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:

The standard deviation and mean of five observations are $0$ and $9$ respectively. If one of the observations is changed such that the mean of the new set of five observations becomes $10$,then their standard deviation is

The mean and standard deviation of $100$ items are $50$ and $4$,respectively. Find the sum of all the items and the sum of the squares of the items.

If the standard deviation of the first $n$ natural numbers is $2$,then the value of $n$ is

Let $x_1, x_2, \ldots, x_{10}$ be ten observations such that $\sum_{i=1}^{10}(x_i-2)=30$,$\sum_{i=1}^{10}(x_i-\beta)^2=98$,$\beta > 2$ and their variance is $\frac{4}{5}$. If $\mu$ and $\sigma^2$ are respectively the mean and the variance of $2(x_1-1)+4\beta, 2(x_2-1)+4\beta, \ldots, 2(x_{10}-1)+4\beta$,then $\frac{\beta\mu}{\sigma^2}$ is equal to:

Let $x_1, x_2, \dots, x_n$ be $n$ observations such that $\sum x_i^2 = 300$ and $\sum x_i = 60$. Which of the following is a possible value for $n$?