. The remaining lines on the graph show that the use of the moving average method (line with cut ends) allows you to significantly align the levels of the dynamic series and, accordingly, make the broken curved line on the graph smoother and smoother. However, straight lines are still crooked lines. Constructed on the basis of theoretical values ​​of the series obtained using mathematical formulas, the line strictly corresponds to a straight line.

Each of the three methods discussed has its own advantages, but in most cases the analytical alignment method is preferable. However, its application is associated with large computational work: solving a system of equations; checking the validity of the selected function (form of communication); calculating the levels of the aligned series; plotting. To successfully complete such work, it is advisable to use a computer and appropriate programs.

1. Indicate the approximate population of the globe: 1) 3.5 billion people; 3) 4.5-5 billion people;

2) 5.1-6.0 billion people; 4) 7 billion people.

2.Indicate the absolute annual growth of the Earth's population:

1) 20-30 million people; 3) 80-100 million. Human;

2) 50-70 million. Human; 4) 120-130 million. Human.

3.Indicate in the proposed list countries whose population exceeds 100 million people:

1) China; 2) Mexico; 3) India; 4) Bangladesh.

4.Indicate the group, which includes only states with a population of more than 100 million people:

1) Russia. Ethiopia, Nigeria, India;

2) Vietnam, Italy, France, Germany;

3) Brazil, Japan, Pakistan, Nigeria;

4) Bangladesh, Pakistan, Ukraine, Australia.

5. Indicate the largest country by population in the proposed list of European countries:

1) Spain; 2) Hungary; 3) Sweden; 4) Denmark.

6. Indicate the largest country by population in the proposed list of countries in America:

1) Colombia; 2) Argentina; 3) Canada; 4) Mexico.

7. List the three largest countries in Africa by population:

1) Algeria; 6) Chad;

2) Ethiopia; 7) Morocco;

3) Zaire; 8) Botswana;

4) South Africa;9) Egypt;

5) Nigeria; 10) Tanzania.

8. Indicate the correct statements:

1) More population is concentrated in the eastern hemisphere than in the western;

2) The population in the northern hemisphere is smaller than in the southern;

3) Most of the Earth's inhabitants are settled at an altitude of up to 2000 m above sea level;

4) The average population density on Earth is about 20 people per 1 km2.

9. Indicate the correct statements:

1) The population density in Asia is almost 4 times higher than the average population density of the Earth;

2) Population density in Africa is approximately 2 times lower than the world average;

3) The population density in Europe is about 70 people. per 1 km2;

4) The population density in Australia and Oceania is greater than in South America;

10. Indicate the correct statements:

1) Of all the countries in the world (not counting dwarf ones), Japan has the highest population density;

2) About half of the inhabitants of the land have a population density of less than a quarter of the land area;

3) Areas uninhabited by humans occupy about a quarter of the land area;

4) There are areas on the globe where the population density exceeds 1000 people per 1 km2.

11. Indicate on which of the following continents 1/5 of the population lives at an altitude of more than 1000 m above sea level:

1) Africa; 2) North America; 3) Australia; 4) Eurasia.

12. In the proposed list of European countries, indicate five states with approximately the same population:

1) Germany; 6) Belgium;

2) France; 7) Greece;

3) The Netherlands; 8) Norway;

4) Greece; 9) Sweden;

5) Bulgaria; 10) Poland.

13. Among the regions of the world, indicate three with the largest population:

1) Europe; 4) North America;

2) Asia; 5) Latin America;

3) Africa; 6) Australia and Oceania.

14. In the following list of European countries, name five countries with approximately the same population:

1) France; 6) Denmark;

2) Italy; 7) Belgium;

3) Norway; 8) Czech Republic;

4) Hungary;9) Slovakia;

5) Bulgaria; 10) Portugal;

15. Indicate the group in which all countries have low population density: 1) Oman, Paraguay, Belgium; 2) Vietnam, Laos, Cambodia; 3) USA, Japan, Germany; 4) Russia, Libya, Mongolia

Key to the test "Geography of the World Population"

Absolute annual increase in the production of mineral fertilizers for 1958-1970[...]

The absolute increase is defined as the difference between the levels of the series and is expressed in units of measurement of the indicators of the series. The growth rate characterizes the ratio of one level of a series to another and is expressed in coefficients or percentages.[...]

The growth of rainbow trout fry is greatly influenced by the oxygen content in the water. At low oxygen concentrations, growth slows down by half, absolute and relative indicators of feed consumption, and payment for it decrease. This is explained, in particular, by the deterioration of protein digestibility.[...]

The growth rate is determined by the ratio of absolute growth to the basic level of the indicator. The absolute value of one percent of growth is the ratio of absolute growth to the growth rate expressed as a percentage.[...]

In 1970, the world population growth was 1.8%, but in the 80s. annual growth fell to 1.7% (in absolute numbers it decreased by hundreds of millions of people). This is consistent with the theory of demographic transition, developed in 1945 by F. Notestoin, according to which there are three stages of population growth, determined by economic and social development. [...]

The decrease in the rate of increase in freon content is due to the fact that in the second half of the 1980s. Many industrialized countries have imposed restrictions on the production and consumption of these products. We can expect a further decline in the trend in the coming years due to international agreements reached to phase out the use of chlorofluorocarbons. However, the absolute concentrations of freons in the atmosphere will likely increase for many years, even after their production has completely ceased. From the table 3.7 it is clear that more than half of the CEC1:) produced by 1991 is in the troposphere, about 19% has moved to the stratosphere, and about 22% is still in active (refrigeration units, etc.) or passive (in the composition of products from porous polymers such as polypenurethanes) in use and will gradually be released into the environment.[...]

To analyze the dynamics of growth, the average values ​​of absolute growth over decades were considered. Noticeable differences in the amount of growth at different distances from the road were observed in the 1960-1970s, when the trees adapted to the replanting conditions and actively formed a crown (Fig. 1). In the 1980-1990s. the increase at different distances from the road had similar average values ​​(the differences are small and not significant at the 0.05 significance level).[...]

In the zone of post-fire growth, changes occur in the width and structure of annual layers. Our materials obtained from the study of the Dvina and Verkhnevychegda burnt forests show that trees injured by ground fires in conditions of green zilch are characterized by an increase in the width of the annual layer in the lower parts of the trunks, which occurs due to the absolute increase in both the early and late parts of it, with In this case, a relative increase in some cases occurs in the width of late wood (especially on the side damaged by fire). [...]

However, if the yield increase is assessed not by the absolute value of the gain obtained, but per unit of nutrients, then a dose of fertilizers of 30 kg of nitrogen, phosphorus and potassium turns out to be more profitable, at which 8.4 quintals of grain fall for each centner of nutrients. Increasing the dose of nitrogen to 90 kg per 1 ha turned out to be ineffective.[...]

12

Knowing the weight and length of the fish before the experiment and at the end of the experiment, the increase in weight and length over a given period of time is calculated. I express growth! in absolute values, as a percentage of the original value or in a logarithmic dependence.[...]

Most statistical characteristics are based on an absolute or relative comparison of the levels of dynamic series of dynamics indicators: absolute growth of the indicator, growth and growth rates. The level being compared is called the current level, and the level with which the comparison is made is called the base level. The base level is often taken to be either the previous level or the initial level in a given dynamic series.[...]

The loss of carbonates from solution and their use for growth in terms of 1 g of absolutely dry matter ranges from 1.1 to 6.4 mg/day.[...]

Based on the dynamics series data, indicators characterizing absolute growth, growth and growth rates, and absolute values ​​of one percent of growth are calculated.[...]

The use of liquid nitrogen fertilizers in the United States is systematically increasing both on an absolute and relative scale, and in terms of the rate of growth in consumption they are ahead of all nitrogen fertilizers in general.[...]

If the difference is negative, then there has been a reduction in discharge and on line 11 in column 6 the absolute reduction is given, indicating in subsequent lines (12, 13 and 14) the reasons for which this was achieved. If the difference is positive, then an increase in discharge has occurred. In this case, on line 11 in column 6, the absolute increase in pollution is given with a minus sign (-), lines 12, 13 and 14 are not filled in, and the reasons are given in the explanation to the report.[...]

During a spark breakdown of water, part of the energy released in the spark channel is converted into heat. In absolute terms, the temperature increase can be significant. According to our observations, such an increase in temperature at disinfection costs of 11 - 22 J/ml reaches 2.6 ± 0.24 ° C, and at 44 J/ml - 5.8 ± 0.17 ° C. [...]

Phytomass is usually expressed in kilograms, tons or kilocalories of dry matter per hectare. The increase in phytomass is the main indicator of biological productivity. The maximum values ​​of phytomass are observed in tropical rain forests (700-1000 t/ha of absolutely dry matter), the minimum in the tundra (25-30 t/ha). At the same time, the increase in phytomass or primary production (productivity) is 25-30 t/ha in tropical forests, and 2-2.5 t/ha in the tundra. Phytomass consists of complex organic compounds, which are the basis for the existence of living organisms that use them as nutritional material. [...]

The huge range of sound perception is explained by the ability of human hearing to respond not to an absolute, but to a relative increase in sound volume. This means that the physiological sensation of equal increases in volume occurs when the sound intensity changes not by the same number of units, but by the same number of times. Thus, a change in sound pressure by 10 times (from 1 to 10 bar, from 10 to 100 bar, etc.) is always perceived as the same increase in volume. The same thing happens with the perception of vibration frequency. Our hearing has the ability to respond equally not to absolute increases in frequency, but to its relative changes. Thus, doubling any frequency always leads to the sensation of raising the tone by a certain amount, called an octave.[...]

This method of determining the growth rate is very simple and is most often used in practice (the absolute growth rate of an animal is used to judge its growth rate). It is used to control growing young animals, the growth of fattened animals, etc.[...]

Of the developed countries, only the United States, which ranks third in the world in terms of population, is on the list of leaders in terms of absolute growth. India and China stand out, accounting for a third of the absolute growth. From the list of countries it is clear that 10 large Asian countries provided more than half, or more precisely 52.2% of the world population increase and more than 4/5 or 83.7% of the increase in Overseas Asia. In Africa, the situation is much more dispersed and therefore the contribution of countries with an increase of more than 1 million people per year to the world and African “demographic piggy bank” looks modest and amounts to 9.6% and 40.1%, respectively. Meanwhile, the same figures taken in total for the USA and Mexico are 4.3% and 67.3%, and for Brazil - 2.5% and 41.6%.[...]

The contribution of different countries and continents to the overall picture of population growth is far from the same (Fig. 5.6, Table 5.1). In terms of absolute numbers, the largest increase was achieved by large Asian countries - China, India, Indonesia; The fastest growth rates were observed in Africa and Latin America. In some African countries, the relative increase reached 4% per year. In most more developed countries and regions (Western Europe, North America), the situation of population explosion was observed much earlier - back in the 19th century. Many of them are currently characterized by the development of a demographic transition towards population stabilization.[...]

Pruning a fan-shaped tree. The skeleton of a plum formed by a fan, starting from a one-year-old seedling, is created in exactly the same way as that of a peach formed by a fan (see pp. 138-145). After this, pruning is done differently, since the plum bears fruit on short spurs of two, three, and even four years old, as well as on the previous year's growth. The purpose of pruning is to stimulate the formation of spurs and, if necessary, replace old branches.[...]

The rate of increase in the production of cellulose acetates is currently not very high. However, a small relative increase (in 1971 about 4%) in absolute terms amounts to a fairly significant amount, equal to 17 thousand tons. The total amount of cellulose ethers produced in the USA in 1968 is estimated at 458 thousand tons.[...]

Apple tree seedlings were planted in 1953 in growing containers. Fertilizers were applied at the rate of: N - 85 mg, P2Os - 70 mg and K2O - 95 mg per 1 kg of absolutely dry soil. The growth of these apple trees in 1953 was about 35 cm per tree.[...]

Observations of the development of all three ravines of the thermal erosion system No. 5 of the UKPG-1B site show that from the age of 5 to 6 years, the main increase in length of the gully system occurs mainly due to the formation of new holes. These holes occur continuously due to ongoing disturbances of the tundra surface, increasing snow cover in the built-up area and redistribution of snow cover. Typically, some screwdrivers stop functioning in certain seasons, quickly reaching the attenuation stage, while others actively develop under favorable conditions. The intensity of development depends on the flow of the watercourse. In this regard, it should be noted that when developing anti-erosion measures, absolutely all such forms of mesorelief should be taken into account.[...]

Young generative plants (§1). Seed production in a young generative state is sparse and irregular. The trees are distinguished by their maximum absolute height growth (50 cm), individual shoots reach 175 cm. A regular pointed conical crown is formed, the main axis is clearly visible from its base to the top. A crust appears at the base of the trunk. In individuals raised in dry areas, the condition lasts about 50 years. During such a long and active growth period, significant changes occur in the appearance of the pine tree. From 12 years of age, when individual individuals in pine populations enter the seed-bearing season, and up to 60 years of age, when most plants enter the middle-aged state, the following morphological changes occur: 1) the average height of trees increases from 5.5 to 24 m ; 2) the average diameter of the trunk at chest level increases from 9 to 36 cm; 3) the order of branching in the shoot system varies from 5 to 8; 4) crown diameter increases from 2 to 7 m; 5) the trunk is cleared of lower branches up to 13 m; 6) the length of the crown increases to 11 m; 7) a crust appears at the base of the trunk over a distance of 7 m; 8) the average length of the needles reaches a maximum size of 84 mm. The young generative state is characterized by the most active growth processes; at this time, the typical life form of pine is formed - a single-trunk tree.[...]

Determination of growth rate. The growth rate of animals at different periods of their life is not the same. Growth is determined by live weight and measurements. There is a distinction between absolute and relative increase in live weight. Absolute gain is understood as an increase in live weight and measurements of young animals over a certain period of time (day, decade, month, year), expressed in kilograms. The absolute growth of animals is the difference between the final and initial body weight, divided by the number of days.[...]

In Fig. Figure 9.9 shows graphs of changes in the volume of destruction for the studied objects of the Medvezhye deposit (see Table 8.5). The dynamics of U(T) clearly demonstrates an increase in the absolute values ​​of the volume of gully destruction with a significant decrease in the annual growth rate (see Fig. 8.16). To reduce forecasting errors due to possible fluctuations in precipitation, duration of erosion, etc., the volume of disturbances of the previous, studied and subsequent years should be averaged for the year under study. It should be noted that, according to field observations, the transition of gully formation from the active to the decaying stage is associated with the cessation of the increase in the length of the gully system (see Table 8.6). The natural limitation on the maximum length of a ravine is mainly the length of the slope and the basis of erosion, the catchment area, and the energy characteristics of the watercourse associated with the quality of the soil and vegetation cover when moving along the slope of the top of the ravine.[...]

Particularly significant population growth occurred and is occurring in the second half of the 20th century, during which the population more than doubled. The greatest relative population growth increased, reaching in the late 60s. maximum equal to 2.06% per year. Since then, relative growth has declined, but absolute growth continues to increase, from 65 million per year in 1965 to 80 million in 1985, and approximately 90 million people. in 1995. It is expected that the absolute annual growth of the world's population will soon decline. According to forecasts, stabilization of the world population will occur in the middle of the next century at the level of 10±2 billion people[...]

In the spring of 1954, a week before bud break, fertilizers containing P32 were applied to the apple trees. At the same time, fertilizers were applied to some apple trees at the rate of 35 mg, and to others at the rate of 105 mg of each active substance per 1 kg of absolutely dry soil. The amount of labeled phosphorus was the same in both cases. Seven days after the buds began to open, leaves, one-year growth of shoots, trunk, first-order roots, second-order roots, and third-order roots were examined.[...]

