If the mean and variance of six observations $7, 10, 11, 15, a, b$ are $10$ and $\frac{20}{3}$ respectively,then the value of $|a-b|$ is equal to:

The mean and standard deviation of $100$ observations $x_1, x_2, \ldots, x_{100}$ were calculated as $40$ and $5.1$ respectively by a student who took by mistake $50$ instead of $40$ for one observation. Then the correct value of $\sum_{i=1}^{100} x_i^2=$

$A$ $100$ 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 variance of $7$ observations are $8$ and $16$ respectively. If five of the observations are $2, 4, 10, 12, 14$,find the remaining two observations.

The range of the observations $20, 28, 40, 12, 30, 15, 50$ is $ . . . . . . $.

Integers $1, 2, 3, \ldots, n$ $(n \geq 3)$ are written on a blackboard and an integer $k$ $(1 < k < n)$ is erased. The average of the remaining numbers is $16$. Then $n + k$ is