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.

For mode:

Here, highest frequency is 10.

So, the modal class = 30-35

Mode is given by

Where,

L = Lower class limit of the modal class = 30

h = class interval of the modal class = 5

f₁ = frequency of the modal class = 10

f₀ = frequency of the class preceding the modal class = 9

f₂ = frequency of the class succeeding the modal class = 3

Substituting values in the formula of mode,

⇒

⇒ Mode = 30 + 0.625

⇒ Mode = 30.625

Or approximately, mode = 30.6

For mean:

Let’s solve by using direct method as values are small.

Let’s draw a table showing midpoints and frequencies.

Mean is given by

⇒ Mean = 1022.5/35

⇒ Mean = 29.2

Thus, mode is 30.6 and mean is 29.2.

Mode implies that most states have student teacher ratio of 30.6 and mean implies that on an average, student teacher ratio in most states is found to be 29.2.