Mean of N numbers is X̅, the new mean when each number is multiplied by k is

Concept use:

Mean of Numbers = sum of observation/Total no of observation.

Calculations:

Mean of N numbers is X̅ 

Let the numbers are x_1, x₂, ........, x_n 

⇒ Mean = x1 + x2 +  ........ + xn / n = X̅      ------(1)

If each number is multiplied by k then the numbers are kx1, kx2, ........, kxn 

⇒ new Mean = kx1 +  kx2 + ........+ kxn / n = k(x1 + x2 +  ........ + xn / n) = kX̅     from (1)

Hence, The Correct Answer is kX̅.