MATHEMATICAL APPROACH TO POPULATION STUDIES

MATHEMATICAL APPROACH TO POPULATION STUDIES. Population studies usually is associated with lots of calculations and it is very important students to understand and get used to various formulae for solving specific problems associated with population.

Some population formulae

  • Formula 1

Population density      =          Total population

                                                     Land area

  • Formula 2

Total population = No. of males + No of all females

  • Formula 3

Total population = Population density x Land area

  • Formula 4

Land area        =          Total population

                                    Population density

Example of mathematical approach to population studies

The total number of males in a country which has a total land area of 140,000 square kilometers is 150,000,000, while that of the females is 130,000,000 including all migrants calculate:

  •  The total population of the country
  •  The population density of the country

Solution

  • Total population

=          No of all males + No of all females

=          150,000,000 + 130,000,000

=          280,000,000 people

  • Population density = Total population

Land area

280,000,000

= 140,000

= 2000 persons / sq km

Alternatively, (a) can be solved by

Total population

=          population density x land area

=          2000 x 140,000

=          280,000,000 people

Example 2 of mathematical approach to population studies

If the population density if tanko district is 3,500 persons per square kilometer and the total population is 1,400,000 people. Calculate the total land area of tanko district.

Solution

Land area        =          Total population

                        =          population density

                        =          1,400,000 people\

                                    3,500 persons /km2

                        =          400 square kilometers

Formula 5

Rate of population growth R,

= Birth rate – Death + Net migration

Formula 6 of mathematical approach to population studies

Net migration = Immigrants – emigrants

I.e. Net migration is the difference between the number of immigrants and emigrants

Formula 7 of mathematical approach to population studies

Natural increase = birth rate – death rate

Formula 8 of mathematical approach to population studies

Percentage increase

= New population – old population

            Old population            x 100

Formula 9

Dependency ratio

=          Dependent population

Working or Independent population

Note: Dependency ratio may be defined as the ratio o

f dependent population to independent population i.e. DR = DP:IP

Example 3 of mathematical approach to population studies

Use the information table in 11.1 and answer the following questions

Table 11.1: Population statistics of a country in 1980 and 1996

Year19801996
No of births in million No of deaths in million No of immigrants in million No of emigrants in million Total population in million        5648 12 10 4 98

Calculate following using mathematical approach to population studies

  • The natural increase of the population in 1966
  • Determine the net migration within the period
  • The rate of growth of the population in 1966
  • Calculate the population of the country in 1966
  • What is the percentage increase in the population of the country from 1980 to 1966

Solution

  •  Natural Increase

                              = Birth rate – Death rate

                              = 48 million – 12 million

                              = 36 million 

  • Net migration        = Immigrants – Emirates

                              = 10 million – 4 million

                              = 6 million

  • Rate of population growth R, = Birth rate – Death rate + Net migration

No of Birth                       = 48 million

No of death                       = 12 million

Net migration = (immigrants – emigrants)

R   =          (48 – 12) + (10 – 4)

      =          36 + 6 = 42 million 

  • Population of the country in 1996

= 1980 population + Net migration

+ (Number of births – Number of deaths)

= 56 million + 6 million

+ (48 million – 12 million)

= 62 million + 36 million

= 98 million 

  • Percentage increase from 1980 to 1996

= New population – Old population   x 100

                  Old population

= 98 million – 56 million x 100

           56 million

= 42 million x 100

    56 million

= 75%

Example 4

The data in table 11.2 show a hypothetical age distribution of the population of a town in Nigeria.

Table. 11.2 shows a hypothetical age distribution of the population of a town in Nigeria

SexAge in years 10 and below11 – 14 15 – 3536 – 6465 and above
Male135022751135Y3250
Female2650272513654265Z
Total4000X250075006000

From this data, calculate:

  • X, Y, Z.
  • The total population of the town.
  • The difference between the population of male and female aged 14 and below
  • The percentage of the population aged 14 years and below.
  • The dependency ratio in the town (SSCE June 1997).

Solution

1(a) X = Male (2275) + Female (2725) = 5000

       Y = Total – Female = 7500 – 4265 = 3235

       Z = Total – Male = 6000 – 3250 = 2750 

 (b)  Total population

         10 and below                 =          4, 000

         11 – 14                           =          5, 000

         15 – 35                           =          2, 500

         36 – 64                           =          7, 500

         65 and above                  =          6, 000

         Total                               =          25, 000

Total population of the town is 25, 000 people.

