Arithmetic Increase Method of Population Forecast

Arithmetic increase method for population forecast is the simplest method amongst the methods of population forecasting.

Arithmetic Increase Method Concept

Arithmetical increase method of predicting population gives lower values of population generally. This method of population forecast is analogous to simple interest calculations.

In arithmetic increase method, the population is forecasted by taking into consideration the population of last 3-4 decades.

Average increase in population from the past decades is calculated first in this method. To find the population of the next decade, the average increase from the past decades is added to the present population.

Assumption used in arithmetic increase method

“The rate of increase in population from decade to decade is constant.”

In other words, population is increasing at a constant rate.

Where Arithmetic Increase Method is Used?

Arithmetical increase method of predicting population is suitable for population forecasting of large cities which have achieved the saturation point in their population growth.

This means,

• For old and developed towns, where the population growth rate is constant as the population is saturated.
• Hence, the assumption above for this method that increase is constant is valid in this case.

Arithmetic Increase Method Formula

Pn = Population (predicted) after n number of decades from the decade of last known population

P = last known population

n = number of decades between P & Pn

Arithmetic Increase Method Derivation

As said above, rate of change of population with time is assumed to be constant.

In the above equation, suffix 1 represents last decade while suffix 2 represents first decade.

Hence,

From the population data of last 4-5 decades, population increase per decade is calculated.

The average population growth is taken as the design growth rate for calculating the future population. (As mentioned earlier in this article, this growth rate is assumed constant in this method.)

Population after 2 decades:

In this way, the formula to calculate population after n years will be:

In the above formula,

P_n = Population after n decades from present

P₀ = Population at present, or, last known population

n = number of decades between present and future

= Arithmetic average of population increase in the known decades

Steps to do Arithmetical Increase Method

1. Find increment in population in each decade from the census data of the past 3-4 decades.
2. Find the average increment (I) per decade by taking average of increments from each of the given decades.
3. Calculate the number of decades (n) between the last decade where the census data is available and the current year (P) for which the population is to be forecasted.
4. Now, fill in the values in the above formula to calculate the population.

Arithmetic Increase Method Example

Find the population of Delhi, India for the year 2021 from the population census data:

Year	1971	1981	1991	2001	2011
Population	40,65,698	62,20,406	94,20,644	1,38,50,507	1,67,87,941

Step-1: Given Data-

Population of last decade (2011) P = 1,67,87,941

Number of decades n = 2021-2011/10 = 1

Step-2: Find average increase per decade = I

Year	Population	Increment per Decade (I)
1971	40,65,698	–
1981	62,20,406	21,54,708
1991	94,20,644	32,00,238
2001	1,38,50,507	44,29,863
2011	1,67,87,941	29,37,434
Average increase per decade =		1,27,22,243/4 =31,80,560.75 = 31,80,561

Step-     3: Calculate Pn from the formula

Pn = P + nI        

= 1,67,87,941 + (1)(I)

= 1,67,87,941 + (1)( 31,80,561)

= 19,96,8,502

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