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	3
45-50	0
50-55	2

Mode: The class which has the highest frequency.
In this case, class interval 30-35 is the modal class.
Now, Lower limit of modal class, l = 30, h = 5, f1 = 10, f0 = 9, f2 = 3
We know that,
Mode = l + ((f1 - f0) / (2f1 - f0 - f2)) * h
= 30 + ((10 - 9) / (2(10) - 9 - 3)) * 5
= 30 + (1 / (20 - 12)) * 5
= 30 + (1 / 8) * 5
= 30 + 5/8
Mode = 30.625 ≈ 30.6

for mean,
Mean, x̄ = Σfiui / Σfi
To calculate the mean, we need to find the midpoints of each class interval and multiply them by their respective frequencies:

Therefore,
Most states/U.T. have a student-teacher ratio of 30.6 and on an average, the ratio is 32.86.