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 these observations is $2$,then $|a|$ equals:

For a data consisting of $15$ observations $x_i$,$i=1, 2, 3, \ldots, 15$,the following results are obtained: $\sum_{i=1}^{15} x_i = 170$ and $\sum_{i=1}^{15} x_i^2 = 2830$. If one of the observations,namely $20$,was found to be wrong and was replaced by its correct value $30$,then the corrected variance is:

The variance of the first $10$ multiples of $3$ is:

Find the standard deviation of the first $n$ natural numbers.

Let $\mu$ be the mean and $\sigma$ be the standard deviation of the distribution:

$X_i$	$0$	$1$	$2$	$3$	$4$	$5$
$f_i$	$k+2$	$2k$	$k^2-1$	$k^2-1$	$k^2-1$	$k-3$

where $\sum f_i=62$. If $[x]$ denotes the greatest integer $\leq x$,then $[\mu^2+\sigma^2]$ is equal to:

Let population $A$ contain $100$ observations $101, 102, \dots, 200$ and another population $B$ contain $100$ observations $151, 152, \dots, 250$. If $V_A$ and $V_B$ represent the variances of the two populations respectively,then what is $V_A / V_B$?