Find the median for the following frequency distributution

Explanation

The given series is in inclusive form . Converting it to exclusive form and preparing the cumulative frequncy table , we get

Now, `N=400 rArr N/2=200`
The cumulative freqeuency just greater than 200 is 268 and the corresponding class is 165.5-168.5.
Thus the median class is 165.5-168.5
`therefore l=165.5, h=3. f=136, cf=c.f " of preceding class " =132 and N/2=200`
Median `M_e=l+{hxx((N/2-cf))/f}`
`165.5+{3xx((200-132))/(136)}=165.5+((3xx68)/(136)))`
=165.5+1.5=167
Hence, median hieght is 167 cm