Question

If the median of the following data is 40 then the value of p is

Class	0-10	10-30	30-60	60-80	80-90
Frequency	5	15	30	p	2

• A. $7$
• B. $8$
• C. $9$
• D. $7.6$

Answer 1

Answer: (B)

$8$

Median=$L+\frac{\left(\frac{n}{2}\right)-cfb}{fm}\times w$
Where,
L=is the lower class boundary of the group containing the median.
n=the total number of data.
cfb=the cummulative frequency of the groups before the median group.
fm=the frequency of the median group.
w=group width

Class	frequency	cf
$0-10$	$5$	$5$
$10-30$	$15$	$20$
$30-60$	$30$	$50$
$60-80$	$p$	$50+p$
$80-90$	$2$	$52+p$
	total $n=55+p$

Here,
$\frac{n}{2}=\frac{52+p}{2}$
Median m=$40$,is in $30-60$ class.
Therefore,
$l=30,cfb=20,w=30,fm=30$
Therefore,
Median=$L+\frac{\left(\frac{n}{2}\right)-cfb}{fm}\times w$
$40=L+\frac{\left(\frac{52+p}{2}\right)-20}{30}\times 30$
$=>10=\frac{52+p}{2}-20$
$=>30\times 2=52+p$
$=>p=8$