Q56 / 90 · JEE Main 2013 (25 Apr Online) · Mathematics

In a set of $2 n$ observations, half of them are equal to ' $\mathrm{a}$ ' and the remaining hall are equal to ' $-\mathrm{a}^{\prime}$ '. If the standard deviation of all the observations is 2 ; then the value of $|a|$ is :

  • Correct answer
    A
    2
  • B
    $\sqrt{2}$
  • C
    4
  • D
    $2 \sqrt{2}$

Solution

Clearly mean $\mathrm{A}=0$ Now, standard deviation $\sigma=\sqrt{\frac{\Sigma(x-\mathrm{A})^2}{2 n}}$ $$ \begin{aligned} 2=& \sqrt{\frac{(a-0)^2+(a-0)^2+\ldots \ldots+(0-a)^2+\ldots . .}{2 n}} \\ &=\sqrt{\frac{a^2 \cdot 2 n}{2 n}}=|a| \end{aligned} $$ Hence, $|a|=2$

Hence, the correct answer is option: 'A'.

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