Page 223 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Quantitative Techniques – I

Notes
Example: From the chain base index numbers given below, prepare fixed base index
numbers; (a) when 1975 is not the base year and (b) when 1975 is taken as base year.
Years : 2007 2008 2009 2010 2011
Index : 80 110 120 90 140
Solution:
Chain Base Index Fixed Base Index
×
Fixed Base Index of current year = of current year of previous year
100
Calculation of Fixed Base Index Numbers
F.B.I. F.B.I.
Years C.B.I.
1975 100 1975=100
2007 80
80 100
110×80 110×100
2008 110 =88 =110
100 100
120×88 120×110
2009 120 100 =105.6 100 =132
90×105.6 90×132
=95 =118.8
2010 90 100 100
140×95 140×118.8
=133 =166.32
2011 140 100 100

Some additional weighted index numbers
Notes

1. Walsh’s Index: Geometric mean of base and current year quantities are used as
weights in this index number.

p q q
Wa 1 0 1
P 100
01
p 0 q q
0 1
2. Kelly's Fixed Weights Aggregative Index: The weights, in this index number, are
quantities which may not necessarily relate to base or current year. The weights,
once decided, remain fixed for all periods. The main advantage of this index over
Laspeyres's index is that weights do not change with change of base year. Using
symbols, the Kelly's Index can be written as

p q
Ke 1
P 01 100
p q
0

!
Caution An index number can be computed by using a number of formulae and different
formulae will give different results. Unless a proper method is used, the results are likely
to be inaccurate and misleading.

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