Page 144 - DMGT404 RESEARCH_METHODOLOGY

Research Methodology

Notes n
 i X
X  i 1
n
(b) Shortcut Method: This method is used when the magnitude of individual observations
is large. The use of shortcut method is helpful in the simplification of calculation
work.
Let A be any assumed mean. We subtract A from every observation. The difference
between an observation and A, i.e., X – A is called the deviation of ith observation
i
from A and is denoted by d . Thus, we can write; d = X – A, d = X – A, ..... d = X –
i 1 1 2 2 n n
A. On adding these deviations and dividing by n we get
 i d  (X  A )  X i  nA  X i  A


i
n = n n n
  d i 
–
or d = X A  where d  
 n 
On rearranging, we get
 d
X = A d  A  i
n
This result can be used for the calculation of X .

Notes Theoretically we can select any value as assumed mean. However, for the purpose
of simplification of calculation work, the selected value should be as nearer to the value of
X as possible.

Example: The following figures relate to monthly output of cloth of a factory in a given
year:

Months Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Output 80 88 92 84 96 92 96 100 92 94 98 86
(in ’000 metres)

Calculate the average monthly output.
Solution:
(a) Using Direct Method:












80 88 92 84 96 92 96 100 92 94 98 96
X =
12
= 91.5 (‘000 mtrs)
(b) Using Shortcut Method:
Let A = 90.
X 80 88 92 84 96 92 96 100 92 94 98 86 Total
i
d = X – A –10 –2 2 –6 6 2 6 10 2 4 8 –4 d = 18
i
i
i

18
X = 90 
12
= 90 + 1.5 = 91.5 thousand mtrs
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