Question

From the following data, construct a weighted index number for 2011 with 2000 as base year.

$\begin{array}{cccc}\text{Items}& \text{Weight}& \underset{2000}{\text{Prices}}& \underset{2011}{\text{Prices}}\\ \text{Wheat}& 15& 10& 15\\ \text{Rice}& 10& 8& 16\\ \text{Pulses}& 5& 5& 10\\ \text{Milk}& 4& 2& 4\\ \text{Oil}& 6& 4& 6\\ \text{Sugar}& 7& 3& 6\\ \text{Salt}& 3& 1& 2\end{array}$

Answer 1

$\begin{array}{cccccc}\text{Items}& \underset{\left(W\right)}{Weight}& \underset{P_0\left(2000\right)}{\text{Prices}}& \underset{P_1\left(2011\right)}{\text{Prices}}& R=\frac{P_1}{P_0}\times 100& \text{RW}\\ \text{Wheat}& 15& 10& 15& \frac{15}{10}\times 100=150& 2250\\ \text{Rice}& 10& 8& 16& \frac{16}{8}\times 100=200& 2000\\ \text{Pulses}& 5& 5& 10& \frac{10}{5}\times 100=200& 1000\\ \text{Milk}& 4& 2& 4& \frac{4}{2}\times 100=200& 800\\ \text{Oil}& 6& 4& 6& \frac{6}{4}\times 100=150& 900\\ \text{Sugar}& 7& 3& 6& \frac{6}{3}\times 100=200& 1400\\ \text{Salt}& 3& 1& 2& \frac{2}{1}\times 100=200& 600\\ & \sum W=50& & & & \sum RW=8950\end{array}$

$P_{01}=\frac{\sum RW}{\sum W}=\frac{8950}{50}=179$.