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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 2015 as the base:
  1. Simple Aggregative Price Index.
  2. Index of Average of Price Relatives.
Items
A
B
C
D
E
Prices ₹ (2015)
6
2
4
10
8
Prices ₹ (2016)
10
2
6
12
12
Prices ₹ (2017)
15
3
8
14
16
✓

Answer

Items
$p_0$
$p_1$
$p_2$
$\frac{\text{p}_1}{\text{p}_0}\times100$
$\frac{\text{p}_2}{\text{p}_0}\times100$
A
6
10
15
166.66
250
B
2
2
3
1000.00
150
C
4
6
8
150.00
200
D
10
12
14
120.00
140
E
8
12
16
150.00
200
 
$\Sigma\text{p}_0=30$
$\Sigma\text{p}_1=42$
$\Sigma\text{p}_2=56$
$\Sigma\Big(\frac{\text{p}_1}{\text{p}_0}\times100\Big)=686.66$
$\Sigma\Big(\frac{\text{p}_2}{\text{p}_0}\times100\Big)=940$
  1. Simple Aggregative Price Index:
$\text{p}_{01}=\frac{\Sigma\text{p}_1}{\Sigma\text{p}_0}\times100$

$=\frac{42}{30}\times100=140$ (For 2016)

$\text{p}_{02}=\frac{\Sigma\text{p}_2}{\Sigma\text{p}_0}\times100$

$=\frac{56}{30}\times100=186.66$ (For 2017)
  1. Index of Average of price Relatives:
$\text{P}_{01}=\frac{\Sigma\Big(\frac{\text{p}_1}{\text{p}_0}\times100\Big)}{\text{N}}=\frac{686.66}{5}=137.33$

$\text{P}_{02}=\frac{\Sigma\Big(\frac{\text{p}_2}{\text{p}_0}\times100\Big)}{\text{N}}=\frac{940}{5}=188$

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