1.

Interpolate the index for 2008 from the following data.Year20062007200820092010Index No.278281-313322

Answer»

Let X and Y be the year and index no. From the data there are 4 known values of y are given, so expand the Binomial (y -1)4 = 0

i.e. y4 – 4y3 + 6y2 – 4y1 + y0 =0

322 – 4 × 313 + 6y2 = 4 × 281 +278 = 0

322 – 1252 + 6y2 – 1124 + 278 = 0

600 – 2376 + 6y2 = 0

-1776 + 6y2 = 0

∴ y2 = 1776/6 = 296.



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