Suppose values taken by a variable x are such that a le {xᵢ} le b , where {xᵢ} denotes value of

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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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