In the usual notations,$Z - M = \ldots \ldots \ldots \quad (M - \bar{x})$

The mean of $10$ observations is $15.7$. If a new observation $19$ is included,the new mean is ..........

The maximum bowling speeds,in $km/h$,of $33$ players at a cricket coaching centre are given as follows:

Speed $(km/h)$	$85-100$	$100-115$	$115-130$	$130-145$
Number of players	$11$	$9$	$8$	$5$

Calculate the median bowling speed (in $km/h$).

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

The mean of the following frequency distribution is $60$ and the total frequency is $120$. Find the missing frequencies $f_{1}$ and $f_{2}$.

Class	$10-30$	$30-50$	$50-70$	$70-90$	$90-110$
Frequency	$17$	$f_{1}$	$32$	$f_{2}$	$19$

Will the median class and modal class of grouped data always be different? Justify your answer.