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

Solution:

The given data is an inclusive series. So, firstly convert it into an exclusive series as given below.

Here, the maximum frequency is 142 so the modal class is 165.5−168.5.

Therefore,

$l=165.5$

$h=3$

$f=142$

$f_{1}=118$

$f_{2}=127$

Now,

Mode $=l+\frac{f-f_{1}}{2 f-f_{1}-f_{2}} \times h$

$=165.5+\frac{142-118}{284-118-127} \times 3$

$=165.5+\frac{24}{39} \times 3$

$=165.5+\frac{24}{13}$

$=165.5+1.85$

 

$=167.35$

Thus, the average height of maximum number of students is 167.35 cm.