If the mean and variance of eight numbers $3, 7, 9, 12, 13, 20, x$,and $y$ are $10$ and $25$ respectively,then $x \cdot y$ is equal to

What is the weighted mean of the first $n$ natural numbers when the weights are equal to the corresponding natural numbers?

If $\bar{x}_1$ and $\bar{x}_2$ are the means of two distributions such that $\bar{x}_1 < \bar{x}_2$ and $\bar{x}$ is the mean of the combined distribution,then

Let $a, b \in R$. Let the mean and the variance of $6$ observations $-3, 4, 7, -6, a, b$ be $2$ and $23$,respectively. The mean deviation about the mean of these $6$ observations is:

The mean of $5$ observations is $4.4$ and the variance is $8.24$. If three of the five observations are $1, 2,$ and $6$,then the values of the other two observations are:

Let sets $A$ and $B$ have $5$ elements each. Let the mean of the elements in sets $A$ and $B$ be $5$ and $8$ respectively,and the variance of the elements in sets $A$ and $B$ be $12$ and $20$ respectively. $A$ new set $C$ of $10$ elements is formed by subtracting $3$ from each element of $A$ and adding $2$ to each element of $B$. Then the sum of the mean and variance of the elements of $C$ is $.......$.