Question

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

Answer 1

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 (f₁) of modal class = 10

Frequency (f₀) of class preceding modal class = 9

Frequency (f₂) of class succeeding modal class = 3

It represents that most of the states/U.T have a teacher-student ratio as 30.6.

To find the class marks, the following relation is used.

Taking 32.5 as assumed mean (a), d_i, u_i, and f_iu_i are calculated as follows.

Number of students per teacher	Number of states/U.T (fi)	xi	di = xi − 32.5		fiui
15 − 20	3	17.5	− 15	− 3	− 9
20 − 25	8	22.5	− 10	− 2	− 16
25 − 30	9	27.5	− 5	− 1	− 9
30 − 35	10	32.5	0	0	0
35 − 40	3	37.5	5	1	3
40 − 45	0	42.5	10	2	0
45 − 50	0	47.5	15	3	0
50 − 55	2	52.5	20	4	8
Total	35				− 23

Therefore, mean of the data is 29.2.

It represents that on an average, teacher−student ratio was 29.2.