The following distribution gives the state-wise teacher-student

Solution:

Here, the maximum frequency is 10 so the modal class is 30−35.

Therefore,

$l=30$

$h=5$

$f=10$

$f_{1}=9$

$f_{2}=3$

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

$=30+\frac{10-9}{20-9-3} \times 5$

$=30+\frac{1}{8} \times 5$

$=30+0.625$

Mode $=30.6$

Thus, the mode of the data is 30.6.

Now,

Mean of the data $=\frac{\sum f_{i} x_{i}}{\sum f_{i}}=\frac{1022.5}{35}=29.2$

Thus, the mean of the data is 29.2.

The mode of the number of students per teacher in the states is more than the mean of the number of students per teacher in the states.