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 :

Question

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 :

Infinity Learn · Accepted Answer

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

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

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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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Ready to Test Your Skills?

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