If the mean of $12, 13, x, 17, 18$ and $20$ is $16,$ then $x = \ldots \ldots \ldots \ldots .$

The mode of the following frequency distribution is $37$. Find the missing frequency $x$.

Class	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$
Frequency	$4$	$7$	$x$	$18$	$15$	$8$	$7$

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 mean of the following frequency distribution is $46$. Find the missing frequency $f$.

Class	$0-20, 20-40, 40-60, 60-80, 80-100, 100-120$
Frequency	$10, f, 7, 6, 5, 4$

The mean of the following frequency distribution is $28.5$ and the total frequency is $60$. Find the missing frequencies $f_{1}$ and $f_{2}$.

Class	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$
Frequency	$6$	$f_1$	$20$	$15$	$f_2$	$4$

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: