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 ...... .

If the sum of squares of deviations of $10$ observations from their mean $50$ is $250$,what is the coefficient of variation?

For $10$ observations $x_1, x_2, ..., x_{10}$,if $\sum_{i=1}^{10} (x_i + 2)^2 = 180$ and $\sum_{i=1}^{10} (x_i - 1)^2 = 90$,then their standard deviation is:

The mean of a set of $10$ observations is $5$ and the standard deviation is $2\sqrt{6}$. If the mean of another set of $20$ observations is $5$ and the standard deviation is $3\sqrt{2}$,what is the standard deviation of the combined set of $30$ observations?

If each observation of a distribution with variance $\sigma^2$ is multiplied by $\lambda$,find the standard deviation of the new observations.

$A$ scientist weighs $30$ fish. Their mean weight is $30 \text{ g}$ and the standard deviation is $2 \text{ g}$. Later,it is discovered that the weighing scale was not calibrated correctly and every fish's weight was recorded $2 \text{ g}$ less than the actual weight. What are the correct mean and standard deviation (in grams) of the fish weights,respectively?