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MHT CET20228 Aug 2022Evening ShiftMathematicsStatisticsActual

If both mean and the standard deviation of 50 observations x₁, x₂, ., x₅₀ are equal to 16 , then mean of (x₁-5 )^2, (x₂-5 )^2, ., (x₅₀-5 )^2 is

Options

  1. A378
  2. B377
  3. C357
  4. D397

Correct answer

B. 377

Step-by-step solution

x =16 and S.D. =16 if we subtract 5 from each observations mean will become 16-5=11 and S.D. remains unchanged i.e., 16 aligned & (x_i-5 )^2 50 -11^2 =16 & (x_i-5 )^2 50 =256+121=377 aligned hence, the required mean is 377

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