Question:
For the frequency distribution:
Variate $(x): \quad x_{1} \quad x_{2} \quad x_{3} \ldots x_{15}$
Frequency $(f): \begin{array}{lll}f_{1} & f_{2} & f_{3} \ldots f_{15}\end{array}$
where $0
standard deviation cannot be :
Correct Option: , 3
Solution:
If variate varries from $a$ to $b$ then variance
$\operatorname{var}(x) \leq\left(\frac{b-a}{2}\right)^{2}$
$\Rightarrow \operatorname{var}(x)<\left(\frac{10-0}{2}\right)^{2}$
$\Rightarrow \operatorname{var}(x)<25$
$\Rightarrow$ standard deviation $<5$
It is clear that standard deviation cann't be 6 .
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