For some given data,if $Z - M = 12$,then $M - \bar{x} = \ldots \ldots \ldots$

If $3 \bar{x} = 2 M = 60,$ then $Z = \dots$

Find the mean,median and mode of the following frequency distribution:

Class	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$
Frequency	$5$	$12$	$18$	$40$	$15$	$7$	$3$

The median of an ungrouped data and the median calculated when the same data is grouped are always the same. Do you think that this is a correct statement? Give reason.

The median of the following frequency distribution is $49$ and the total frequency is $100$. Find the missing frequencies $x$ and $y$.

Class	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$
Frequency	$2$	$6$	$8$	$x$	$20$	$18$	$y$	$14$

If $M - \bar{x} = 2$ and $Z = 20.5$,then the median $M = \ldots$ (in $.5$)