Let $\mathrm{X}=\{x \in \mathrm{~N}: 1 \leq x \leq 19\}$ and for some $a, b \in \mathbb{R}, \mathrm{Y}=\{a x+b: x \in \mathrm{X}\}$. If the mean and variance of the elements of Y are 30 and 750 , respectively, then the sum of all possible values of $b$ is

The mean and variance of a data of 10 observations are 10 and 2 , respectively. If an observations $\alpha$ in this data is replaced by $\beta$, then the mean and variance become 10.1 and 1.99 , respectively. Then $\alpha+\beta$ equals

If the mean and the variance of the data

$$ \begin{array}{|c|c|c|c|c|} \hline \text { Class } & 4-8 & 8-12 & 12-16 & 16-20 \\ \hline \text { Frequency } & 3 & \lambda & 4 & 7 \\ \hline \end{array} $$

are $\mu$ and 19 respectively, then the value of $\lambda+\mu$ is :

Let the mean and variance of 8 numbers $-10,-7,-1, x, y, 9,2,16$ be $\frac{7}{2}$ and $\frac{293}{4}$, respectively.

Then the mean of 4 numbers $x, y, x+y+1,|x-y|$ is :