For the frequency distribution:
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 $0<x_{1}<x_{2}<x_{3}<\ldots<x_{15}=10$ and $\sum_{i=1}^{15} f_{i}>0$, the

standard deviation cannot be :

  1. (1) 4

  2. (2) 1

  3. (3) 6

  4. (4) 2


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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