Multiple choice

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

  1. $\cfrac { \sqrt { 2 } }{ n } $
  2. ${ \sqrt { 2 } }$
  3. $2$
  4. $\cfrac { 1 }{ n }$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Observations: n of 'a' and n of '-a'. Mean = (n*a + n*(-a)) / 2n = 0. Variance = sum(x_i^2) / 2n - mean^2 = (n*a^2 + n*(-a)^2) / 2n = 2n*a^2 / 2n = a^2. Standard deviation = sqrt(a^2) = |a|. Given SD = 2, so |a| = 2.

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