Question

The marks obtained by $120$ students in a test are given below.

Marks	No. of students
$0-10$	$5$
$10-20$	$9$
$20-30$	$16$
$30-40$	$22$
$40-50$	$26$
$50-60$	$18$
$60-70$	$11$
$70-80$	$6$
$80-90$	$4$
$90-100$	$3$

Draw an ogive for the given distribution on a graph sheet. Using suitable scale for ogive to estimate the following:
(i) The median.
(ii) The number of students who obtained more than $75\%$ marks in the test.
(iii) The number of students who did not pass the test if minimum marks required to pass is $40$.

Answer 1

Marks	No. of students $\left(f\right)$	Cumulative Frequency
$0-10$	$5$	$5$
$10-20$	$9$	$14$
$20-30$	$16$	$30$
$30-40$	$22$	$52$
$40-50$	$26$	$78$
$50-60$	$18$	$96$
$60-70$	$11$	$107$
$70-80$	$6$	$113$
$80-90$	$4$	$117$
$90-100$	$3$	$120$
	$n=120$

On the graph paper, we plot the following points:
$(10,5),(20,14),(30,30),(40,52),(50,78),(60,96),(70,107),(80,113),(90,117),(100,120).$

(i) Median $={\left(\frac{n}{2}\right)}^{th}$ term $[\because n=120,$ even$]$

$=\frac{120}{2}={60}^{th}$ term

From the graph ${60}^{th}$ term $=42$

(ii) The number of students who obtained more than $75\%$ marks in test
$=120-110$
$=10$.

(iii) The number of students who did not pass the test if the minimum pass marks $40$ is $52$.