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

If the mode of a distribution is $18$ and the mean is $24$,then what is the median?

In any discrete series (when all values are not same),the relationship between $M.D.$ about mean and $S.D.$ is:

Consider the following frequency distribution:

Class	$0-6$	$6-12$	$12-18$	$18-24$	$24-30$
Frequency	$a$	$b$	$12$	$9$	$5$

If $\text{mean} = \frac{309}{22}$ and $\text{median} = 14$,then the value of $(a-b)^{2}$ is equal to $.....$

In a series,if $4$ appears $3$ times,$5$ appears $4$ times,$6$ appears $5$ times,$7$ appears $8$ times,$8$ appears $7$ times,and $9$ appears $6$ times,then the mode of the numbers is = .......

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.