The mean of a set of 30 observation is 75 . If each observations is multiplied by non-zero number λ and then each of them is decreased by 25 , their mean remains the same. Then, λ is equal to :

Step-by-step solution

Let 30 observations be x 1 ,     x 2 ,   . . . . . … ,   x 30 . Given mean = 75 ⇒ x 1 +   x 2 + … + x 30 = 75 × 30 Now according to question, λ ( x 1 +   x 2 + … + x 30 ) - 25 × 30 30 = 75 × 30 30 ⇒ λ 75 × 30 = 100 × 30 ⇒ λ = 4 3