home Knitting Dynamic series. World population by year Analysis of time series

Dynamic series. World population by year Analysis of time series

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 level of significance).[...]

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.[...]

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 the 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 a temperature increase with 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 of the maximum length of a 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. [...]

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 processing 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.

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

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

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 base growth rates: the product of the chain growth coefficients is equal to the base growth rate for the entire period, and the quotient of dividing the subsequent base growth rate by the previous one is equal to the chain growth rate.

Absolute increase

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

where уi is the level of the period being compared;

Уi-1 - Level of the previous period;

Y0 is the level of the base period.

Chain and basic absolute increases are related each other in this way: the sum of successive chain absolute increases is equal to the base, i.e., the total increase for the entire period of time:

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

(Tpr) shows the relative magnitude of the increase and shows by what percentage the compared level is greater or less than the level taken as the basis of comparison. 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 absolute growth to the absolute level taken as the base:

The growth rate can be obtained from the growth rate:

The growth rate can be obtained as follows:

Absolute value of 1% increase

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

Absolute value of one percent increase equal to one hundredth of the previous or base level. It shows what absolute value is hidden behind the relative indicator - one percent increase.

Examples of calculations of dynamics indicators

Before studying the theory on the topic of dynamics indicators, you can look at examples of problems on finding: growth rate, growth rate, absolute growth, average dynamics

About dynamics indicators

When studying the dynamics of social phenomena, the difficulty arises in describing the intensity of change and calculating the average indicators of dynamics that are asked to students.

Analysis of the intensity of change over time occurs using indicators that are obtained by comparing levels. These indicators include: growth rate, absolute growth, absolute value of one percent growth. To generalize the dynamics of the phenomena under study, the following are determined: the average levels of the series and the average indicators of changes in the levels of the series. Dynamics analysis indicators can be determined using 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 is the base level.

For calculation dynamics indicators on a permanent basis, you need to compare each level of the series with the same basic level. As a base level, only the initial level in the dynamics series or the level from which a new stage in the development of a phenomenon begins is used. The indicators that are calculated in this case are called basic. To calculate dynamics analysis indicators on a variable basis, you need to compare each subsequent level of the series with the previous one. The calculated dynamics analysis indicators will be called chain indicators.

The world's population growth rate is declining, but the absolute number of people on the planet is still growing rapidly

The previous edition of the World Population Barometer looked at global population growth trends as they appear. The US Bureau of Census conducts its own research and develops projections of changes in world population. In March 2004, it presented a new report, World Population Profile 2002. ("Global Population Profile: 2002"). It analyzes trends in the size and composition of the world population, the spread of contraceptive methods in developing countries, and the development of the AIDS pandemic in the 21st century, based on data as of early 2002 and forecast calculations up to 2050 for 227 countries and territories.

As of mid-2002, the world population was approximately 6.2 billion. Population growth in 2002 was 74 million people. This increase was partly due to the still quite high, despite a significant decline in recent decades, birth rate, at which the number of children born exceeds that necessary for the simple reproduction of generations. But a more important growth factor at present is the gender and age structure of the population, in which the proportion of women of reproductive age is relatively large. On the other hand, despite the continuing decline in the mortality rate of the world population, the population dynamics of many countries are significantly influenced by the spread of AIDS, which must be taken into account when making forecast calculations.

The most striking of them is the rapid growth of the population of developing countries against the backdrop of stabilization of the population of developed countries at just over 1 billion people (Fig. 1). If in 1950 approximately one in three lived in developed countries, today only one in five lives.

Figure 1. Population change in developed and developing countries, 1950-2010, billion people

Asia has been and remains the most populous region of the world (Fig. 2). In 1950-1960, 53.5% of the world's population lived there, in 2002 - 56.5%. Until recently, Europe remained the second most populous region, but in the last half century its share has been rapidly declining: from 22.4% in 1950 to 12.9% in 2002. Back in 1970, the number of its inhabitants was almost twice the number of inhabitants of Africa - the third most populous region of the world, but already in 2000 they were equal, concentrating 13.2% of the world's population, and in 2002 the share of Europe was 12.9%, Africa - 13.5%.

The trend of relative population decline, in addition to Europe, is also characteristic of North America (from 6.5% in 1950 and 1960 to 5.1% in 2002). Oceania's share of the population has remained stable over recent decades at 0.5% of the world's population. The share of Latin American and Caribbean countries, having increased from 6.5% in 1950 to 8.7% in 2002, has also shown a tendency to stabilize in recent years.

On the other hand, rapid population growth is typical, in addition to Africa, for the countries of the Middle East, whose share increased from 1.7% in 1950 to 2.9% in 2002.

