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

If the variance of the distribution is $45.8$,then find the variance of the distribution given below:

$x_i$	$4$	$8$	$11$	$17$	$20$	$24$	$32$
$f_i$	$3$	$5$	$9$	$5$	$4$	$3$	$1$

$y_i$	$10$	$18$	$24$	$36$	$42$	$50$	$66$
$f_i$	$3$	$5$	$9$	$5$	$4$	$3$	$1$

Suppose values taken by a variable $x$ are such that $a \le x_i \le b$,where $x_i$ denotes the value of $x$ in the $i^{th}$ case for $i = 1, 2, ..., n$. Then:

The mean and variance of six observations are $6$ and $12$ respectively. If each observation is multiplied by $3$,then the new variance of the resulting observations is:

If the variance of the data $2, 4, 5, 6, 8, 17$ is $23.33$,then the variance of $4, 8, 10, 12, 16, 34$ will be

In a data set with $15$ observations $x_1, x_2, x_3, \ldots, x_{15}$,we are given $\sum_{i=1}^{15} x_i^2 = 3600$ and $\sum_{i=1}^{15} x_i = 175$. If the value of one observation $20$ was found to be incorrect and was replaced by its correct value $40$,then the corrected variance of the data is: