Find the mean of the following frequency distribution:

$x_i$	$3$	$6$	$9$	$12$
$f_i$	$1$	$2$	$3$	$4$

Let $x_1, x_2, \ldots, x_{11}$ be $11$ distinct positive integers. If we replace the largest of these integers by the median of the other $10$ integers,then:

The number of observations in a group is $40$. If the average of the first $10$ observations is $4.5$ and the average of the remaining $30$ observations is $3.5$,then the average of the whole group is:

Find the median for the following distribution:

Class	Frequency
$10-20$	$180$
$20-30$	$82$
$30-40$	$34$
$40-50$	$180$
$50-60$	$136$
$60-70$	$23$
$70-80$	$50$

If the mean of the set of numbers ${x_1}, {x_2}, {x_3}, ..., {x_n}$ is $\bar x$,then the mean of the numbers ${x_i} + 2i$,$1 \le i \le n$ is

The mean of the values $\sin^2 10^{\circ}, \sin^2 20^{\circ}, \sin^2 30^{\circ}, \ldots, \sin^2 90^{\circ}$ is $........$