Question

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

Weight (in kg)	No. of students
Less than 38	0
Less than 40	3
Less than 42	5
Less than 44	9
Less than 46	14
Less than 48	28
Less than 50	32
Less than 52	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.

• A. $47.65$ kg
• B. $46.5$ kg
• C. $45.32$ kg
• D. $43.45$ kg

Answer 1

The correct option is B $46.5$ kg

$\Rightarrow$ From the given table in question we have draw less than type ogive curve.

$\Rightarrow$ $\sum f_i=35$. So, $n=35$

$\therefore$ $\frac{n}{2}=\frac{35}{2}=17.5$

We draw a line parallel to x-axis where, number of students $=17.5$

Where the line line intersects are equation, it is the median

$\therefore$ $Median=46.5$

$Weight$ $\left(inkg\right)$	$No.ofstudents$ $\left(f_i\right)$	$cf$
$0-38$	$0$	$0$
$38-40$	$3-0=3$	$3$
$40-42$	$5-3=2$	$5$
$42-44$	$9-5=4$	$9$
$44-46$	$14-9=5$	$14$
$46-48$	$28-14=14$	$28$
$48-50$	$32-28=4$	$32$
$50-52$	$35-32=3$	$35$
	$\sum f_i=35$

We know, $\frac{n}{2}=17.5$

$\therefore$ Median class $=46-48$

$\Rightarrow$ $l=46cf=14,f=14$ and $h=40-38=2$

$Median=l+\frac{\frac{n}{2}-cf}{f}\times h$

$=46+\frac{17.5-14}{14}\times 2$

$=46+0.5$

$=46.5$