Absolute annual land growth. The world population growth rate is declining, but the absolute number of the planet's inhabitants is still growing rapidly. The main stages of the growth of the world's population

(Tr) is an indicator of the intensity of the change in the level of the series, which is expressed as a percentage, and the growth coefficient (Kr) is expressed in shares. Кр is defined as the ratio of the next level to the previous one or to the indicator taken as the base of comparison. It determines how many times the level has increased in comparison with the baseline, and in the case of a decrease - what part of the baseline is the compared one.

We calculate the growth rate, multiply by 100 and get the growth rate

It can be calculated using the formulas:

Also, the growth rate can be determined as follows:

The growth rate is always positive. There is a certain relationship between the chain and basic growth rates: the product of chain growth rates is equal to the basic growth rate for the entire period, and the quotient from dividing the subsequent basic growth rate by the previous one is equal to the chain growth rate.

Absolute gain

Absolute gain characterizes the increase (decrease) in the level of the series for a certain period of time. It is determined by the formula:

where уi is the level of the compared period;

Vi-1 - Level of the previous period;

Y0 - the level of the base period.

Chain and basic absolute gains are related among themselves in this way: the sum of successive chain absolute increments is equal to the base one, i.e. overall growth for the entire period of time:

Absolute gain can be positive or negative. It shows how much the level of the current period is higher (lower) than the baseline, and thus measures the absolute rate of growth or decline in the level.

(Тпр) shows the relative magnitude of the increase and shows how many percent the compared level is more or less than the level taken as the comparison base. It can be either positive or negative or equal to zero, it is expressed in percentages and shares (growth rates); is calculated as the ratio of the absolute growth to the absolute level taken as the base:

The growth rate can be obtained from the growth rate:

The gain factor can be obtained as follows:

Absolute value of 1% gain

The absolute value of 1% growth (A%) is the ratio of the absolute growth to the growth rate, expressed as a percentage, and shows the significance of each percentage of the growth over the same period of time:

The absolute value of one percent gain equal to one hundredth of the previous or baseline level. It shows what absolute value is hidden behind a relative indicator - one percent increase.

Examples of calculating dynamics indicators

Before studying the theory on the topic dynamics indicators, you can see examples of tasks for finding: growth rate, growth rate, absolute growth, average values ​​of dynamics

About dynamics indicators

When studying the dynamics of social phenomena, it becomes difficult to describe the intensity of change and calculate the average indicators of dynamics that are assigned to students.

The analysis of the intensity of change over time is carried out using indicators that are obtained as a result of comparing levels. These indicators include: growth rate, absolute increase, the absolute value of one percent of the increase. For the generalizing characteristics of the dynamics of the studied phenomena, the following is determined: the average levels of the series and the average indicators of the change in the levels of the series. Dynamics analysis indicators can be determined by constant and variable comparison bases. Here it is customary to call the comparable level the reporting level, and the level from which the comparison is made - the baseline.

For calculation dynamics indicators on a permanent basis, each level of the series must be compared with the same baseline. Only the initial level in a series of dynamics or the level from which a new stage in the development of the phenomenon begins is used as the basic one. The indicators that are calculated in this case are called basic. To calculate the indicators of the analysis of dynamics on a variable basis, each subsequent level of the series must be compared with the previous one. The calculated indicators of the analysis of the dynamics will be called chain.

Rows of dynamics- a series of statistical indicators characterizing the development of natural and social phenomena in time. Statistical compilations published by the Goskomstat of Russia contain a large number of series of dynamics in tabular form. The series of dynamics make it possible to reveal the patterns of development of the phenomena under study.

The series of dynamics 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 the series of dynamics can be expressed in absolute values ​​(production of a product in tons or rubles), relative values ​​( specific gravity urban population in%) and average values ​​(average wage industry workers by year, etc.). A dynamic row contains two columns or two rows.

1. all indicators of a number of dynamics must be scientifically grounded, reliable;
2. indicators of a number of dynamics should be comparable in time, i.e. must be calculated for the same periods of time or for the same dates;
3. indicators of a number of dynamics should be comparable across the territory;
4. indicators of a number of dynamics should be comparable in content, i.e. calculated according to a unified methodology, in the same way;
5. indicators of a number of dynamics should be comparable across the range of considered farms. All indicators of a number of dynamics should be given in the same units of measurement.

