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 $.........$.

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 standard deviation of $n$ observations $a_{1}, a_{2}, a_{3}, \ldots, a_{n}$ is $\sigma$. Then, the standard deviation of the observations $\lambda a_{1}, \lambda a_{2}, \ldots, \lambda a_{n}$ is

The standard deviation of the first $10$ multiples of $4$ is:

Find the mean and variance for the first $n$ natural numbers.

The marks obtained by students $A$ and $B$ in $3$ examinations are given below:
| | Exam $1$ | Exam $2$ | Exam $3$ |
|---|---|---|---|
| Marks of $A$ | $30$ | $20$ | $40$ |
| Marks of $B$ | $70$ | $0$ | $5$ |
The ratio of the coefficient of variation of marks of $A$ and the coefficient of variation of marks of $B$ is: