QJEEM20Ma8c0c: JEE Main 2020 Mathematics - Class 11 JEEM20Ma8c0c Solution: For the frequency distribution : Variate (x) :…

Question

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For the frequency distribution :
Variate (x) : x₁ x₂ x₃ .... x₁₅
Frequency (f) : f₁ f₂ f₃ ...... f₁₅
where 0 < x₁ < x₂ < x₃ < ... < x₁₅ = 10 and

\sum_{i = 1}^{15} f_{i}

> 0, the standard deviation cannot be :

Accepted Answer

If variate varries from m to M then variance

σ^{2} \leq \frac{1}{4} {(M - m)}^{2}

(M = upper bound of value of any random variable,

m = Lower bound of value of any random variable)

Here M = 10 and m = 0

∴

σ^{2} \leq \frac{1}{4} {(10 - 0)}^{2}

\Rightarrow

σ^{2} \leq 25

\Rightarrow

- 5 \leq σ \leq 5

∴

σ

\neq

6

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