Find the coefficient of variation of the first $n$ natural numbers.

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

If the variance of the numbers $9, 15, 21, \ldots, (6n+3)$ is $P$,then the variance of the first $n$ even numbers is

If the variance of $6, 7, 8, 9, 10, 11$ is $\sigma^2$,then the variance of $12, 14, 16, 18, 20, 22$ is

If each observation of a distribution with standard deviation $\sigma$ is increased by $\lambda$,find the variance of the new observations.

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 $4\bar x$.