If the standard deviation of the numbers $ 2,3,a $ and $11$ is $3.5$  then which of the following is true ?

The mean and variance of $10$ observations were calculated as $15$ and $15$ respectively by a student who took by mistake $25$ instead of $15$ for one observation. Then, the correct standard deviation is$.....$

In a series of $2n$ observations, half of them equal to $a$ and remaining half equal to $-a$. If the standard deviation of the observations is $2$, then $|a|$ equals

The mean and standard deviation of $20$ observations are found to be $10$ and $2$, respectively. On respectively, it was found that an observation by mistake was taken $8$ instead of $12$ . The correct standard deviation is

In any discrete series (when all values are not same) the relationship between $M.D.$ about mean and $S.D.$ is

Let $X=\{\mathrm{x} \in \mathrm{N}: 1 \leq \mathrm{x} \leq 17\}$ and $\mathrm{Y}=\{\mathrm{ax}+\mathrm{b}: \mathrm{x} \in \mathrm{X}$ and $\mathrm{a}, \mathrm{b} \in \mathrm{R}, \mathrm{a}>0\} .$ If mean and variance of elements of $Y$ are $17$ and $216$ respectively then $a + b$ is equal to