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Index Numbers — Economics STD 11 Commerce — Question

CBSE BoardEnglish MediumSTD 11 CommerceEconomicsIndex Numbers6 Marks
Question
Construct the following indices by taking 2014 as the base year
  1. Simple Aggregative Price Index.
  2. Index of Average of Price Relative.
Item
A
B
C
D
E
Price in 2014 (₹)
6
2
4
10
8
Price in 2015 (₹)
10
2
6
12
12
Price in 2016 (₹)
15
3
8
14
 16
✓

Answer

Construction of Index number:
Item
Price in 2014 (₹)
Price in 2015 (₹)
Price in 2016 (₹)
$\text{I}\bigg(\frac{\text{p}_1}{\text{p}_0}\times100\bigg)$
$\text{I}_2\bigg(\frac{\text{p}_2}{\text{p}_0}\times100\bigg)$
A
6
10
15
166.67
250
B
2
2
3
100.00
150
C
4
6
8
150.00
200
D
10
12
12
120.00
140
E
8
12
16
150.00
200
n = 5
$\Sigma\text{p}_0=30$
$\Sigma\text{p}_1=42$
$\Sigma\text{p}_2=56$
$\Sigma\text{I} _1=686.67$
$\Sigma\text{I}_2=940$
  1. Simple Aggregative Price Index:
$\text{P}_{01}=\frac{\Sigma\text{p}_1}{\Sigma\text{p}_0}\times100=\frac{42}{30}\times100=140(\text{for 2015}),$

$\text{p}_{02}=\frac{\Sigma\text{p}_2}{\Sigma\text{p}_0}\times100=\frac{56}{30}\times100=186.67(\text{for 2016})$
  1. Index of Avrege of Price Relative:
$\text{p}_{01}=\frac{\Sigma\text{I}_1}{\text{n}} =\frac{686.67}{5}=137.34(\text{for 2015}),$

$\text{p}_{02}=\frac{\Sigma\text{I}_2}{\text{n}}=\frac{940}{5}=188(\text{for 2016})$

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