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AP EAMCET2016MathematicsStatistics

The variance of the first 50 even natural numbers is

Options

  1. A833 4
  2. B833
  3. C437
  4. D437 4

Correct answer

B. 833

Step-by-step solution

Given, 50 even natural numbers are 2,4,6, .100 Mean, x = x i n = 2+4+6+ +98+100 50 aligned & x = 2(1+2+3+ +49+50) 50 & x = 2 50 51 2 50 =51 aligned Variance, ^2= x₁^2 n -( x )^2 aligned & = (2^2+4^2+6^2+ .+98^2+100^2 ) 50 -(51)^2 & = 2^2 (1^2+2^2+3^2+ .+49^2+50^2 )-(51)^2 50 50 & = 4(50)(51)(101)-(51) (51) 50 6 6 50 =833 aligned

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