Q. If a variable $x$ takes values $x_{i}$ such that $a \leq x_{i} \leq b$, for $i = 1,\ 2,\ \ldots n$, then
A) $a^{2} \leq var(x) \leq b^{2}$
B) $a \leq var(x) \leq b$
C) $\frac{a^{2}}{4} \leq var(x)$
D) $(b - a)^{2} \geq var(x)$
Explanation
(d)
Since, $SD < Range$
$\Rightarrow \ \sigma \leq (b - a)$
$\Rightarrow \ \sigma^{2} \leq (b - a)^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.