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

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

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

Time series of dynamics

The levels of the interval series characterize the result of the process under study for a period of time: production or sales of products (for a year, quarter, month, etc. periods), the number of people employed, the number of births, etc. The levels of an interval series can be summed up. In this case, we get the same indicator for longer intervals of time.

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

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

Let us consider the methodology for calculating the average level of the interval series of dynamics using the example of data on sugar sales in Russia.

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

Momentary series of dynamics

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

If we add up these indicators, we get a repeated count of those workers who worked during the entire month. The resulting amount has no economic content, it is a calculated indicator.

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

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

Let us consider the methodology for such a calculation based on 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- enterprises:

The calculation was carried out according to the average chronological formula. The average payroll number of employees of the enterprise for the 1st quarter was 155 people. In the denominator - 3 months in the quarter, and in the numerator (465) - this is a calculated number, it has no economic content. In the overwhelming 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 according to the formula of the arithmetic weighted average. The weights of the average are taken as the duration of time (t- days, months). Let's perform the calculation using this formula.

The listed number of employees of the enterprise in October is as follows: as of October 1 - 200 people, October 7 hired 15 people, October 12 dismissed 1 person, October 21 hired 10 people and until the end of the month there were no employees hired or fired. This information can be presented as follows:

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

In this formula, the numerator () has economic content... In this example, the numerator (6,665 person-days) is the plant's employees for October. The denominator (31 days) is the calendar number of days in a month.

In those cases when we have moment series dynamics with unequal time intervals, and the specific dates of the change in the indicator are unknown to the researcher, then first you need to calculate average() for each time interval using the arithmetic simple average formula, and then calculate the average level for the entire series of dynamics, weighing the calculated average values ​​with the duration of the corresponding time interval. The formulas look like this:

The series of dynamics considered above consist of absolute indicators obtained as a result of statistical observations. The originally constructed series of dynamics of absolute indicators can be transformed into series of derivatives: series of mean values ​​and series of relative values. The series of relative values ​​can be chain (in% to the previous period) and basic (in% to the initial period taken as the comparison base - 100%). The calculation of the average level in the derived series of dynamics is performed using other formulas.

A range of average values

First, we transform the above momentary series of dynamics with equal time intervals into a series of average values. To do this, we calculate the average payroll 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 represent it in tabular form.

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

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

Series of averages derived from moment or interval series of dynamics should not be confused with series of dynamics in which the levels are expressed by the average. For example, the average wheat yield by years, average wages, etc.

Relative series

V economic practice ranks are used very widely. 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 number with the relative values ​​of the dynamics.

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

Time series analysis

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

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

Absolute gains (Δy) show how many units the next level of the series has changed in comparison with the previous one (column 3. - absolute chain increments) or in comparison with the initial level (column 4. - basic absolute increments). Calculation formulas can be written as follows:

With a decrease in the absolute values ​​of the series, there will be, respectively, "decrease", "decrease".

The indices of absolute growth indicate that, for example, in 1998 the production of product "A" increased by 4 thousand tons as compared to 1997, and by 34 thousand tons as compared to 1994; for the rest of the years see table. 11.5 g 3 and 4.

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

Rates of growth show how many percent is the next level of the series in comparison with the previous one (column 7 - chain growth rates) or in comparison with the initial level (column 8 - basic growth rates). Calculation formulas can be written as follows:

So, for example, in 1997 the volume of production of product "A" in comparison with 1996 amounted to 105.5% (

Growth rate show how many percent the level of the reporting period has increased in comparison with the previous one (column 9 - chain growth rates) or in comparison with the initial level (column 10 - basic growth rates). Calculation formulas can be written as follows:

T pr = T p - 100% or T pr = absolute increase / 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%, and compared to 1994 - by 9% (109% - 100%).

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

Absolute value of 1% gain(column 11) shows how many units must be produced in this period to increase the level of the previous period 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.

