Question

Find the median for the following distribution

Marks	0-10	10-30	30-60	60-80	80-90
No. of Students	5	15	30	8	2

• A. $38$
• B. $43$
• C. $40$
• D. $42$

Answer 1

Answer: (C)

$40$

Step 1-Construct the cumulative frequency distribution.

Marks	no.of student(frequency)	Cumulative frequency
0-10	5	5
10-30	15	20
30-60	30	50
60-80	8	58
80-90	2	60

Step 2-Decide the class that contain the median

$\Rightarrow \frac{n}{2}=\frac{60}{2}=30$

$\therefore$The 3 rd class is median class

Step 3-Find the median with this formula$=L+\frac{\left(\frac{n}{2}\right)-B}{G}\times W$

Where

L=lower class boundary containing the median.

n=total number of value.

B=cumulative frequency of the groups before the median group.

G=frequency of the median group.

W=Group width

$\therefore L=30,n=30,B=20,G=30,W=30$

$\Rightarrow 30+\frac{30-20}{30}\times 30$

$\Rightarrow 30+10=40$

$\therefore$ Median=40