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:

Find the unknown entries $a, b, c, d, e, f$ in the following distribution of heights of students in a class:

Height (in $cm$)	Frequency	Cumulative frequency
$150-155$	$12$	$a$
$155-160$	$b$	$25$
$160-165$	$10$	$c$
$165-170$	$d$	$43$
$170-175$	$e$	$48$
$175-180$	$2$	$f$
Total	$50$	-

The following table gives the number of pages written by Sarika for completing her own book over $30$ days:

Number of pages written per day	$16-18$	$19-21$	$22-24$	$25-27$	$28-30$
Number of days	$1$	$3$	$4$	$9$	$13$

Find the mean number of pages written per day.

An aircraft has $120$ passenger seats. The number of seats occupied during $100$ flights is given in the following table:

Number of seats	$100-104$	$104-108$	$108-112$	$112-116$	$116-120$
Frequency	$15$	$20$	$32$	$18$	$15$

Determine the mean number of seats occupied over the flights. (in $.92$)

The formula to find the mode of a grouped data is $\ldots \ldots \ldots . . .$

For some given data,if $\bar{x} + Z = 37.5$ and $\bar{x} - Z = 1.5$,then $M = \ldots$