There are two ways to determine the magnitude of the absolute value of a 1% increase:

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

Absolute value of 1% gain =

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

Note that the considered method of analyzing the series of dynamics is applicable both for the series of dynamics, the levels of which are expressed in absolute values ​​(t, thousand rubles, the number of employees, etc.), and for the series of dynamics, the levels of which are expressed by relative indicators (% of scrap ,% ash content of coal, etc.) or average values ​​(average yield in centners / ha, average wages, etc.).

Along with the analytical indicators considered, calculated for each year in comparison with the previous or initial level, when analyzing the series of dynamics, 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 series of dynamics we are considering, the average level of the series is calculated by the simple formula:

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

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

Annual absolute increments 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 average growth rate and average growth rate require more detailed consideration... Let us consider them using the example of the annual indicators of the series level shown 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 the 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 the annual growth rate? This value is called the average annual growth rate.

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

Average annual growth rate (determined by subtracting 100% from the growth rate.

The average annual growth (decline) rate according to the geometric mean formulas can be calculated in two ways:

1) on the basis of absolute indicators of a number of dynamics according to the formula:

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

2) based on the annual growth rates according to the formula

• m- the number of coefficients.

The results of the calculation by 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, for the 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 volume of production of product "A" on average for the year increased by 4.0%. Annual growth rates ranged from 1.7% in 1998 to 5.5% in 1997 (for each year, see the growth rates in Table 11.5, column 9).

The average annual growth rate (growth) allows one to compare the dynamics of the development of interrelated phenomena over a long period of time (for example, the average annual growth rate of the number of employees by industry, the volume of production, etc.), to compare the dynamics of a phenomenon in different countries, to study the dynamics of a certain or phenomena according to the periods of the country's historical development.

Seasonal Analysis

The study of seasonal fluctuations is carried out in order to identify regularly recurring differences in the level of the series of dynamics depending on the season. For example, the sale of sugar to the population in summer period increases significantly due to the canning of fruits and berries. Need in labor force in agricultural production is different depending on the season. The task of statistics is to measure seasonal differences in the level of indicators, and in order for the revealed seasonal differences to be regular (and not random), it is necessary to build an analysis on a database for several years, at least for at least three years. Table 11.6 shows the initial data and methodology for the analysis of seasonal fluctuations by the method of simple arithmetic mean.

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

Seasonality index(table. 11.5 gr. 7.) is calculated by dividing the average values ​​for each month by the total average monthly value, taken as 100%. The monthly average for the entire period can be calculated by dividing the total fuel consumption for three years by 36 months (1,188,082 tons: 36 = 3280 tons) or by dividing by 12 the sum of the monthly average, i.e. total total for gr. 6 (2022 + 2157 + 2464 etc. + 2870): 12.

For clarity, based on the seasonality indices, a seasonal wave graph is plotted (Fig. 11.1). Months are plotted on the abscissa, and the seasonality indices in percent are plotted on the ordinate (Table 11.6, column 7). The total monthly average for all years is at the level of 100%, and the average monthly seasonality indices are plotted in the form of dots on the chart field in accordance with the accepted scale along the ordinate.

The points are connected with each other by a smooth broken line.

In the given example, the annual volumes of fuel consumption differ slightly. If, in the series of dynamics, along with seasonal fluctuations, there is a pronounced upward (downward) tendency, i.e. levels in each subsequent year systematically significantly increase (decrease) in comparison with the levels previous year, then more reliable data on the size of seasonality will be obtained as follows:

1. for each year, we calculate the average monthly value;
2. 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 arithmetic mean simple formula of the monthly seasonality indices calculated for each year. So, for example, for January, we obtain the average seasonality index if we add the January values ​​of the seasonality indices for all years (for example, 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 upward (downward) trend in the series of dynamics 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 demand of the population for certain types of goods. The results of the study of seasonal fluctuations are important for the effective management of economic processes.

Bringing rows of dynamics to the same base

In economic practice, it is often necessary to compare several series of dynamics with each other (for example, indicators of the dynamics of electricity production, grain production, sales passenger cars and etc.). To do this, it is necessary to transform the absolute indicators of the compared series of dynamics into derived series of relative basic values, taking the indicators of any one year as a unit or as 100%. Such a transformation of several series of dynamics is called bringing them to the same base. Theoretically, the absolute level of any year can be taken as a comparison base, 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 comparison base.

