Question

Find the median for the following data given below$:-$

X	$4-7$	$7-10$	$10-13$	$13-14$
F	$2$	$5$	$3$	$2$

• A. $11$
• B. $10$
• C. $9$
• D. $8$

Answer 1

The correct option is C $9$

X	F(f)	Cumulative frequency (cf)
$4-7$	$2$	$2$
$7-10$	$5$	$2+5=7$
$10-13$	$3$	$7+3=10$
$13-14$	$2$	$10+2=12$
	$n=\Sigma f=12$ $\frac{n}{2}$$=\frac{12}{2}=6$

Median $=l+\left(\frac{\frac{n}{2}-cf}{f}\right)\times h$
$n=\Sigma f=$ total number of frequency $=12$
$\frac{n}{2}=\frac{12}{2}=6$
So, the median class is $10-13$
$L=$ Lower limit of median class $=10$
$cf=$ Cumulative frequency of the class preceding the median class $=7$
$f=$ frequency of the median class $=3$
$h=$ class width $=3$
Therefore, Median $=l+\left(\frac{\frac{n}{2}-cf}{f}\right)\times h$
$=10+\left(\frac{\frac{12}{2}-7}{3}\right)\times 3$
$=10+\left(\frac{6-7}{3}\right)\times 3$
$=10-1$
$=9$
Hence, the median is $9$