If the mean of the numbers $a, b, 8, 5, 10$ is $6$ and the variance is $6.80$,then which of the following is a possible value for $a$ and $b$?

Let ${x_1}, {x_2}, \ldots, {x_n}$ be $n$ observations,and let $\bar x$ be their arithmetic mean and ${\sigma ^2}$ be the variance.
Statement-$1$: The variance of $2{x_1}, 2{x_2}, \ldots, 2{x_n}$ is $4{\sigma ^2}$.
Statement-$2$: The arithmetic mean of $2{x_1}, 2{x_2}, \ldots, 2{x_n}$ is $4\bar x$.

The standard deviation of the numbers $22, 26, 28, 20, 24, 30$ is

The average marks of $10$ students in a class was $60$ with a standard deviation of $4$,while the average marks of another $10$ students was $40$ with a standard deviation of $6$. If all the $20$ students are taken together,their combined standard deviation will be:

All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of $10$ to each of the students. Which of the following statistical measures will not change even after the grace marks were given?

The $S.D.$ of a variate $x$ is $\sigma$. The $S.D.$ of the variate $\frac{ax + b}{c}$,where $a, b, c$ are constants,is