According to forecasts, the absolute population of large regions of the world will continue to grow in the coming years, but in the longer term - closer to 2050 - the population of Europe and a number of developed countries in other regions of the world will begin to decline.

Figure 2. Population changes in major regions of the world, 1950-2010, million people

Absolute annual growth in the world's population has been steadily declining since 1990, when the absolute maximum was reached - 87.4 million people from mid-1989 to mid-1990, but the peak intensity of growth in percentage terms was overcome back in 1963-1964, when the coefficient growth rose to 2.2% (for 1989-1990 it was 1.7% on average per year, in 2000-2010 - 1.1%). However, the world's population is still growing rapidly - an increase of 74 million people in 2002 is equivalent to the emergence of a fairly large country, slightly larger than Egypt and slightly smaller than Vietnam (15th place in the world ranking), and in five years - the emergence of a large region, equal in population to modern Western Europe.

Population growth trends by region of the world have some peculiarities (Fig. 3-4). The rate of annual population growth in developed countries as a whole has been steadily declining for many decades, gradually approaching zero: from 1.2% in 1950-1960 it fell to 0.3% in 2000-2010. The population growth rate of developing countries increased until the 1970s (the highest value - 2.4% per year - was noted in the 1960-1970s), and then began to decline steadily - to 1.3% in 2000-2010. Thus, the differences between developed and developing countries in terms of population growth rates are gradually smoothing out, but still remain very significant.

Figure 3. Average annual population growth rate of developed and developing countries of the world, 1950-2010, in%

The most pronounced trend of declining population growth down to zero growth is in Europe, where the average annual growth rate decreased from 1.1% in the 1950-1960s to 0.1% in 2000-2010 (Fig. 4).

A similar trend, but at higher levels, is characteristic of Latin America and the Caribbean. If in the 1950s-1960s this region, along with the Middle East, had the highest rates of population growth - 2.7% per year - then after a period of consistently high growth it confidently approached the level of other regions of the world, which were distinguished by less straightforward trend of decreasing population growth rates.

The countries of the Middle East experienced a noticeable acceleration in growth rates - up to 3.0% - in the 1970s and 1980s, but they also experienced a slowdown in population growth in subsequent decades. But even now the Middle East has the highest population growth rate - 2.2% on average per year in 2000-2010. In Africa, Latin America and the Caribbean it is 1.3%, in Oceania - 1.2%, Asia - 1.1%, North America - 0.9%.

A slight deviation from the trend of decreasing growth rates was observed in North America: in 1980-1990, the average annual growth rate there was 1.0%, and in 1990-2000 - 1.2%.

Figure 4. Average annual population growth rate of the main regions of the world, 1950-2010, %

1 - The developed (“more developed”) countries in the report include the countries of North America (except for the countries of Latin America and the Caribbean) and Europe (including the Baltic states and four CIS republics - Russia, Ukraine, Belarus and Moldova), Japan, Australia and New Zealand. All other countries, in accordance with the UN convention, are classified as developing ("less developed").

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 is 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 by 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 supplies 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

Preview:

GEORRAPHY OF THE WORLD POPULATION»

Option 1

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 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 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 land inhabitants 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) 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;

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

Test for thematic control of the level of basic knowledge of 10th grade students in geography on the topic “Reproduction and age-sex composition of the population"

Option 2

1) The ratio of men and women in the world is determined by the significant preponderance of the number of women over the number of men in India and China;

2) In the world as a whole, the number of women is significantly greater than the number of men;

3) In developed countries, as a rule, women predominate;

4) More boys are born than girls, but by the age of 15 the sex ratio levels out, and at older ages women usually predominate.

2. Indicate errors in the list of countries in which men predominate:

1) Paraguay; 6) Bulgaria;

2) Mexico; 7) Ireland;

3) Peru; 8) Philippines;

4) China; 9) Japan;

5) Egypt; 10) Mongolia.

3. Indicate in the list provided the five countries with the highest birth rates:

1) Pakistan; 6) Cuba;

2) Afghanistan; 7) Brazil;

3) India; 8) Chile;

4) China; 9) Mali;

5) Nigeria; 10) Democratic Republic of the Congo.

4. Indicate in the list provided the five countries with the highest natural increase:

1) Mongolia; 6) Chad;

2) Albania; 7) Madagascar;

3) South Africa; 8) Nicaragua;

4) Egypt; 9) Algeria;

5) Nigeria; 10) Australia.

5. Indicate the country with the highest natural population growth in Europe:

1) Greece; 3) Bulgaria;

2) Albania; 4) Portugal.

6. Indicate the correct statements:

1) In developing countries, children make up 40-45% of the population;

2) In developing countries, the share of the working-age population is 70-80%;

3) In developing countries, the proportion of children is 4-5 times higher than the proportion of elderly people;

4) In developed countries, the proportion of older people is higher than average.