Time series alignment methods

To study the patterns (tendencies) of the development of the phenomenon under study, data are needed over a long period of time. The development trend of a specific phenomenon is determined by the main factor. But along with the effect 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 repeated (years favorable for Agriculture, arid, etc.). Almost all rows of dynamics economic indicators on the chart, they are shaped like a curve, a broken line with ups and downs. In many cases, it is difficult to determine even general trend development. But statistics should not only determine the general trend of the development of the phenomenon (increase or decrease), but also provide quantitative (digital) characteristics of development.

• Interval coarsening method
• Moving average method

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

The method of enlarging the time intervals (column 3).

Taking into account that the number of dynamics is small, the intervals were taken for three years and for each interval the averages were calculated. The average annual volume of grain production for three-year periods is calculated using the arithmetic average simple 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 results of the calculation in gr. 3.

Given in gr. 3 indicators of the average annual 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 columns 4 and 5) is also based on the calculation of averages over aggregated periods of time. The goal is the same - to abstract from the influence of random factors, to mutually extinguish their influence in certain years. But the calculation method is different.

In the given example, five-bar (for five-year periods) moving averages are calculated and referred to the middle year in the corresponding five-year period. So, for the first five years (1981-1985), according to the arithmetic average simple formula, the average annual 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 excluding the initial year and adding the year following the five-year period and dividing the amount received 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 question is decided by the researcher. In principle, the longer the period, the more smoothing occurs. But one must take into account the length of the dynamics series; do not forget that the moving average method leaves the 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.

Analytical alignment method

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

To determine the parameters, you need to solve the system of equations:

The necessary values ​​for solving the system of equations are calculated and given in the table (see gr. 6 - 8), we substitute them into the equation:

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

Substitute the value of the parameters and get the equation of the straight line:

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

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

Phenomena can develop in dynamics evenly (increase or decrease). In these cases, the straight line equation is most often appropriate. If the development is uneven, for example, first a very slow growth, and from a certain moment a sharp increase, or, conversely, first a sharp decline and then a slowdown in the rate of decline, then the alignment must be performed according to other formulas (the equation of a parabola, hyperbola, etc.). If necessary, it is necessary to refer to textbooks on statistics or special monographs, where the issues of choosing a formula for an adequate reflection of the actually existing trend of the studied series of dynamics are described in more detail.

For clarity, the indicators of the levels of the actual series of dynamics and aligned series will be plotted on the graph (Fig. 11.2). The actual data is a broken black line indicating ups and downs in grain production. The rest of the lines on the chart show that the use of the moving average method (line with cut ends) allows you to substantially align the levels of the time series and, accordingly, make the broken curve line smoother and smoother on the chart. However, aligned lines are still curved lines. Constructed on the basis of the theoretical values ​​of the series obtained by mathematical formulas, the line strictly corresponds to a straight line.

Each of the three considered methods has its own merits, but in most cases the analytical alignment method is preferable. However, its application is associated with large computational work: solving a system of equations; verification of the validity of the selected function (form of communication); calculation of the levels of the aligned row; building a schedule. For the successful implementation of such work, it is advisable to use a computer and appropriate programs.

Based on data set out in UN projections for the world's population

Around 8000 BC, the world's population was approximately 5 million. Over the 8000-year period up to 1 A.D. it has grown to 200 million people (according to some estimates, 300 million or even 600 million), with a growth rate of 0.05% per year. A huge change in population size happened with the arrival of the industrial revolution:

• In 1800, the world's 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, in 1974 it will reach the fourth billion.
• 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 today. Due to the slowdown in population growth, it will take more than 200 years to double the population from today's data.

Table with data on population by years and dynamics of population growth in the world by years until 2017

The world's 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 about 80 million. The annual growth rate peaked in the late 1960s, when it was 2% or more. The population growth rate peaked at 2.19 percent per year in 1963.

