Page 250 - DMGT404 RESEARCH_METHODOLOGY

Research Methodology

Notes é å logQ ù
Q = Antilog ê ú
(b) Taking G.M. 01
ê ë n ú û
3. Weighted aggregative index
La å q p
1
(a) Q 01 = å q p 0 0 ´ 100 (base year prices are taken as weights)
0
Pa å q p
1
(b) Q 01 = å q p 1 1 ´ 100 (current year prices are taken as weights)
0
å q p 0 å q p
Q = 1 ´ 1 1 ´ 100
Fi
(c) 01 å q p 0 å q p 1 Other aggregative formulae can also be written in a
0
0
similar way.
4. Weighted average of quantity relatives
å Qw
(a) Taking A.M. Q =
å w
01
é å wlogQù
(b) Taking G.M. Q = Antilog ê ê ë å w ú ú û
01
Like weighted average of price relatives, values are taken as weights.

Example: Using Fisher's formula, the quantity index number from the following data:

1974 1976
Article
Price (Rs) Value (Rs) Price (Rs) Value (Rs)
A 5 50 4 48
B 8 48 7 49
C 6 18 5 20

Solution:
Calculation Table

1974 1976
Article V V p q p q
p 0 V 0 q = p 0 p 1 V 1 q = p 1 0 1 1 0
0
1
0 1

A 5 50 1 0 4 48 12 60 40
B 8 48 6 7 49 7 56 42
C 6 18 3 5 20 4 24 15
Total å p q = 116 å p q = 117 140 97
1
0
0
1
å q p 0 å q p 140 117
Q = 1 ´ 1 1 ´ 100 = ´ = 120.65
Fi
å q p 0 å q p 1 116 97
01
0
0
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