The variance of first 20 natural numbers is

Question

The variance of first 20 natural numbers is (A) (399/2)  (B) (379/12)  (C) (133/2)  (D) (133/4)

Tardigrade Admin · Accepted Answer

Since, variance of first n natural number is ( S.D.)2=(n2-1/12) ∴ Variance of first 20 natural number is (S.D.)2 =((20)2-1/12) =(400-1/12) =(399/12)=(133/4)

Q. The variance of first 20 natural numbers is

$\frac{399}{2}$

$\frac{379}{12}$

$\frac{133}{2}$

$\frac{133}{4}$

$\frac{169}{2}$

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

Q. The variance of first 20 natural numbers is

2399​

12379​

2133​

4133​

2169​