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:

If $\sum\limits_{i = 1}^{18} {(x_i - 8) = 9}$ and $\sum\limits_{i = 1}^{18} {(x_i - 8)^2 = 45}$,then the standard deviation of $x_1, x_2, \dots, x_{18}$ is:

Find the coefficient of variation for the given observations: $10, 14, 11, 9, 8, 12, 6$. (in $\%$)

The mean and variance of a set of $15$ numbers are $12$ and $14$ respectively. The mean and variance of another set of $15$ numbers are $14$ and $\sigma^2$ respectively. If the variance of all the $30$ numbers in the two sets is $13$,then $\sigma^2$ is equal to $.........$.

Variance of first $2n$ natural numbers is

The mean and standard deviation of a distribution of weights of a group of $20$ boys are $40 \ kg$ and $5 \ kg$ respectively. If two boys of weights $43 \ kg$ and $37 \ kg$ are excluded from this group,then the variance of the distribution of weights of the remaining group of boys is