Question

Find the median for the following distribution

Class	0-5	5-10	10-15	15-20	20-25
Frequency	3	5	8	5	4

• A. $10$
• B. $12.5$
• C. $14$
• D. $11.5$

Answer 1

The correct option is B $12.5$

Step 1-Construct the cumulative frequency distribution.

Class	frequency	Cumulative frequency
0-5	3	3
5-10	5	8
10-15	8	16
15-20	5	21
20-25	4	25

Step 2-Decide the class that contain the median

$\Rightarrow \frac{n}{2}=\frac{25}{2}=12.5$

$\therefore$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

$\therefore L=10.5,n=25,B=8,G=8,W=5$

$\Rightarrow 10.5+\frac{12.5-8}{8}\times 5$

$\Rightarrow 10.5+\frac{17.5}{8}$

$\Rightarrow \frac{101.5}{8}=12.5$