  • Female 14 years and below

= 2650 + 2725 = 5375

Male of 14 years and below

= 1350 + 2275 = 3625

/ Difference between the populations of male and female aged 14 and below:

            = 5375 – 3625 = 1750

  • Percentage of population aged 14 years and below:

Female aged 14 years and below + male aged 14 years and below:

= 5375 + 3625 + 9000

Or

4000 + 500 = 9000

= 9,000            x          100

    25,000                       1

= 36%

  • Dependency ratio

 =       population of less than 14 years +

           population of more than 65 years

           Population of 15 – 35 + population of 36 – 64 years

           Dependency ratio =                  9000 + 6000

                                                            2500 + 7500

                                           =               15,000 = 3

                                                            10,000 2

                                           =               3: 2

Formula 10

Population figures can be represented in form for table (as in table 11.1 and table 11.2) and in bar and pie charts (see chapter 2 units 2.4 and 2.5).

Example 5

The pie chart in fig 11.3 represents the age distribution of population is 240 million.

age distribution of population

From the information in the diagram calculate the:

  • Population of children between 0 and 17 years
  • Population of old people (60 + years)
  • Working population 18 – 59 years
  • Calculate the dependency ratio.

Solution

  • Population of children between 0 and 17 years

= 120 x 240 = 80 million

360          1

  • Population of old people (60 + years)

= 90 x 240 = 60 million

    360     1

  • Working population 18 – 59 years

= 150 x 240 = 100 million

    360 x   1

  • Calculate the dependency ratio.

Population of children (0 – 17 years ) +

= population of old people (65 years)

 Working population of (18 – 64 years)

= 80,000,000 + 60,000,000

      100,000,000

Dependency ratio = 140,000,000

                                    100,000,000

= 1.4

        1

= 1.4:1

= 7:5

Example 6

The pie chart below shows the age distribution of population in thousand of an island for the year 2000. The total population of the island is 245,000.

Use the information supplied to answer the question that follows. (Show all workings clearly).

  • Calculate the number of person in the different age groups.
  • What is the dependency ratio of the population?
  • Give three implications of the above population structure.

Solution

Age group 0-16 years  =          149,722.20

            220 x 245,000

            360      1

Age group 17-45 years            =          51,041.70

            75 x 245,000

            360      1

Age group 46-60 years            =          29, 263, 90

            43x 245,000

            360      1

Age group 60+ years               =          14, 972.20      

            22 x 245,000

            360      1

  • Dependency ratio

= 145,722.20 +14,972.20

    51,041.70 + 29,263.90

= 164,694.40

    80,305.60

= 2:1 (2 to 1)

   Or

   (2:1 to 1)

Implications of population structure

Increased demand for goods and service required by the youth and old ones because they form the large percentage of the population.

Implications of population structure

Increased demand for goods and service required by the youth and old ones because they form the large percentage of the population.

Implications of population structure

Increased demand for goods and service required by the youth and old ones because they form the large percentage of the population.

Implications of population structure

Increased demand for goods and service required by the youth and old ones because they form the large percentage of the population.

  • If the items required by the young and old ones re not produced locally, there will be increased importation and resultant stain on the balance of payment.

  • Low level of savings and investment because of the high dependency ratio.
  • Increased taxation and borrowing by government to meet increased demand for consumable items because the taxable population is small.

  • High prospective labour force because of the large proportion of young ones.
  • The current labour is low.

Example 7

The table shows the natural growth rate of the population of country N over a period of time. Use the information contained in the table to answer the following questions.

  • Determine L P QS and T
  • With the use of a bar chart graphically present the changes in the natural growth rate over the year. (use of graph sheet is essential)
  • Outline any three reasons for changes in birth rate.

Solution

  •  Early or late marriages. Early marriages increase birth rates while late marriages reduce it.
  • The higher the number of females in a population the higher the birth rate and vice versa.
  • Population control methods and campaigns can also reduce birth rates.
  • Improved medical facilities increase birth rates
  • Changes in traditional attitudes and beliefs of people to have large facilities can reduce birth rates.
  • Improved economic situations can affect birth rates particularly in developing societies

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