The median of the following observations arranged in ascending order is $53 :$ $41, 48, x+1, x+5, 62, 72$. Find $x$.

The marks obtained (out of $50$ marks) by $30$ students in a mathematics test are as given below:
$37, 22, 35, 42, 10, 16, 31, 22, 20, 27$
$27, 20, 31, 40, 35, 40, 27, 16, 47, 22$
$40, 22, 35, 20, 37, 20, 37, 47, 42, 31$
Represent this data in a frequency distribution table.

Find the mode of the following observations: $14, 25, 28, 29, 17, 14, 19, 22, 14, 30, 16, 28, 14, 25$.

The mean of $10$ observations is $16.5$. It was later noticed that one observation was taken as $57$ instead of $75$ by mistake. Find the correct mean of the data.

The frequency distribution of the marks scored by $35$ students in a $60$ marks test is as below:

Marks scored	No. of students
$0-10$	$2$
$10-20$	$7$
$20-30$	$8$
$30-40$	$7$
$40-50$	$8$
$50-60$	$3$

Represent the data by a histogram.

Prepare a continuous grouped frequency distribution from the following data:

Mid-point	Frequency
$5$	$4$
$15$	$8$
$25$	$13$
$35$	$12$
$45$	$6$

Also,find the size of the class intervals.