Question

During the medical check-up of $35$ students of a class, their weights were recorded as follows:

Weight (in kg)	Number of students
Less than $38$ Less than $40$ Less than $42$ Less than $44$ Less than $46$ Less than $48$ Less than $50$ Less than $52$	$0$ $3$ $5$ $9$ $14$ $28$ $32$ $35$

Draw a less than type ogive for the given data. Hence obtain the median weight from the graph and verify the result by using the formula.

Answer 1

Let us now plot the points corresponding to the ordered pairs given by $(38,0),(40,3),(42,5),(44,9),(46,14),(48,28),(50,32)$ and $(52,35)$ on a graph paper and join them by a free hand smooth curve.

Now,

Weight (in kg)	Number of students (Frequency)
$0-38$	$0$
$38-40$	$3-0=3$
$40-42$	$5-3=2$
$42-44$	$9-5=4$
$44-46$	$14-9=5$
$46-48$	$28-14=14$
$48-50$	$32-28=4$
$50-52$	$35-32=3$

Mode: The class which have highest frequency.

In this case, class interval $46-48$ is the modal class.

Now,

Lower limit of modal class, $l=46,h=2,f_1,=14,f_0=5,f_2=4$

We know that,

Mode $=l+\left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)\times h$$=46+\left(\frac{14-5}{2\left(14\right)-5-4}\right)\times 2$

$=46+\frac{9}{19}\times 2$

$=46+0.95$

Mode $=46.95$, verified.