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Q.

If 5 is subtracted from each observation, then the coefficient of variation is 10% and if 5 is added to each observation, then the coefficient of variation is 6%, then the coefficient of  variation of given observations is ______

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a

7.5%

b

4.5%

c

8%

d

4%

answer is C.

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Detailed Solution

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y=x5                 y¯=x¯5                sy=sx C.V. =sx×100    10=sx¯5×100      (1)y=x+5                        y¯=x¯+5               sy=sx C.V. =sx×100         6=sx¯+5×100         (2)
Divide equation (1) by (2),
53=x¯+5x¯5 5x¯25=3x¯+15  x¯=20
From (1), 10 =s15×100 s=1.5
The coefficient of variation V=sx¯×100=1.520×100=7.5%

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