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COMEDK20269 May 2026Morning ShiftMathematicsStatisticsActual

If for a distribution of 20 items, (x - 4) = 10 and (x - 4)^2 = 85 then the standard deviation is:

Options

  1. A1.41
  2. B2
  3. C4
  4. D4.25

Correct answer

B. 2

Step-by-step solution

Let y_i = x_i - 4 . Given n = 20 , y_i = 10 , and y_i^2 = 85 . The standard deviation of x is equal to the standard deviation of y since it is independent of the change of origin. Variance ^2 = y_i^2 n - ( y_i n )^2 ^2 = 85 20 - ( 10 20 )^2 ^2 = 4.25 - (0.5)^2 ^2 = 4.25 - 0.25 = 4 Standard deviation = 4 = 2 . Answer: 2

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