AP EAMCET202422 May 2024Morning ShiftMathematicsStatisticsActual

If x₁, x₂, x₃ x_n are n observations such that (x_i+2 )^2=28 n and (x_i-2 )^2=12 n , then the variance is:

Options

Correct answer

A. 12

Step-by-step solution

aligned & Given that (x_i+2 )^2=28 n & x_i^2+4 x_i+4 n=28 n & x_i^2+4 x_i=24 n ....(i) aligned Similarly (x_i-2 )^2=12 n x_i^2-4 x_i=8 n On solving equation (i) and (ii), we get x_i^2=16 n and x_i=2 n Variance = x_i^2 n - ( x_i n )^2= 16 n n - ( 2 n n )^2=16-4=12

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