The annual growth rate is currently declining and is projected to continue to decline in the coming years. Population growth is projected to be less than 1% per annum by 2020 and less than 0.5% per annum by 2050. It means that world population will continue to grow in the 21st century, but at a slower pace than in 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 now projected to increase by another 50% in 39 years, to 9 billion by 2038.

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

The main stages of the growth of the world's population

10 billion (2056)

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

8 billion (2023)

The world's 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 population of the Earth 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 population of the entire world was 6 billion. According to the US Census Bureau, this value was reached on July 22, 1999, at approximately 3:49 am GMT.

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

The absolute gain is determined as the difference in 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 the series to another and is expressed in coefficients or percentages. [...]

The growth of rainbow trout fry is strongly influenced by the oxygen content in the water. At a low oxygen concentration, growth slows down by half, the absolute and relative indicators of feed consumption, its payment decreases. This is explained, in particular, by the deterioration of the digestibility of proteins. [...]

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

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

The decrease in the rate of increase in the content of freons is due to the fact that in the second half of the 1980s. in many industrialized countries, restrictions were imposed on the production and consumption of these products. A further decrease in the trend can be expected in the coming years in connection with the international agreements reached on the gradual phase-out of the use of fluorochlorocarbons. However, the absolute concentrations of freons in the atmosphere will probably increase for many years to come, even after the complete cessation of their production. From table. 3.7 it can be seen 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 (as part of products from porous polymers such as polyethylene urethanes) use and will gradually be released into environment.[ ...]

To analyze the dynamics of growth, the average values ​​of absolute growth over decades were considered. Noticeable discrepancies in the growth rate at different distances from the road were observed in the 1960s – 1970s, when the trees adapted to the transplanting conditions and actively formed the crown (Fig. 1). In the 1980s-1990s. the increase at different distances from the road had close average values ​​(the differences are small and insignificant at the significance level of 0.05). [...]

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

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

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

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

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

According to the series of dynamics, indicators are calculated that characterize the absolute growth, growth and growth rates, the absolute values ​​of one percent of growth. [...]

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

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

With a spark breakdown of water, part of the energy released in the spark channel is converted into heat. In absolute terms, the increase in temperature can be significant. According to our observations, such an increase in temperature at a disinfection cost 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, using them as a nutrient material. [...]

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

The specified way Determination of the growth rate is very simple and is most often used in practice (the rate of its growth is judged by the magnitude of the absolute growth of an animal). It is used to control growing young stock, the growth of fattened animals, etc. [...]

Of the developed countries, only the United States, which ranks third in the world in terms of population, was included in the list of leaders in terms of absolute growth. India and China stand out, accounting for a third of the absolute growth. The list of countries shows that 10 large Asian countries provided more than half, or rather 52.2% of the world population growth and more than 4/5 or 83.7% of the growth 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, these same indicators, taken together for the United States and Mexico, are 4.3% and 67.3%, and for Brazil - 2.5% and 41.6%. [...]

Contribution different countries and continents in 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 given by large Asian countries - China, India, Indonesia; the fastest growing was in Africa and Latin America. In some African countries, relative growth has been as high as 4% per year. In most of the more developed countries and regions (Western Europe, North America), the situation baby boom was observed much earlier - back in the 19th century. Many of them are currently characterized by the development of a demographic transition to stabilization of the population. [...]

Pruning a fan shaped tree. The skeleton of a fan-shaped plum, starting from a one-year sapling, is created in exactly the same way as for a fan-shaped peach (see pp. 138-145). After that, pruning is carried out in a different way, since the plum bears fruit on short spurs of two, three, and even four years of age, as well as on the growth of the previous year. The purpose of pruning is to stimulate spur formation and replace old branches as needed. [...]

The rate of increase in the production of cellulose acetate is currently not very high. However, a small relative increase (in 1971 about 4%) in absolute terms is quite significant, 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 vegetative vessels. 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 amounted to about 35 cm per tree. [...]

