The variance of $20$ observations is $5$. If each observation is multiplied by $3$ and then $8$ is added to each number,then the variance of the resulting observations is:

If the variance of the numbers $-1, 0, 1, k$ is $5$,where $k > 0$,then $k$ is equal to

Let $X_{1}, X_{2}, \ldots, X_{18}$ be eighteen observations such that $\sum_{i=1}^{18}(X_{i}-\alpha)=36$ and $\sum_{i=1}^{18}(X_{i}-\beta)^{2}=90$,where $\alpha$ and $\beta$ are distinct real numbers. If the standard deviation of these observations is $1$,then the value of $|\alpha-\beta|$ is ...... .

The standard deviation of the numbers $31, 32, 33, \ldots, 46, 47$ is

Let $a_1, a_2, \ldots, a_{10}$ be $10$ observations such that $\sum_{k=1}^{10} a_k = 50$ and $\sum_{k < j} a_k a_j = 1100$. Then the standard deviation of $a_1, a_2, \ldots, a_{10}$ is equal to:

Given that the total of $16$ values is $528$ and the sum of the squares of deviations from $33$ is $9158$. The variance is: