Question

The variance of first 49 natural numbers

Answer 1

Given :  first 49 natural numbers

To Find : Variance of   first 49 natural numbers

Solution:

Variance of   first n natural numbers   =  (n + 1)(n - 1) /12

n = 49

Variance  = (49 + 1) (49 - 1) /12

= 50 * 48 / 12

= 50 * 4

= 200

Variance = 200

Variance of   first n natural numbers   =  (n + 1)(n - 1) /12 can be found using

Variance = ( ∑n² ) / n  -  ((∑n) / n)²  

= n(n + 1)(2n +1)/6n   -   (n (n + 1) /2n)²

 (n + 1)(n - 1) /12

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Answer 2

Answer:

$\huge \sf variance \: = \: 200$