Observations of the development of all three ravines of the thermoerosion system No. 5 of the UKPG-1V section show that from the age of 5 to 6 years, the main increase in the length of the ravine system occurs mainly due to the formation of new screwdrivers. These screwdrivers appear continuously in connection with the continuing disturbance of the tundra surface, the increase in the snow cover of the built-up area and the redistribution of the snow cover. Usually, some screwdrivers cease to function in certain seasons, quickly reaching the attenuation stage, while others are actively developing under favorable conditions. The intensity of development depends on the flow rate 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). Semination in a young generative state is not abundant and irregular. Trees differ in maximum absolute increments in height (50 cm), individual shoots reach 175 cm. A regular peaked conical crown is formed, the main axis is well traced from its base to the top. A crust appears at the base of the trunk. In individuals raised on dry land, the state lasts for about 50 years. During such a long and active growth period, significant transformations take place in the external appearance of the pine. From 12 years of age, when individual individuals in pine populations enter the seedling season, and up to 60 years of age, when most plants pass into a middle-aged state, the following morphological changes occur: 1) the average height of trees increases from 5.5 to 24 m ; 2) the average trunk diameter at chest level increases from 9 to 36 cm; 3) the order of branching in the shoot system varies from 5 to 8; 4) the 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 for 7 m; 8) the average length of the needles reaches the maximum size - 84 mm. The young generative state is distinguished by the most active growth processes, at this time a typical life form of a pine is formed - a single-trunk tree. [...]

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

In fig. 9.9 shows the graphs of changes in the volume of destruction for the investigated objects of the Medvezhye field (see Table 8.5). The dynamics of Y (T) clearly demonstrates the growth of the absolute values ​​of the volume of ravine destruction with a significant decrease in the coefficient of annual growth (see Fig. 8.16). To reduce the forecasting error due to possible fluctuations in the amount of precipitation, the duration of erosion, etc., the volume of violations of the previous, investigated and subsequent years should be averaged for the studied year. It should be noted that, according to field observations, the transition of gully formation from the active stage to the decaying one is associated with the termination of the increase in the length of the gully system (see Table 8.6). The natural limitation of the maximum length of the ravine is mainly the length of the slope and the basis of erosion, the catchment area, 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. [...]

In particular, significant population growth took place and continues to occur in the second half of the 20th century, during which the population more than doubled. The largest relative population growth increased, reaching at the end of the 60s. a maximum equal to 2.06% per year. Since then, relative growth has declined, but absolute growth has continued to increase, from 65 million per year in 1965 to 80 million in 1985, and about 90 million. in 1995. It is expected that the absolute growth of the world's population for the year will soon begin to decline. According to forecasts, the stabilization of the world's 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 budding, fertilizers containing P32 were applied under the apple tree. At the same time, fertilizers were applied under some apple trees at the rate of 35 mg, and under others at the rate of 105 mg of each active ingredient per 1 kg of absolutely dry soil. The amount of labeled phosphorus was the same in both cases. Seven days after the beginning of budding, the leaves, annual growth of shoots, trunk, first-order roots, second-order roots, and third-order roots were examined. [...]

In any complex system of the real world, it is of paramount importance to maintain processes going against the temperature gradient. As Schrödinger showed, to maintain internal order in a system located at a temperature above absolute zero, when there is thermal motion of atoms and molecules, constant work is required to pump out the 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 expenditures for the maintenance of vital activity to the energy contained in the structure, or as a measure of thermodynamic ordering. If you express R and B in calories (energy units) and divide them by absolute temperature, then the RIB ratio becomes the ratio of the entropy gain (and the corresponding work) associated with maintaining the structure to the entropy of the ordered part. The more biomass, the greater the maintenance cost; 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 going against the temperature gradient, in terms of the structural unit of biomass, will be lower. One of the intensely debated now theoretical issues- whether nature seeks to maximize the ratio of "structural" metabolism to "supportive" (see Margalef, 1968; Morowitz, 1968), or does it refer to the flow of energy itself. [...]

The biological and productive effect of fish hydrolyzate in the composition of mixed fodders 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 rate (speed) of growth of juveniles was judged by the absolute daily increments. The survival rate was calculated according to the data of the registration of dead juveniles during the daily cleaning of the pools. [...]

