Page 99 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Quantitative Techniques – I

Notes Short-cut Method
This method is used when the magnitude of individual observations is large. The use of short-
cut 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 i observation from A and is denoted by
th
i
d . Thus, we can write ; d = X – A, d = X – A, ..... d = X – A. On adding these deviations and
i 1 1 2 2 n n
dividing by n we get
d i X i A X i nA X i
A
n n n n
d i
or d X A (Where d )
n

d i
On rearranging, we get X A d A
n
This result can be used for the calculation of X

Remarks: 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:
:
:
000
Calculate the average monthly output.
Solution:

1. Using Direct Method
80 +88 +92 +84 +96 +92 +96 +100 +92 +94 +98+86
X =
12
= 91.5 (‘000 mtrs)
2. Using Short-cut Method
Let A = 90.

X 80 88 92 84 96 92 96 100 92 94 98 86 Total
i
d i X i A 10 2 2 6 6 2 6 10 2 4 8 4 d i 18
18
X = 90 + = 90 + 1.5 = 91.5 thousand mtrs
12

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