Calculate the variance if $\Sigma x_i^2 = 18000$ and $\Sigma x_i = 960$,for $60$ observations.

If the mean and standard deviation of $5$ observations $x_1, x_2, x_3, x_4, x_5$ are $10$ and $3$,respectively,then the variance of $6$ observations $x_1, x_2, x_3, x_4, x_5$ and $-50$ is equal to: (in $.5$)

Let $n$ observations $x_1, x_2, ....., x_n$ be such that $\sum {x_i}^2 = 400$ and $\sum x_i = 80$. Then,which of the following is a possible value for $n$?

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 $4\bar x$.

If $v$ is the variance and $\sigma$ is the standard deviation,then

The variance of the numbers $8, 21, 34, 47, \ldots, 320$ is . . . . . . .