The mean and the standard deviation 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 standard deviation (s.d.) become half of the original values, then q is equal to

Step-by-step solution

Mean =20 and SD =2, n =10 If each observation is multiplied by p and then reduced by q. New Mean = x ₁= p x - q aligned & 10=p(20)-q & 20 p-q=10 ...(i) aligned New SD = ₁=| p | Squaring on both sides, aligned & 1= p ^2 4 & p ^2= 1 4 & p = 1 2 aligned From (i) When, p = -1 2 , q =-20 When, p = 1 2 , q =0