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13.Statistics
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Suppose values taken by a variable $x$ are such that $a \le {x_i} \le b$, where ${x_i}$ denotes the value of $x$ in the $i^{th}$ case for $i = 1, 2, ...n.$ Then..
A
$a \le {\rm{Var}}(x) \le b$
B
${a^2} \le {\rm{Var}}(x) \le {b^2}$
C
$\frac{{{a^2}}}{4} \le {\rm{Var}}(x)$
D
${(b - a)^2} \ge {\rm{Var}}(x)$
Solution
(d) Since $S.D.$ $ \le $ Range = $b -a.$
$ Var$ $(x) \le {(b – a)^2}$ or ${(b – a)^2} \ge $$Var$ $(x).$
Standard 11
Mathematics
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