The following table gives the distribution of students of sections $A$ and $B$ of a class according to the marks obtained by them.

Marks	Section $A$ Frequency	Section $B$ Frequency
$0-15$	$3$	$3$
$15-30$	$12$	$16$
$30-45$	$28$	$25$
$45-60$	$30$	$27$
$60-75$	$35$	$40$
$75-90$	$13$	$10$

Represent the marks of the students of both the sections on the same graph by two frequency polygons. What do you observe?

(N/A) To construct the frequency polygons,we first calculate the class marks (mid-points) for each interval:

Marks	Class Mark	Section $A$ Frequency	Section $B$ Frequency
$0-15$	$7.5$	$3$	$3$
$15-30$	$22.5$	$12$	$16$
$30-45$	$37.5$	$28$	$25$
$45-60$	$52.5$	$30$	$27$
$60-75$	$67.5$	$35$	$40$
$75-90$	$82.5$	$13$	$10$

$1$. For Section $A$,we plot the points $(7.5, 3), (22.5, 12), (37.5, 28), (52.5, 30), (67.5, 35), (82.5, 13)$ and join them with solid line segments.
$2$. For Section $B$,we plot the points $(7.5, 3), (22.5, 16), (37.5, 25), (52.5, 27), (67.5, 40), (82.5, 10)$ and join them with dotted line segments.
$3$. Observation: The frequency polygon for Section $B$ is higher in the range of $60-75$ marks compared to Section $A$,indicating that more students in Section $B$ achieved higher marks in that range. Overall,the performance of Section $B$ is better in the higher marks bracket.