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In a series of 2 n observations, half of them equal a and remaining half equal -a . If the standard deviation of the observations is 2 , then |a| equals

Options

  1. A1 n
  2. B2
  3. C2
  4. D2 n

Correct answer

C. 2

Step-by-step solution

x_i=a for i=1,2, , n and x_i=-a for i=n, ., 2 n S.D. = 1 2 n _ i=1 ^ 2 n (x_i- x )^2 2= 1 2 n _ i=1 ^ 2 n x_i^2 ( . Since . _ i=1 ^ 2 n x_i=0 ) 2= 1 2 n 2 n a^2 |a|=2

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