In any complex system of the real world, maintaining processes that run against the temperature gradient is of paramount importance. As Schrödinger showed, to maintain internal order in a system located at a temperature above absolute zero, when there is thermal movement of atoms and molecules, constant work is required to pump out disorder. In an ecosystem, the ratio of the total respiration of a community to its total biomass (R/B) can be considered as the ratio of energy expenditure to maintain life activity to the energy contained in the structure, or as a measure of thermodynamic order. If we express R and B in calories (units of energy) and divide them by absolute temperature, the ratio RIB becomes the ratio of the increase in entropy (and associated work) associated with maintaining the structure to the entropy of the ordered part. The larger the biomass, the higher the maintenance costs; but if the size of the units into which the biomass is divided (individual organisms, for example) is large enough (say, these are trees), then the costs of maintaining processes that go against the temperature gradient, in terms of the structural unit of biomass, will be lower. One of the currently intensely debated theoretical questions is whether nature seeks to maximize the ratio of “structural” to “maintenance” metabolism (see Margalef, 1968; Morowitz, 1968) or whether this refers to the flow of energy itself.[...]

The biological and productive effect of fish hydrolyzate in the composition of feed was assessed by weight growth, survival and fatness of juveniles. The sample size when assessing weight growth is at least 25 specimens. from each pool. The growth rate (speed) of juveniles was judged by absolute daily growth. Survival rate was calculated based on data from recording dead juveniles during daily cleaning of the pools.[...]

In the absence of cytokinins, callus formation at the core of the tobacco stem practically does not occur. It begins only in samples containing cytokinin. The onset of the process can be detected under a microscope within 2-4 days, but usually the effect of cytokinins is judged by the increase in wet and dry weight of callus 4-5 weeks from the moment of planting. To determine the weight, the callus is transferred from the flask to a weighing bottle and weighed to find out its wet weight. Then it is brought to a constant weight in a thermostat at 105° and the dry weight is determined. Within a certain concentration limit, a linear relationship is found between the weight of callus and the concentration of cytokinin. At lower concentrations, the effect of cytokinin is not manifested, but at higher concentrations, a decrease in the effect may be observed. The absolute values ​​of stimulating concentrations vary depending on the cytokinin taken.[...]

For the second experiment, three-year-old apple trees of the Calvil snow variety were taken. Before the experiment, apple trees were grown for two years in growing vessels. In the first year, they received fertilizers at the rate of N - 200 mg (applied in three periods), P2O5 and K2O 150 mg (applied in one period) per 1 kg of absolutely dry soil. In the second year, the fertilizer rate was halved. The growth of apple trees over two years was approximately 40 cm per tree.[...]

As can be seen from table. 1, light extinction strongly depends on the purity of the bidistillate containing air. Boiling leads to a decrease in extinction, while freezing leads to a slight increase. After magnetic treatment, light extinction by water increases in all cases. In absolute units, the greatest extinction is characteristic of magnetized water after freezing and thawing. But the increase in extinction is most noticeable after treating boiled (degassed) water. It is possible that this is due to the influence of the process of dissolution of gases in water.[...]

In today's developed countries, a noticeable increase in the share of the urban population was observed approximately a century ago. Over the course of the current fifty years (1975-2025), the share of the urban population of these countries has increased slightly, approaching the upper limit of the transition (logistic) curve. But about 90% of the urban population growth occurs in developing countries. Residents of Africa and Asia, only a third of whom now live in cities, will also cross the 50% mark by 2025. The size and proportion of the rural population will stabilize or decline, depending on the continent. With the absolute predominance of urban populations on all continents, the ecosphere as a whole will become different, with a relatively sparse rural population and numerous cities of various sizes, including super-large, so-called megalopolises. Understanding this transition process in the ecosphere in its relationship with the activities of society is one of the most important problems of geoecology as an interdisciplinary field.[...]

