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. 2.00
• B. 02
• C. 2.0
• D. 2

Answer 1

Answer: (A), (B), (C), (D)

Number of observations $=2n$
And observations are
$a,a,\dots ,n$ times, $-a,-a,\dots ,n$ times
Here
$\overline{x}=\frac{na+(-na)}{2n}=0$
$\because S.D.=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{N}}=\sqrt{\frac{\sum x_i^2}{2n}}(\because \overline{x}=0)$
$\Rightarrow 2=\sqrt{\frac{2n{a}^2}{2n}}=|a|(\because S.D.=2)$