Population Forecasting Methods-1

 

Population Forecasting Methods

The various methods adopted for estimating future populations are given below.

1.     Arithmetic Increase Method

2.     Geometric Increase Method

3.     Incremental Increase Method

4.     Decreasing Rate of Growth Method

5.     Simple Graphical Method

6.     Comparative Graphical Method

7.     Ratio Method

8.     Logistic Curve Method

9.     Master plan Method

Arithmetic Increase Method

This method is based on the assumption that the population increases at a constant rate.

This method is most applicable to large and established cities.

dP/dt=constant=k

where

Pn = Population after 'n' decades

Po = present Population

n = number of decades ( 1 decades=10 years)

X' = average increase in population.

Problem:-

The population of 5 decades from 1930 to 1970 are given below. Find the population after one, two, three decades. By using  Arithmetic Increase Method.

Year	1930	1940	1950	1960	1970
population	25000	28000	34000	42000	47000

Solution:-

year	population	Incresae in population
1930	25000	28000-25000=3000
1940	28000	34000-28000=6000
1950	34000	42000-34000=8000
1960	42000	47000-42000=5000
1970	47000
Total		3000+6000+8000+5000=22000
X' = average increase in population.		=22000/4 =5500

Now using Arithmetic Increase formula

P ₁₉₈₀  = 47000 + 1*5500=52500

P ₁₉₉₀   = 47000 + 2*5500=58000

P ₂₀₀₀ = 47000 + 3*5500=63500

Geometric Increase Method

This method is based on the assumption that percentage growth rate is constant.

this method is also known as uniform growth method.

where

P n = Population after 'n' decades

Po = present Population

n = number of decades ( 1 decades=10 years)

r = growth rate in %

The assumed growth rate is computed in several ways. some of the given below:-

Problem:-

The population of 5 decades from 1930 to 1970 are given below. Find the population after one, two, three decades. By using  Geometric Increase Method

Year	1930	1940	1950	1960	1970
population	25000	28000	34000	42000	47000

Solution:-

year	population	Increase in population	% Growth rate
1930	25000	28000-25000=3000	(3000/25000)*100 =12%
1940	28000	34000-28000=6000	(6000/28000)*100=21.4%
1950	34000	42000-34000=8000	(8000/34000)*100=23.5%
1960	42000	47000-42000=5000	(5000/42000)*100=11.9%
1970	47000

r= (12x21.4x23.5x11.9)^1/4

= 16.37%

Then using geometric increase formula

P ₁₉₈₀  = 47000(1+16.37/100)¹  =54694

P ₁₉₉₀ = 47000(1+16.37/100)²  =63647

P ₂₀₀₀ = 47000(1+16.37/100)³  =74066

Incremental Increase Method

Growth rate is assumed to be progressively increasing or decreasing, depending upon whether the average of the incremental increases in the past is positive or negative.

P n = Population after 'n' decades

Po = present Population

n = number of decades ( 1 decades=10 years)

X' = average increase in population.

Y' = Average of Incremental Increase

Problem:-

The population of 5 decades from 1930 to 1970 are given below. Find the population after one, two, three decades. By using  Incremental Increase Method

Year	1930	1940	1950	1960	1970
population	25000	28000	34000	42000	47000

Solution:-

year	population	Increase in population	Incremental increase
1930	25000	28000-25000=3000	6000-3000=3000
1940	28000	34000-28000=6000	8000-6000=2000
1950	34000	42000-34000=8000	5000-8000=-3000
1960	42000	47000-42000=5000
1970	47000
Total		3000+6000+8000 +5000=22000	3000+2000+(-3000)=+2000
X' =average increase in population.		=22000/4 =5500	Y' = Average of Incremental Increase =(2000/3)=+667

Then usuing Incremental Increase formula

P ₁₉₈₀  =47000+ 1*5500+1{(1+1)/2} *667 = 53167

P ₁₉₉₀ =47000+ 2*5500+1{(2+1)/2} *667 = 60001

P ₂₀₀₀  =47000+ 3*5500+1{(3+1)/2} *667 =67502

Decreasing Rate of Growth Method

In this method, the average decrease in the percentage increase is worked out, and is then subtracted from the latest percentage increase to get the percentage increase of next decade.

Problem:-

The population of 5 decades from 1930 to 1970 are given below. Find the population after one, two, three decades. By using  Decreasing Rate of Growth Method

Year	1930	1940	1950	1960	1970
population	25000	28000	34000	42000	47000

Solution:-

year	population	Increase in population	% Growth rate	% decrease
1930	25000	28000-25000=3000	(3000/25000)*100 =12%	12%-21.4%= -9.40%
1940	28000	34000-28000=6000	(6000/28000)*100=21.4%	21.4%-23.5%= -2.1
1950	34000	42000-34000=8000	(8000/34000)*100=23.5%	23.5%-11.9%= +11.6%
1960	42000	47000-42000=5000	(5000/42000)*100=11.9%
1970	47000
Total		22000		(-9.40+(-2.1)+11.6)%=0.1%
Average per decade				0.1%/3=0.03% Decrease

P ₁₉₈₀  = 47000 + {(11.9-0.03)/100} x 47000

          = 47000 + {11.87/100} x 47000 =52570

P ₁₉₉₀  = 52570 + {(11.87-0.03)/100} x 52570

          = 52570 + {11.84/100} x 47000 =58800

P ₂₀₀₀  = 58800 + {(11.84-0.03)/100} x 58800

          = 58800 + {11.81/100} x 58800 =65750