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

Answer: (A)

2

Answer 2

Here, mean $= \frac{na + n(-a)}{2n }= 0$ Hence variance $= \frac{na^2 + n(-a)^2}{2n} - (mean)^2$ $\Rightarrow \, 2 = a^2 - 0^2 \, \Rightarrow \, a^2 = 2$