Question

The variance of first 20 natural numbers is

• A. $\frac{399}{2} $
• B. $\frac{379}{12} $
• C. $\frac{133}{2} $
• D. $\frac{133}{4} $
• E. $\frac{169}{2} $

Answer 1

Answer: (D)

Since, variance of first $n$ natural number is
$( S.D.)^{2}=\frac{n^{2}-1}{12}$
$\therefore $ Variance of first 20 natural number is
$(S.D.)^{2} =\frac{(20)^{2}-1}{12}$
$=\frac{400-1}{12}$
$=\frac{399}{12}=\frac{133}{4}$