Question

Construct Index Number for each year from the following average annual wholesale prices of cotton with 2001 as base .

Year	Wholesale Prices (in ₹)	Year	Wholesale Prices (in ₹)
2001	75	2006	70
2002	50	2007	69
2003	65	2008	75
2004	60	2009	84
2005	72	2010	80

Answer 1

Prices in 2001 (p0)	Prices in 2002 (p1)	Prices in 2003 (p2)	Prices in 2004 (p3)	Prices in 2005 (p4)	Prices in 2006 (p5)	Prices in 2007 (p6)	Prices in 2008 (p7)	Prices in 2009 (p8)	Prices in 2010 (p9)
75	50	65	60	72	70	69	75	84	80

$$\begin{gathered} p_{01}=\frac{\mathrm{\Sigma }{p}_1}{\mathrm{\Sigma }{p}_0}\times 100=\frac{50}{75}\times 100=66.67 \\ {p}_{02}=\frac{\mathrm{\Sigma }{p}_2}{\mathrm{\Sigma }{p}_0}\times 100=\frac{65}{75}\times 100=86.67 \\ {p}_{03}=\frac{\mathrm{\Sigma }{p}_3}{\mathrm{\Sigma }{p}_0}\times 100=\frac{60}{75}\times 100=80 \\ {p}_{04}=\frac{\mathrm{\Sigma }{p}_4}{\mathrm{\Sigma }{p}_0}\times 100=\frac{72}{75}\times 100=96 \\ {p}_{05}=\frac{\mathrm{\Sigma }{p}_5}{\mathrm{\Sigma }{p}_0}\times 100=\frac{70}{75}\times 100=93.33 \\ {p}_{06}=\frac{\mathrm{\Sigma }{p}_6}{\mathrm{\Sigma }{p}_0}\times 100=\frac{69}{75}\times 100=92 \\ {p}_{07}=\frac{\mathrm{\Sigma }{p}_7}{\mathrm{\Sigma }{p}_0}\times 100=\frac{75}{75}\times 100=100 \\ {p}_{08}=\frac{\mathrm{\Sigma }{p}_8}{\mathrm{\Sigma }{p}_0}\times 100=\frac{84}{75}\times 100=112 \\ {p}_{09}=\frac{\mathrm{\Sigma }{p}_9}{\mathrm{\Sigma }{p}_0}\times 100=\frac{80}{75}\times 100=106.67 \end{gathered}$$