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Q.

The mean and the standard deviation (s.d.) of 10 observations are 20 and 2 respectively. Each of these 10 observations is multiplied by p and then reduced by q , where p≠0 and q≠0 . If the new mean and new s.d. become half of their original values, then q is equal to :

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a

10

b

-10

c

-20

d

-5

answer is C.

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Detailed Solution

If each observation is multiplied with p& then q is subtracted New mean x1¯=px¯-q ⇒10=p(20)-q ……(1)and new standard deviationsσ2=|p|σ1⇒1=|p|(2)⇒p=12⇒p=±12 If p=12 then q=0( from equation (1)) If p=-12, then q=-20

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