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

Step-by-step solution

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