Question

For the frequency distribution :

Variate (x) :	$x_{1}$	$x_{2}$	$x_{3} ...x_{15}$
Frequency (f) :	$f_{1}$	$f_{2}$	$f_{3}...f_{15}$

where $0< x _{1}< x _{2}< x _{3}<\ldots< x _{15}=10$ and $\displaystyle\sum_{i=1}^{15} f_{i}>0,$ the standard deviation cannot be :

• A. 2
• B. 1
• C. 4
• D. 6

Answer 1

Answer: (D)

$\because \sigma^{2} \leq \frac{1}{4}( M - m )^{2}$
Where $M$ and $m$ are upper and lower bounds
of values of any random variable.
$\therefore \sigma^{2} < \frac{1}{4}(10-0)^{2}$
$\Rightarrow 0 < \sigma < 5$
$\therefore \sigma \neq 6$.