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The variance of the first 50 even natural numbers is :

Options

  1. A4 3 7
  2. B4 3 7 4
  3. C8 3 3 4
  4. D8 3 3

Correct answer

D. 8 3 3

Step-by-step solution

Variance of a set of n numbers x 1 ,   x 2   . . . x i ,   . . . x n is given σ 2 = 1 n Σ i = 1 n x i - x ¯ 2 , where x ¯ is the average of the numbers. We want the variance of 2 ,   4 ,   6 ,   8   . . . . .   48 ,   50 ,   52 ,   . . . . .   98 ,   100 Here x ¯ = 51 . x i - x ¯ will be symmetric about 51 , ∴ σ 2 = 2 50 1 2 + 3 2 + 5 2 + . ..  49 2 Now, 1 2   +   3 2   +   5 2   +

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