The following is the distribution of height of students of a certain class in a certain city:

Solution:

First we prepare the following cummulative table to compute the median.

Now, $N=420$

$\therefore \frac{N}{2}=210$

Thus, the cumulative frequency just greater than 210 is 275 and the corresponding class is $166-168$.

 

Therefore, $166-168$ is the median class.

$I=166, f=142, F=133$ and $h=2$

We know that,

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

$=166+\left\{\frac{210-133}{142}\right\} \times 2$

$=166+\frac{77 \times 2}{142}$

$=166+\frac{154}{142}$

$=166+1.08$

 

$=167.08$

Hence, the median height is approximately 167.1 cm.