Question:
For the frequency distribution:
Variate $(\mathrm{x}): \quad \mathrm{x}_{1} \quad \mathrm{x}_{2} \quad \mathrm{x}_{3} \ldots \ldots \mathrm{x}_{15}$
Frequency (f) : $\quad \mathrm{f}_{1} \quad \mathrm{f}_{2} \quad \mathrm{f}_{3} \ldots . \mathrm{f}_{15}$
where $0<\mathrm{x}_{1}<\mathrm{x}_{2}<\mathrm{x}_{3}<\ldots .<\mathrm{x}_{15}=10$ and
$\sum_{i=1}^{15} f_{i}>0$, the standard deviation cannot be :
Correct Option: , 4
Solution:
$\because \sigma^{2} \leq \frac{1}{4}(\mathrm{M}-\mathrm{m})^{2}$
Where $\mathrm{M}$ and $\mathrm{m}$ are upper and lower bounds of values of any random variable.
$\therefore \quad \sigma^{2}<\frac{1}{4}(10-0)^{2}$
$\Rightarrow 0<\sigma<5$
$\therefore \sigma \neq 6$