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Index Numbers — Economics STD 11 Commerce — Question

CBSE BoardEnglish MediumSTD 11 CommerceEconomicsIndex Numbers6 Marks
Question
Calculate weighted index number for 2018 by Weighted Aggregative Method and Weighted Average of Relative Method for the following data:
Item Weight Prices in 2017 Prices in 2018
A 10 100 161
B 7 200 210
C 15 50 60
D 9 20 30
E 10 10 14
✓

Answer

Item Weight $p_0$ $p_1$ $p_0W$ $p_1W$ $\text{R}=\frac{\text{p}_1}{\text{p}_0}\times100$ WR
A 10 100 161 1000 1610 161 1610
B 7 200 210 1400 1470 105 735
C 15 50 60 750 900 120 1800
D 9 20 30 180 270 150 1350
E 10 10 14 100 140 140 1400
  $\Sigma\text{W}=51$     $\Sigma\text{p}_0\text{W}=3430$ $\Sigma\text{p}_1\text{W}=4390$   $\Sigma\text{WR}=6895$
Weighted Aggregative Methode:
$\text{P}_{01}=\frac{\Sigma\text{p}_1\text{W}}{\Sigma\text{p}_0\text{W}}\times100=\frac{4390}{3430}\times100=127.98$
Weighted Average of Price Method:
$\text{p}_{01}=\frac{\Sigma\text{WR}}{\Sigma\text{W}}=\frac{6895}{51}=135.19$

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