Question

Calculate the median for the following data given below$:$

X	$5-9$	$9-13$	$13-17$	$17-21$
F	$3$	$8$	$9$	$4$

• A. $11.44$
• B. $12.44$
• C. $13.44$
• D. $15.44$

Answer 1

Answer: (C)

$13.44$

X	Frequencies (f)	Cumulative frequency (cf)
$5-9$	$3$	$3$
$9-13$	$8$	$3+8=11$
$13-17$	$9$	$11+9=20$
$17-21$	$4$	$20+4=24$
	$n=\Sigma f=24$ $\frac{n}{2}=\frac{24}{2}=12$

Median $=l+\left(\frac{\frac{n}{2}-cf}{f}\right)\times h$
$n=\Sigma f=$ Total number of frequency $=12$
$\frac{n}{2}=\frac{24}{2}=12$
So, the median class is $13-17$
L$=$ Lower limit of the median class $=13$
cf$=$ Cumulative frequency of the class preceding the median class $=11$
f$=$ Frequency of the median class $=9$
h$=$ class width$=4$
Therefore, Median $=l+\left(\frac{\frac{n}{2}-cf}{f}\right)\times h$
$=13+\left(\frac{\frac{24}{2}-11}{9}\right)\times 4$
$=13+\left(\frac{12-11}{9}\right)\times 4$
$=13+0.44$
$=13.44$
Hence, the median is $13.44$.