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

No 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

Given data:

Modal class = 30 – 35,

l = 30,

Class width (h) = 5,

f_m = 10, f₁ = 9 and f₂ = 3

Mode Formula:

Mode = l+ [($\frac{f_m-f_1}{2f_m-f_1-f_2}$]×h

Substitute the values in the given formula

Mode = 30+($\frac{10-9}{20-9-3}$)×5

Mode = 30+$\frac{5}{8}$ = 30+0.625

Mode = 30.625

Therefore, the mode of the given data = 30.625

Calculation of mean:

Find the midpoint using the formula, x_i =$\frac{upper limit+lower limit}{2}$

Mean = x̄ = $\frac{{\displaystyle \sum _{ }}{f}_i{x}_i}{\sum _{ }{f}_i}$

= $\frac{1022.5}{35}$

= 29.2

Therefore, mean = 29.2