Given below is the distribution of IQ of 100 students . Find the median IQ

Explanation

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

Now `N=100 rArr N/2=50`
The cumulative freqeuency just greater than 50 is 76 and the corresponding class is 104.5-114.5
Thus the median class is 104.5-114.5
` l=104.5, h=10, f=31, cf=c.f " of preceding class " =45 and N/2=50`
Median `M_e=l+{hxx((N/2-cf))/f}`
`104.5+{10xx((50-45))/(31)}=104.5+(50)/(31)`
104.5+1.6=106.1.
Hence , the median IQ is 106.1