7.Indicate a country in which the proportion of elderly people is higher than the proportion of children:

1) Kenya; 3) Kuwait;

2) Germany; 4) India.

8. Among the regions of the world, indicate two with the maximum proportion of children

3) Africa; 6) Australia and Oceania.

9. Among the regions of the world, indicate two with the highest proportion of older people:

1) Foreign Europe; 4) North America;

2) Foreign Asia; 5) Latin America;

3) Africa; 6) Australia and Oceania.

10. Name a country in which the proportion of children makes up less than a quarter of the population, and the proportion of elderly people is significantly higher than the world average:

1) Brazil; 4) India;

2) Mexico; 5) Kuwait;

3) Bulgaria; 6) Kenya.

11. Indicate the Asian state that has the highest mortality rate:

1) Japan; 4) Afghanistan;

2) India; 5) Kuwait;

3) Iran; 6) Republic of Korea.

12. Indicate the region in which the proportion of children is 9 times higher than the proportion of elderly people:

3) Africa; 6) Australia and Oceania.

13. Indicate the region in which the highest proportion of people of working age (from 15 to 59 years old):

1) Foreign Asia; 4) Latin America;

2) Foreign Europe; 5) North America;

3) CIS; 6) Australia and Oceania.

14. In the world, for every 1000 women there are approximately (indicate the correct option):

1) 990 men; 3) 1010 men;

2) 1001 men; 4) 1100 men.

15. Currently, around the world as a whole (indicate the correct option):

1) the birth rate is about 35%, the mortality rate is about 20%;

2) the birth rate is about 25%, the mortality rate is about 10%;

3) the birth rate is about 20%, the mortality rate is about 15%;

4) the birth rate is about 15%, the mortality rate is about 10%.

Test for thematic control of the level of basic knowledge of 10th grade students on the topic “National composition of the population»

Option 3

1. Indicate the correct statements:

1) About half of the world's states are multinational;

2) The USA is the most multinational country in the world;

3) India is a multinational state;

4) The most common language in the world is English.

2. Indicate multinational countries from the proposed list

1) Sweden; 6) Spain;

2) Russia; 7) Denmark;

3) USA; 8) Germany;

4) Great Britain; 9) Hungary;

5) Albania; 10) Portugal.

3. Indicate in the proposed list three countries with extremely complex national composition:

1) Poland; 6) Norway;

2) India; 7) Indonesia;

3) China; 8) Australia;

4) Nigeria; 9) Libya;

5) France; 10) Argentina.

4. Indicate the two largest families of the listed languages:

1) Niger-Kordofanian; 6) Indo-European;

2) Sino-Tibetan; 7) Dravidian;

3) Afroasiatic; 8) North Caucasian;

4) Altai; 9) Austronesian;

5) Ural-Yukaghir; 10) Australian.

5. Indicate the 5 most numerous peoples from the list presented

1) Chinese;

2) Koreans;

3) Japanese;

4) English;

5) Spaniards;

6) Russians;

7) French;

8) Hindustani;

9) Bengalis;

10) Vietnam.

6. Indicate the two most common languages from the list provided

1) German;

2) English;

3) Hindi;

4) French.

7. Match:

Official language A country

1) English; A) Venezuela

2) Portuguese; B) Mali

3) Spanish; B) Laos

4) French D) Mozambique

D) Netherlands

8. Which people constitute a national minority in Romania

Slovaks;
Ukrainians;
Bulgarians;
Serbs;
Hungarians.

9. Indicate the official languages of Switzerland

10. List three peoples belonging to the same language family

11. Indicate between which races mestizos are an intermediate group

between Caucasoid and Negroid;
between Caucasoid and Mongoloid;
between Caucasoid and Australoid;
between Negroid and Mongoloid.

12. Indicate the region in which the mixing of races occurred most intensively (and is currently occurring)

13. Indicate errors in the list of countries for which the majority of the population speak English as their native language

№/№	Option 1	Option 2	Option 3
			1, 3
		2, 6, 9	2, 3, 4, 6
	1,3,4	1, 2, 5, 9, 10	2, 4, 7
		1, 5, 7, 8, 9	2, 6
			1, 3, 6, 8, 9
		1, 4	2, 3
	2, 5, 9		1-D; 2 – G; 3 – A; 4 - B
		3, 5
	2, 3	1, 4	1, 4, 5, 8
	1, 4		1, 3, 9

	1, 3, 6
	1, 2, 3		3, 6, 8
	4, 5, 7,8 10		3, 7

Evaluation criteria

For each correct answer 1 point is given.

“5” - 14 - 15 points

“4” - 12 - 13 points

“3” - 9 – 11 points

"2" - 1 - 8 points