If the standard deviation of the numbers $2, 3, 2x$,and $11$ is $3.5$,find the possible values of $x$.

Let the mean and the variance of $6$ observations $a, b, 68, 44, 48, 60$ be $55$ and $194$,respectively. If $a > b$,then the value of $a + 3b$ is:

In a series of $2n$ observations,half of them are equal to $a$ and the remaining half are equal to $-a$. If the standard deviation of these observations is $2$,then $|a|$ equals:

If the mean of $100$ observations is $50$ and their standard deviation is $5$,then the sum of squares of all observations is

Assertion $(A)$: The variance of the first $n$ odd natural numbers is $\frac{n^2-1}{3}$.
Reason $(R)$: The sum of the first $n$ odd natural numbers is $n^2$ and the sum of the squares of the first $n$ odd natural numbers is $\frac{n(4n^2-1)}{3}$.
Which of the following alternatives is correct?

If each of given $n$ observations is multiplied by a certain positive number $k$,then for the new set of observations -