Question

Find the median of the following data.

Group	$6-8$	$8-10$	$10-12$	$12-14$	$14-16$	$16-18$	$18-20$
Frequencies	$12$	$20$	$16$	$15$	$17$	$8$	$12$

• A. $12.58$
• B. $12.266$
• C. $11.345$
• D. $14.87$

Answer 1

The correct option is B $12.266$

Converting the given data into frequency distribution table:

Group	Frequency $\left(f\right)$	$cf$
6-8	12	12
8-10	20	32
10-12	16	48
12-14	15	63
14-16	17	80
16-18	8	88
18-20	12	100
	$\Sigma f=100$

Here, $N=100$

Hence the median class $=\frac{N}{2}=\frac{100}{2}=50$

In the above table $12-14$ is the median class and the respective $cf$ is $20$ (nearest to the value of $50$)

According to the question:

$l_1=12$ (lower limit of median class)

$\text{cf}=48$ (cf= cumulative frequency preceding the median class)

$i=l_2-l_1=2$ (width of class interval of median class)

$f=15$ (frequency of median class)

$\text{Median}=l_1+\frac{\frac{N}{2}-C}{f}\times i=12+\frac{50-48}{15}\times 2$

$\text{Median}=12.266$

Hence, option (B) is the correct answer.