There is a limit to how much temperature can drop. The efficiency cannot exceed unity; this would contradict the first law of thermodynamics. It follows that the temperature of the refrigerator cannot become negative, so the natural limit for reducing the temperature of the refrigerator is zero. This limit is also called absolute zero temperature, so no object can become colder. In such an “ice desert,” the efficiency of any machine would be equal to one, since an arbitrarily small portion of heat given to the refrigerator would lead to a huge increase in entropy. This is due to the fact that in the formula describing the change in entropy, temperature is in the denominator. [...]

A pig embryo at the age of 15-20 days doubles its weight in 5 days, and 90-100-day-old piglets - in only 10 days of life, that is, 2 times slower. With a decrease in the overall size of the animal, the number of successive doublings of mass during the embryonic period is shortened. The size of the zygote is almost the same in all mammals. Age-related changes in absolute weight gain over the same periods of intrauterine development proceed differently (Table 9).[...]

If N is small compared to k, then the expression in parentheses is close to unity: in this case, equation (9.7) becomes an equation of exponential growth. The graph of population growth will be close to exponential at small N. When N is close to k, the expression in parentheses is close to zero, i.e., the population size stops increasing. From here it is clear that k in this model is the capacity of the medium. When N is greater than k, the absolute increase in the number becomes negative, and the number decreases to a value equal to the capacity of the environment. The graph of population size versus time, corresponding to the solution of equation (9.7), is a 5-shaped curve similar to that shown in Fig. 9.15 downstairs. This curve is called the logistic curve, and the population growth corresponding to equation 9.7 is logistic growth.[...]

Freezing was carried out in an alkali solution of the same concentration as for further xanthogenation. Carbon disulfide was added to a sample of cellulose after freezing and thawing, and EC was carried out as usual. In Fig. Figure 2.6 shows the solubility curve of wood sulfite cellulose after freezing and, for comparison, the solubility curve of the original cellulose. As can be seen from Fig. 2.6, these two solubility curves are completely different in nature. Frozen cellulose does not show such a sharp increase in solubility as the original; its solubility increases smoothly. However, in the final section, the increase in solubility of frozen cellulose is significantly higher than that of the initial one. In addition, complete dissolution of cellulose fibers after freezing occurs at a 9% alkali concentration, and of the original fiber at 10%. At the same alkali concentration, the solubility of fibers after freezing is always higher than that of the original fiber. Thus, the overall availability of pre-frozen pulp increases.[...]

The accumulation of PAHs in soils is due to their precipitation with precipitation onto the underlying surface and the decomposition of soil organic matter. Based on the results of calculations of the balance of PAHs in the system precipitation - soil - lysimetric waters, an increase in PAHs in soils due to precipitation in terms of phenanthrene was reliably recorded. The amount of other light PAHs introduced with atmospheric precipitation is equal to their amount washed out with lysimetric waters, i.e. the accumulation of light polyarenes mainly occurs during soil formation. Different bioclimatic conditions of the subzones determine the absolute accumulation of PAHs in the organic horizon, which is 5.2 times lower in the soils of the northern taiga than in the middle taiga. The qualitative composition of PAHs in atmospheric precipitation, lysimetric waters and soils of the middle and northern taiga is identical (r = 0.92-0.99 at P = 0.95 and n = 12), which indicates common mechanisms for the formation of polyarenes during pedogenesis in different bioclimatic zones.

Based on data set out in UN projections of world population

Around 8000 BC, the world population was approximately 5 million people. Over the 8000 year period before 1 AD. it grew to 200 million people (some estimates say 300 million or even 600 million), with a growth rate of 0.05% per year. A huge change in population occurred with the advent of the Industrial Revolution:

• In 1800, the world population reached one billion.
• The second billion in population was reached in just 130 years in 1930.
• The third billion was reached in less than 30 years in 1959.
• Over the next 15 years, the fourth billion was reached in 1974.
• In just 13 years, in 1987 - the fifth billion.

During the 20th century alone, the world's population grew from 1.65 to 6 billion.

In 1970 the population was half what it is now. Due to declining population growth rates, it will take more than 200 years for the population to double from today's levels.

