Question

Using interpolation estimate the output of a factory in 1986 from the following data

Year	1974	1978	1982	1990
Output in 1000 tones	25	60	90	170

Answer 1

Let x denote the year and y represent the output. 

The x values are not equidistant. 

So we use Lagrange’s formula 

x₀ = 1974, y₀ = 25 

x₁ = 1978, y₁ = 60 

x₂ = 1982, y₂ = 80 

x₃ = 1990, y₃ = 170 

For x = 1986 we have to find y value

We find the different values separately and substitute in the formula.

y = 6.25 - 60 + 120 + 42.5

y = 108.75

The output of the factory in 1986 is 109 (thousand tonnes)