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 student 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

By formula,

Mode = l + $\Big(\dfrac{f$1 - f0}{2f1 - f0 - f_2}\Big) \times h

Here,

1. Class size is h.

2. The lower limit of modal class is l

3. The Frequency of modal class is f₁.

4. Frequency of class preceding modal class is f₀.

5. Frequency of class succeeding the modal class is f₂.

Class 30 - 35 has the highest frequency.

∴ It is the modal class.

∴ l = 30, f₁ = 10, f₀ = 9, f₂ = 3 and h = 5.

Substituting values we get :

$\text{Mode} = 30 + \Big(\dfrac{10 - 9}{2 \times 10 - 9 - 3}\Big) \times 5 \\[1em] = 30 + \dfrac{1}{20 - 12} \times 5 \\[1em] = 30 + \dfrac{5}{8} \\[1em] = 30 + 0.625 \\[1em] = 30.625 ≈ 30.6$

We will find mean using direct method.

By formula,

Mean = $\dfrac{Σf$ixi}{Σf_i} = \dfrac{1022.5}{35} = 29.2

Hence, mode = 30.6 and median = 29.2 so, most states/U.T. have a student teacher ratio of 30.6 and on an average, this ratio is 29.2