Following is the distribution of I.Q. of 100 students. Find the median I.Q.

Solution:

Here, the frequency table is given in inclusive form. Transforming the given table into exclusive form and prepare the cumulative frequency table.

Here, $N=100$

So, $\frac{N}{2}=50$

Thus, the cumulative frequency just greater than 50 is 67 and the corresponding class is 94.5−104.5.

Therefore, 94.5−104.5 is the median class.

Here, $I=94.5, f=33, F=34$ and $h=9$

We know that,

Median $=l+\left\{\frac{\frac{N}{2}-F}{f}\right\} \times h$

$=94.5+\left(\frac{50-34}{33}\right) \times 10$

$=94.5+\frac{160}{33}$

$=94.5+4.85$

 

$=99.35$

Hence, the median is 99.35.