Question

The population of a city in a census taken once in 10 years is given below.

Year	1951	1961	1971	1981
Population in lakhs	35	42	58	84

Estimate the population in the year 1955.

Answer 1

x	1951	1961	1971	1981
y	35	42	58	84

Let ‘x’ denote the year of the census. 

Let ‘y’ represent the population in lakhs. 

We have to find the population in the year 1955 (i.e) the value of y when x = 1955. 

Since the value of y is required near the beginning of the table, 

we use Newton’s forward interpolation formula.

Thus the estimated population in the year 1955 is 36.784 lakhs