If for some $x \in R$,the frequency distribution of the marks obtained by $20$ students in a test is:
Marks: $2, 3, 5, 7$
Frequency: $(x+1)^2, 2x-5, x^2-3x, x$
Then the mean of the marks is:

The $A.M.$ of a $50$ set of numbers is $38$. If two numbers of the set,namely $55$ and $45$,are discarded,the $A.M.$ of the remaining set of numbers is

If the mean of $3, 4, x, 7, 10$ is $6$,then the value of $x$ is

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?

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

If ${d_i}$ is the deviation of a class mark ${y_i}$ from $a$,the assumed mean,and ${f_i}$ is the frequency,if ${M_g} = x + \frac{1}{{\sum {f_i}}}(\sum {f_i}{d_i})$,then $x$ is: