Question

The marks obtained by $100$ students in a Mathematics test are given below:

Marks	No. of Students
$0-10$	$3$
$10-20$	$7$
$20-30$	$12$
$30-40$	$17$
$40-50$	$23$
$50-60$	$14$
$60-70$	$09$
$70-80$	$06$
$80-90$	$05$
$90-100$	$04$

Draw an ogive for the given distribution on a graph sheet.
(Use a scale of $2cm=10$ units on both axis).
Use the ogive to estimate the lower quartile.

Answer 1

Marks	No. of Students	Cumulative frequency (c.f.)
$0-10$	$3$	$3$
$10-20$	$7$	$10$
$20-30$	$12$	$22$
$30-40$	$17$	$39$
$40-50$	$23$	$62$
$50-60$	$14$	$76$
$60-70$	$09$	$85$
$70-80$	$06$	$91$
$80-90$	$05$	$96$
$90-100$	$04$	$100$

On the graph paper, we plot the following points:
$(10,3),(20,10),(30,22),(40,39),(50,62),(60,76),(70,85),(80,91),(90,96),(100,100)$
Lower quartile $={\left(\frac{n}{4}\right)}^{th}\text{term}$
$=\frac{100}{4}={25}^{th}\text{term}$.
From the graph ${25}^{th}\text{term}=31$.