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Question: Suppose values taken by a variable x are such that \(a \leq x_{i} \leq b\), where \(x_{i}\) denotes ...

Suppose values taken by a variable x are such that a≤xi≤ba \leq x_{i} \leq b, where xix_{i} denotes the value of x in the ith case for i = 1, 2, n. Then

A

a≤Var(x)≤ba \leq \text{Var}(x) \leq b

B

a2≤Var(x)≤b2a^{2} \leq \text{Var}(x) \leq b^{2}

C

a24≤Var(x)\frac{a^{2}}{4} \leq \text{Var}(x)

D

(b−a)2≥Var(x)(b - a)^{2} \geq \text{Var}(x)

Answer

(b−a)2≥Var(x)(b - a)^{2} \geq \text{Var}(x)

Explanation

Solution

Since S.D. ≤\leq Range = b – a

∴ Var (x)≤(b−a)2(x) \leq (b - a)^{2} or (b−a)2≥(b - a)^{2} \geqVar (x).