Table with population data by year and population growth dynamics in the world by year until 2017

Pop%	World population	% increase compared to previous year	Absolute annual increase number of people	Average age of the population	Population density: number of people per 1 sq. km.	Urbanization (urban population) as a percentage of the total population	Urban population
2017	7 515 284 153	1,11%	82 620 878	29,9	58	54,7%	4 110 778 369
2016	7 432 663 275	1,13%	83 191 176	29,9	57	54,3%	4 034 193 153
2015	7 349 472 099	1,18%	83 949 411	30	57	53,8%	3 957 285 013
2010	6 929 725 043	1,23%	82 017 839	29	53	51,5%	3 571 272 167
2005	6 519 635 850	1,25%	78 602 746	27	50	49,1%	3 199 013 076
2000	6 126 622 121	1,33%	78 299 807	26	47	46,6%	2 856 131 072
1995	5 735 123 084	1,55%	85 091 077	25	44	44,8%	2 568 062 984
1990	5 309 667 699	1,82%	91 425 426	24	41	43%	2 285 030 904
1985	4 852 540 569	1,79%	82 581 621	23	37	41,3%	2 003 049 795
1980	4 439 632 465	1,8%	75 646 647	23	34	39,4%	1 749 539 272
1975	4 061 399 228	1,98%	75 782 307	22	31	37,8%	1 534 721 238
1970	3 682 487 691	2,08%	71 998 514	22	28	36,7%	1 350 280 789
1965	3 322 495 121	1,94%	60 830 259	23	21	No data	No data
1960	3 018 343 828	1,82%	52 005 861	23	23	33,8%	1 019 494 911
1955	2 758 314 525	1,78%	46 633 043	23	21	No data	No data

The world population is currently (2017) growing at a rate of about 1.11% per year (up from 1.13% in 2016).

Currently, the average annual population growth is estimated at approximately 80 million people. The annual growth rate peaked in the late 1960s, when it was 2% or higher. The population growth rate peaked at 2.19 percent per year in 1963.

Annual growth rates are currently declining and are projected to continue declining in the coming years. Population growth is projected to be less than 1% per year by 2020 and less than 0.5% per year by 2050. This means that the world population will continue to grow in the 21st century, but at a slower rate compared to the recent past.

The world population doubled (100% increase) in the 40 years from 1959 (3 billion) to 1999 (6 billion). The world's population is currently projected to increase by another 50% in 39 years, to 9 billion by 2038.

Forecast of the world population (all countries of the world) and demographic data for the period until 2050:

date	Population	Number growth % in 1 year	Absolute increase over 1 year in the number of people	Average age of the world's population	Population density: number of people per 1 sq. km.	Urbanization percentage	Total urban population
2020	7 758 156 792	1,09%	81 736 939	31	60	55,9%	4 338 014 924
2025	8 141 661 007	0,97%	76 700 843	32	63	57,8%	4 705 773 576
2030	8 500 766 052	0,87%	71 821 009	33	65	59,5%	5 058 158 460
2035	8 838 907 877	0,78%	67 628 365	34	68	61%	5 394 234 712
2040	9 157 233 976	0,71%	63 665 220	35	70	62,4%	5 715 413 029
2045	9 453 891 780	0,64%	59 331 561	35	73	63,8%	6 030 924 065
2050	9 725 147 994	0,57%	54 251 243	36	75	65,2%	6 338 611 492

Main stages of world population growth

10 billion (2056)

The United Nations projects a world population of 10 billion by 2056.

8 billion (2023)

The world population is expected to reach 8 billion in 2023 according to the United Nations (and in 2026 according to the US Census Bureau).

7.5 billion (2017)

The current world population is 7.5 billion as of January 2017, according to United Nations estimates.

7 billion (2011)

According to the United Nations, the world's population reached 7 billion on October 31, 2011. The US Census Bureau made a lower estimate - 7 billion was reached on March 12, 2012.

6 billion (1999)

According to the United Nations, on October 12, 1999, the world population was 6 billion. According to the US Census Bureau, this value was reached on July 22, 1999, at approximately 3:49 a.m. GMT.