Question

Using suitable method of interpolation, estimate the sales (in lakhs) in 2004 from the following data.

| Year | 2001 | 2002 | 2003 | 2004 | 2005 | 2005 |
| Sales (in lakhs) | 150 | 235 | 365 | - | 525 | 780 |

Answer 1

Let x and y be the year and sales in lakhs.

There are five known values of y, so expand the Binominal expansion (y – 1)5 = 0

(y – 1)5 = y5 – 5y4 + 10y3 – 10y2 + 5y1 – y0 = 0,

780 – 5(525) + 10y3 – 10(365) + 5(235) – 150 = 0

780 – 2625 – 10y3 – 3650 + 1175- 150 = 0

y3 = 447 lakhs (sales).