Let $x_1, x_2, \dots, x_{100}$ be $100$ observations such that $\sum x_i = 0$,$\sum_{1 \le i < j \le 100} |x_i x_j| = 80000$,and the mean deviation from their mean is $5$. Then their standard deviation is:

The coefficient of variation for the following data is:

$x_i$	$5$	$7$	$9$	$11$
$f_i$	$3$	$2$	$1$	$2$

The mean of two samples of size $200$ and $300$ were found to be $25$ and $10$ respectively. Their standard deviations $(S.D.)$ are $3$ and $4$ respectively. Then,the variance of the combined sample of size $500$ is:

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 $4\bar x$.

The variance and mean of $15$ observations are respectively $6$ and $10$. If each observation is increased by $8$,then the new variance and new mean of the resulting observations are respectively:

Find the variance of the sequence $a, a + d, a + 2d, \dots, a + 2nd$.