Question

Calculate Quantity Index Numbers from the following data by simple aggregative method taking quantity of 2011 as base.

Commodity	Quantity (in tons)
	2011	2012	2013	2014	2015
A	0.30	0.33	0.36	0.36	0.39
B	0.25	0.24	0.30	0.32	0.30
C	0.20	0.25	0.28	0.32	0.30
D	2.00	2.40	2.50	2.50	2.60

[Quantity Index No. : 2012 = 117.1; 2013 = 125.1; 2014 = 127.3 ; 2015 = 130.5]

Answer 1

Commodity	Quantity in 2011 (q0)	Quantity in 2012 (q1)	Quantity in 2013 (q2)	Quantity in 2014 (q3)	Quantity in 2015 (q4)
A B C D	0.30 0.25 0.20 2.00	0.33 0.24 0.25 2.4	0.36 0.30 0.28 2.50	0.36 0.32 0.32 2.50	0.39 0.30 0.30 2.60
	∑ q0 = 2.75	∑ q1 = 3.22	∑ q2 = 3.44	∑ q3 = 3.5	∑ q4 = 3.59

$q_{01}=\frac{\mathrm{\Sigma }{q}_1}{\mathrm{\Sigma }{q}_0}\times 100=\frac{3.22}{2.75}\times 100=117.1$
Thus, quantity index for 2012 is 117.1.
$q_{02}=\frac{\mathrm{\Sigma }{q}_2}{\mathrm{\Sigma }{q}_0}\times 100=\frac{3.44}{2.75}\times 100=125.1$
Thus, quantity index for 2013 is 125.1.
$q_{03}=\frac{\mathrm{\Sigma }{q}_3}{\mathrm{\Sigma }{q}_0}\times 100=\frac{3.5}{2.75}\times 100=127.3$
Thus, quantity index for 2014 is 127.3.
$q_{04}=\frac{\mathrm{\Sigma }{q}_4}{\mathrm{\Sigma }{q}_0}\times 100=\frac{3.59}{2.75}\times 100=\frac{359}{2.75}=130.5$
Thus, quantity index for 2015 is 130.5.