Find the mean and variance for the data $6, 7, 10, 12, 13, 4, 8, 12$.

In a series of $2n$ observations,half of them are equal to $a$ and the remaining half are equal to $-a$. If the standard deviation of the observations is $2$,then $|a|$ equals:

The variance of the observations $112, 116, 120, 125, 132$ is $......$

If the variance of the first $n$ natural numbers is $10$ and the variance of the first $m$ even natural numbers is $16$,then $n: m=$

If $x_1, x_2, x_3, \ldots, x_n$ are $n$ observations such that $\sum(x_i+2)^2 = 28n$ and $\sum(x_i-2)^2 = 12n$,then the variance is:

Statement $1$: The variance of the first $n$ odd natural numbers is $\frac{n^2 - 1}{3}$.
Statement $2$: The sum of the first $n$ odd natural numbers is $n^2$ and the sum of the squares of the first $n$ odd natural numbers is $\frac{n(4n^2 - 1)}{3}$.