1)

 The variance of first 50 even natural numbers is 


A) $\frac{833}{4}$

B) 833

C) 437

D) $\frac{437}{4}$

Answer:

Option B

Explanation:

Here,   $\overline{X}=\frac{\sum    X_{i}}{n}$

                       =$\frac{2+4+6+8+...+100}{50}=\frac{50 \times 51}{50}=51$

                                                      [ $\because \sum{}2n=n(n+1), $  , here n=50]

 Variance  ,    $\sigma^{2} =\frac{1}{n}\sum{}Xi^{2}-(\overline{x})^{-2}$

   $\sigma^{2} =\frac{1}{50}(2^{2}+4^{2}+....+100^{2})-(51)^{2}=833$