Question

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

• A. 2
• B. $\sqrt{2}$
• C. $\frac{1}{n}$
• D. $\frac{\sqrt{2}}{n}$

Answer 1

The correct option is A 2

$Here{x}_1=x_2=......x_n=a{x}_n-1=x_n=......x_{2n}=-a\therefore mean\overline{x}=02=S.D.=\sqrt{\frac{\sum (x-{\overline{x}}^2)}{2n}}=\sqrt{\frac{\sum x^2}{2n}-{\overline{x}}^2}=\sqrt{\frac{\sum x^2}{2n}}=\sqrt{\frac{2n{a}^2}{2n}}=|a|\therefore |a|=2$