Let the mean and variance of four numbers $3, 7, x$ and $y$ $(x > y)$ be $5$ and $10$ respectively. Then the mean of four numbers $3+2x, 7+2y, x+y$ and $x-y$ is ..... .

The first of the two samples in a group has $100$ items with mean $15$ and standard deviation $3$. If the whole group has $250$ items with mean $15.6$ and standard deviation $\sqrt{13.44}$,then the standard deviation of the second sample 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:

$A$ $100$ mark examination was administered to a class of $50$ students. Despite only integer marks being given,the average score of the class was $47.5$. The maximum number of students who could have received marks greater than the class average is:

The mean and the standard deviation of $10$ observations are $20$ and $2$ respectively. Each of these $10$ observations is multiplied by $p$ and then reduced by $q$,where $p \neq 0$ and $q \neq 0$. If the new mean and new standard deviation (s.d.) become half of the original values,then $q$ is equal to

Let ${x_1}, {x_2}, ..., {x_n}$ be $n$ observations such that $\sum x_i^2 = 400$ and $\sum x_i = 80$. Then a possible value of $n$ among the following is: