Question

From the following data interpolate the production of cement in 2007.

Answer 1

Let X and Y be the year and production

Using Binomial expansion method We have to estimate y₂ Since there are 5 known values of y, the formula of estimation is, the expansion of (y-1)⁵ = 0 We get the equation,

Y₅ – 5y₄+ 10y₃ – 10y₂+ 5y₁ – y₀ = 0.

Substituting the known values in the equation we obtain,

290 – 5(210)+ 10 x 160 – 10y₂+ 5(90) – 44 =0

290 – 1050+ 1600 – 10y₂ + 450 – 44 =0

-10y₂ – 1246 = 0

– 10y₂ =1246.

∴ y₂ = \(\frac{1246}{10}\) 

⇒ y₂ = 127 is 124.6.