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

Answer 1

The correct option is C

2

Clearly, mean, A=0
Standard deviation, $\sigma =\sqrt{\frac{\sum (x-A{)}^2}{2n}}$
$2=\sqrt{\frac{(a-0{)}^2+(a-0{)}^2+.....(0-a{)}^2+....}{2n}}=\sqrt{\frac{a^2.2n}{2n}}=|a|$