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MHT CET202314 May 2023Evening ShiftMathematicsStatisticsActual

If both mean and variance of 50 observations x₁, x₂, , x₅₀ are equal to 16 and 256 respectively, then mean of (x₁-5 )^2, (x₂-5 )^2, , (x₅₀-5 )^2 is

Options

  1. A357
  2. B367
  3. C377
  4. D387

Correct answer

C. 377

Step-by-step solution

aligned & Mean = x_i n & 16= x_ i 50 & x_ i =800 & Variance = x_ i ^2 n -( x )^2 & 256= x_ i ^2 50 -(16)^2 & x_ i ^2 50 =512 & x_ i ^2=25600 & New mean = (x_ i -5 )^2 n & = x_ i ^2-10 x_ i + 25 50 & = 25600-10(800)+25(50) 50 & = 18850 50 & =377 & aligned

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