If $Z+M=88$ and $Z-M=2$,then $M=\ldots \ldots \ldots \ldots . .$

The mean of the following frequency distribution is $43.75$. Find the missing frequency $f$.

Class	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$	$80-90$	$90-100$
Frequency	$8$	$4$	$20$	$45$	$64$	$32$	$f$	$8$	$2$	$2$

The frequency distribution of marks obtained by $400$ students is given below. If the mean of the frequency distribution is $41.2$,find the missing frequencies $x$ and $y$.

Marks	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$
Number of students	$26$	$26$	$x$	$110$	$84$	$y$	$36$	$32$

The following is the distribution of weights (in $kg$) of $40$ persons:

Weight (in $kg$)	$40-45$	$45-50$	$50-55$	$55-60$	$60-65$	$65-70$	$70-75$	$75-80$
Number of persons	$4$	$4$	$13$	$5$	$6$	$5$	$2$	$1$

Construct a cumulative frequency distribution (of the less than type) table for the data above.

The mean of $15$ observations is $25$. Later on,it was found that one observation was taken by mistake as $20$ instead of $50$. Then,the correct mean is:

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	$2$	$6$	$8$	$x$	$20$	$18$	$y$	$14$