In the absence of cytokinins, callus formation practically does not occur in the core of the tobacco stem. It starts only in samples containing cytokinin. It is possible to detect the beginning of the process under a microscope after 2-4 days, however, usually the action of cytokinins is judged by the increase in the wet and dry weight of the callus after 4-5 weeks from the moment of planting. To determine the weight, the callus is transferred from the flask into a weighing bottle and weighed to determine its wet weight. Then it is brought to constant weight in a thermostat at 105 ° and the dry weight is determined. In a certain concentration limit, a linear relationship is found between the weight of the callus and the concentration of cytokinin. At lower concentrations, the effect of cytokinin is not manifested, and 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 setting up 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 at three times), P2O5 and K2O at 150 mg (applied at one time) per 1 kg of absolutely dry soil. In the second year, the fertilizer rate was halved. The growth of apple trees in two years was about 40 cm per tree. [...]

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

In the now developed countries, a noticeable increase in the proportion of the urban population was noted about a century ago. During the current fifty years (1975-2025), the share of the urban population of these countries has already increased slightly, approaching the upper limit of the transition (logistic) curve. But on the other hand, about 90% of the increase in the urban population is due to developing countries... Inhabitants of Africa and Asia, only a third of whom now live in cities, will also pass 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 the urban population 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 transitional process in the ecosphere in its relationship with the activities of society is one of the most important problems of geoecology as an interdisciplinary direction. [...]

There is a limit to the possible temperature 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 that the natural limit for lowering the temperature of the refrigerator is zero. This limit is also called absolute zero temperature, so that no object can get colder. In such an "icy desert" the efficiency of any machine would be is 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, the 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 - only in 10 days of life, that is, 2 times slower. With a decrease in the overall size of the animal, the number of successive doubling of the mass in the embryonic (the period is reduced. The size of the zygote is practically the same in all mammals. The age-related changes in the absolute. Weight gain for the same periods of time of intrauterine development proceed differently (Table 9). [...]

If N is small in comparison with k, then the expression in parentheses is close to unity: in this case, equation (9.7) becomes the equation of exponential growth. The graph of population growth will be close to exponential for small N. When N is close to k, the expression in parentheses is close to zero, that is, the population size stops increasing. Hence, 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 the dependence of the population size on time, corresponding to the solution of equation (9.7), is a 5-shaped curve similar to that shown in Fig. 9.15 at the bottom. This curve is called the logistic curve, and the growth in population according to Equation 9.7 is the logistic growth. [...]

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

The accumulation of PAHs in soils is due to their deposition with atmospheric precipitation on the underlying surface and the decomposition of soil organic matter. Based on the results of calculations of the balance of PAHs in the system atmospheric precipitation - soil - lysimetric waters, the 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 in the process of soil formation. Different biocimatic conditions of the subzones determine the absolute accumulation of PAHs in the organogenic 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 the common mechanisms of polyarene formation during pedogenesis in different bioclimatic zones.

1.Specify 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 increase in the population of the Earth:

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

2) 50-70 mln. human; 4) 120-130 mln. human.

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

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

4.Specify a group that 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 in terms of population in the proposed list of European countries:

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

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

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

7. What are the three largest countries in Africa in terms of population:

1) Algeria; 6) Chad;

2) Ethiopia; 7) Morocco;

3) Zaire; 8) Botswana;

4) South Africa; 9) Egypt;

5) Nigeria; 10) Tanzania.

8. Provide correct statements:

1) In the eastern hemisphere is concentrated more population than western;

2) In the northern hemisphere, the population is less than in the southern;

3) Most of the inhabitants of the Earth 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. State the correct statements:

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

2) The population density in Africa is about 2 times lower than the world average;

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

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

10. State the correct statements:

1) Of all the states in the world (not counting the 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) Non-populated areas 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 listed 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. Indicate in the proposed list of European countries five states with approximately the same population:

1) Germany; 6) Belgium;

2) France; 7) Greece;

3) Netherlands; 8) Norway;

4) Greece; 9) Sweden;

5) Bulgaria; 10) Poland.

13. List three regions of the world with the largest populations:

1) Europe; 4) North America;

2) Asia; 5) Latin America;

3) Africa; 6) Australia and Oceania.

14. In the following list of European countries, list 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 a 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's population"