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)