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, - 5, 10, - 20, - 10

MARKS App · Accepted Answer

If each observation is multiplied with p & then q is subtracted, then New mean x - 1 = p x - - q ⇒ 10 = p 20 - q . . . . . 1 and new standard deviation σ 2 = p σ 1 ⇒ 1 = p 2 ⇒ p = 1 2 ⇒ p = ± 1 2 If p = 1 2 then q = 0 (from equation (1)) If p = - 1 2 q = - 20

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