For the frequency distribution:
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 :

  1. 2

  2. 1

  3. 4

  4. 6


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.

$\therefore \quad \sigma^{2}<\frac{1}{4}(10-0)^{2}$

$\Rightarrow 0<\sigma<5$

$\therefore \sigma \neq 6$

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