If $\text{mean} = (3 \text{median} - \text{mode}) k$,then the value of $k$ is

If $\text{Mean} = x(3 \times \text{Median} - \text{Mode})$,then what is the value of $x$?

If for a slightly asymmetric distribution,mean and median are $5$ and $6$ respectively,what is its mode?

Let $a_1, a_2, \dots, a_{101}$ be a group of real numbers such that $a_i > a_{i+1}$ for all values of $i$ and the mean square deviation of the group is minimum about the number $a_{51}$. Then the mode of the group will be:

Find the mode of the following distribution:

Marks	$4$	$5$	$6$	$7$	$8$
No. of students	$6$	$7$	$10$	$8$	$3$

Determine which of the following statements is true: $(1)$ The mode can be calculated using a histogram. $(2)$ The median is not independent of the change of scale. $(3)$ Variance is independent of the change of origin and scale.