If the variance of 1,2,3,4,5, ,10 is 99/2 then prove that standard deviation of 3,6,9,12 30 is (3√33)/2 - Maths - Statistics

Question

If the variance of 1,2,3,4,5,…,10 is 99/2 then prove that
standard deviation of 3,6,9,12………30 is
(3√33)/2

Manbar Singh · Accepted Answer

We have :variance of 1,2,3,4,5
,10 = 992Now, when each of the given observations is multiplied by 3, then resulting new observations are :3,6,9,12,15,
30 Now, variance of 3,6,9,12,15,
30 = 32×variance of 1,2,3,4,5
,10 = 9 × 992Now, SD of 3,6,9,12,15,
30 = variance of 3,6,9,12,15,
30 = 9×992 = 3×3×3×3×112 = 9112

If the variance of 1,2,3,4,5,…,10 is 99/2 then prove that standard deviation of 3,6,9,12………30 is (3√33)/2