The following distribution gives the state-wise teacher-student ratio in higher secondary schools of India. Find the mode and mean of this data. Interpret the two measures.

Number of students per teacher	Number of states/$U$.$T$.
$15-20$	$3$
$20-25$	$8$
$25-30$	$9$
$30-35$	$10$
$35-40$	$3$
$40-45$	$0$
$45-50$	$0$
$50-55$	$2$

(N/A) It can be observed from the given data that the maximum class frequency is $10$ belonging to class interval $30-35$.
Therefore,modal class $= 30-35$.
Class size $(h) = 5$.
Lower limit $(l)$ of modal class $= 30$.
Frequency $(f_1)$ of modal class $= 10$.
Frequency $(f_0)$ of class preceding modal class $= 9$.
Frequency $(f_2)$ of class succeeding modal class $= 3$.
Mode $= l + \left(\frac{f_1 - f_0}{2f_1 - f_0 - f_2}\right) \times h = 30 + \left(\frac{10 - 9}{2(10) - 9 - 3}\right) \times 5 = 30 + \left(\frac{1}{20 - 12}\right) \times 5 = 30 + \frac{5}{8} = 30.625$.
Mode $\approx 30.6$.
This represents that most of the states/$U$.$T$. have a teacher-student ratio of approximately $30.6$.
To find the mean,we use the step-deviation method.
Mean $\bar{x} = a + \left(\frac{\sum f_i u_i}{\sum f_i}\right) \times h$.
Using assumed mean $a = 32.5$ and $h = 5$,we calculate $\sum f_i u_i = -23$ and $\sum f_i = 35$.
Mean $\bar{x} = 32.5 + \left(\frac{-23}{35}\right) \times 5 = 32.5 - \frac{23}{7} = 32.5 - 3.2857 \approx 29.21$.
Therefore,the mean of the data is approximately $29.2$.