Question

The price quotation of different commodities for 2011 and 2012 are given below. Calculate the index number for 2012 with 2011 as base year by using (i) Simple average of price relative and (ii) Weighted average of price relative

Answer 1

$\begin{array}{cccccc}\text{Commodity}& \text{W}& P_0& P_1& R=\frac{P_1}{P_0}\times 100& \text{RW}\\ A& 5& 2.00& 4.50& \frac{4.50}{2.0}\times 100=225& 1125\\ B& 7& 2.50& 3.20& \frac{3.20}{2.50}\times 100=128& 896\\ C& 6& 3.00& 3.50& \frac{3.50}{3.00}\times 100=116.67& 700.02\\ D& 2& 1.00& 1.80& \frac{1.80}{1.00}\times 100=180& 360.00\\ & \sum W=20& & & \sum (\frac{P_1}{P_0}\times 100)=649.67& \sum RW=3081.00\end{array}$

Simple average of price relative method:

$P_{01}=\frac{(\frac{P_1}{P_0}\times 100)}{N}=\frac{649.67}{4}=162.41$

Weighted average of price relative method:

$P_{01}=\frac{\sum RW}{\sum W}=\frac{3081.02}{20}=154.05$