If all the natural numbers between 1 and 20 are multiplied by 3 , then what is the variance of the resulting series ?

Step-by-step solution

The series is 1,2,3, 20 Variance ( )= x^2 n - ( x )^2 aligned & = n(n+1)(2 n+1) 6 n - ( n(n+1) 2 n )^2 & = ( n +1) 12 ( n -1) & = n^2-1 12 = (20)^2-1 12 = 399 12 = 133 4 =33.25 aligned Numbers are multiplied by 3 , variance ( )=33.25 9=299.25