Let the Mean and Variance of five observations $x_1=1, x_2=3, x_3=a, x_4=7$ and $x_5=b$,where $a > b$,be $5$ and $10$ respectively. Then the Variance of the observations $n+x_n$ for $n=1, 2, 3, 4, 5$ is:

The sum of $100$ observations and the sum of their squares are $400$ and $2475$,respectively. Later on,three observations,$3, 4$ and $5$,were found to be incorrect. If the incorrect observations are omitted,then the variance of the remaining observations is

The variance of $50$ observations is $7$. Suppose that each observation in this data is multiplied by $6$ and then $5$ is subtracted from it. Then the variance of that new data is

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

The variance of the first $10$ multiples of $3$ is:

The standard deviation and mean of five observations are $0$ and $9$ respectively. If one of the observations is changed such that the mean of the new set of five observations becomes $10$,then their standard deviation is