Page 239 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Quantitative Techniques – I

Notes Solution:
Calculation Table

Year Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
2008 46 45 44 46 45 47 46 43 40 40 41 45
2009 45 44 43 46 46 45 47 42 43 42 43 44
2010 42 41 40 44 45 45 46 43 41 40 42 45
Total 133 130 127 136 136 137 139 128 124 122 126 134
A i 44.3 43.3 42.3 45.3 45.3 45.7 46.3 42.7 41.3 40.7 42.0 44.7
S.I. 101.4 99.1 96.8 103.7 103.7 104.6 105.9 97.7 94.5 93.1 96.1 102.3

In the above table, Ai denotes the average and S.I. the seasonal index for a particular month of
various years. To calculate the seasonal index, we compute grand average G, given by
A 524
G i 43.7 . Then the seasonal index for a particular month is given
12 12
A
by. . .S I i 100
G

Further, S.I. = 1198.9 1200 . Thus, we have to adjust these values such that their total is 1200.
1200
This can be done by multiplying each figure by . The resulting figures are the adjusted
1198.9
seasonal indices, as given below:

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
101.5 99.2 96.9 103.8 103.8 104.7 106.0 97.8 94.6 93.2 96.2 102.3

Remarks: The totals equal to 1200, in case of monthly indices and 400, in case of quarterly
indices, indicate that the ups and downs in the time series, due to seasons, neutralise themselves
within that year. It is because of this that the annual data are free from seasonal component.

Example: Compute the seasonal index from the following data by the method of simple
averages.

Year Quarter Y Year Quarter Y Year Quarter Y
2005 I 106 2007 I 90 2009 I 80
II 124 II 112 II 104
III 104 III 101 III 95
IV 90 IV 85 IV 83
2006 I 84 2008 I 76 2010 I 104
II 114 II 94 II 112
III 107 III 91 III 102
IV 88 IV 76 IV 84

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