If the mean of a data x ¯ is 10 and if all the observations are multiplied by 2 , then the mean of new data is

Step-by-step solution

Let x 1 ,   x 2 ,   x 3 ,   . . . . . . x n   be the observations ∴   Mean = x 1 + x 2 + x 3 + . . . . . + x n n ∴   10 = x 1 + x 2 + x 3 + . . . . . . + x n n . . . . . 1 Now when observations are multiplied by 2 ,   then new observations are 2 x 1 ,   2 x 2 ,   2 x 3 . . . . . . . ,   2 x n New mean = 2 x 1 + 2 x 2 + . . . . . + 2 x n n = 2 x 1 + x 2 + . . . . . + x n n = 2 × 10 = 20