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

If the mean of the series $x_1, x_2, ......., x_n$ is $\bar{x}$,then what will be the mean of the series $x_i + 2i, (i = 1, 2, ......., n)$?

The median of a set of $9$ distinct observations is $20.5$. If each of the largest $4$ observations of the set is increased by $2$,then the median of the new set:

The following data gives the distribution of height of students. The median of the distribution is:

Height (in $cm$)	$160$	$150$	$152$	$161$	$156$	$154$	$155$
No of students	$12$	$8$	$4$	$4$	$3$	$3$	$7$

For a distribution $x_1, x_2, \dots, x_{101}$ such that $x_1 < x_2 < x_3 < \dots < x_{100} < x_{101}$,the mean deviation of this distribution about a number $k$ is minimum. Then $k$ is equal to which of the following?

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: