Question

Construct index numbers of the following data by Fisher's Method:

Commodity	Base Year		Current Year
	Price	Value	Price	Value
A B C D E	3 5 6 4 8	18 35 42 32 24	7 10 11 6 9	10 100 55 60 36

Answer 1

	P0	Value (Base Year)	$q_0=\frac{Value}{P_0}$	P0q0	P1	Value (Current Year)	$q_1=\frac{\mathrm{Value}}{P_1}$	P1q1	P1q0	P0q1
A B C D E	3 5 6 4 8	18 35 42 32 24	6 7 7 8 3	18 35 42 32 24	7 10 11 6 9	14 100 55 60 36	2 10 5 10 4	14 100 55 60 36	42 70 77 48 27	6 50 30 40 32
		151		$\Sigma P_0{q}_0=151$				$\Sigma P_1{q}_1=265$	$\Sigma P_1{q}_0=264$	$\Sigma P_0{q}_1=158$

Fisher's Price Index

$$\begin{gathered} {\mathrm{P}}_{01}=\sqrt{\frac{\Sigma P_1{q}_0}{\Sigma P_0{q}_0}\times \frac{\Sigma P_1{q}_1}{\Sigma P_0{q}_0}}\times 100 \\ or,{\mathrm{P}}_{01}=\sqrt{\frac{264}{151}\times \frac{265}{158}}\times 100=171.24 \end{gathered}$$