For a given frequency distribution,the total frequency is $25$ and $\Sigma f_{i} x_{i} = 120$. Then,the mean is $\ldots$

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.

The following is the cumulative frequency distribution (of less than type) of $1000$ persons each of age $20$ $years$ and above. Determine the mean age.

Age (years)	$30$	$40$	$50$	$60$	$70$	$80$
Cumulative Frequency	$100$	$220$	$350$	$750$	$950$	$1000$

If $M = 72$ and $\bar{x} = 70$,then $Z = \ldots \ldots \ldots \ldots$

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 monthly income of $100$ families is given as follows:

Income (in $Rs.$)	Number of families
$0-5000$	$8$
$5000-10000$	$26$
$10000-15000$	$41$
$15000-20000$	$16$
$20000-25000$	$3$
$25000-30000$	$3$
$30000-35000$	$2$
$35000-40000$	$1$

Calculate the modal income (in $Rs.$).