The variance of first 50 even natural numbers
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Start by taking a mean of first 50 even natural numbers
μ= 2 + 4 + 6 + 8..... + 100/ 50
= 51
sum of the squares of natural numbers = ∑x² = 2² + 4² + 6².....
= 4 x 50 x 51 x 101/ 6
now apply the formula of variance
= ∑x²/ n - μ²
= 4 x 50 x 51 x 101/ 6 divide 50 x 51²
= 2 x 17 x 101 - 2601
= 3434 - 2601
= 833
μ= 2 + 4 + 6 + 8..... + 100/ 50
= 51
sum of the squares of natural numbers = ∑x² = 2² + 4² + 6².....
= 4 x 50 x 51 x 101/ 6
now apply the formula of variance
= ∑x²/ n - μ²
= 4 x 50 x 51 x 101/ 6 divide 50 x 51²
= 2 x 17 x 101 - 2601
= 3434 - 2601
= 833
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