For the frequency distribution:
Variate $(x)$ $x_{1}$ $x_{2}$ $x_{3} \ldots x_{15}$ Frequency $(f)$ $f_{1}$ $f_{2}$ $f_{3} \ldots f_{15}$
where $0 < x_{1} < x_{2} < x_{3} < \ldots < x_{15} = 10$ and $\sum_{i=1}^{15} f_{i} > 0$,the standard deviation cannot be:
| Variate $(x)$ | $x_{1}$ | $x_{2}$ | $x_{3} \ldots x_{15}$ |
| Frequency $(f)$ | $f_{1}$ | $f_{2}$ | $f_{3} \ldots f_{15}$ |
where $0 < x_{1} < x_{2} < x_{3} < \ldots < x_{15} = 10$ and $\sum_{i=1}^{15} f_{i} > 0$,the standard deviation cannot be:
- A$2$
- B$1$
- C$4$
- D$6$
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$\begin{array}{|l|l|l|l|l|l|l|} \hline X & A & 2 A & 3 A & 4 A & 5 A & 6 A \\ \hline f & 2 & 1 & 1 & 1 & 1 & 1 \\ \hline \end{array}$
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where $A$ is a positive integer,has a variance of $160$. Determine the value of $A$.
Medium
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