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	Number of students per Teacher	Number of State/ U.T
15−20 20−25 25−30 30−35	3 8 9 10	35−40 40−45 45−50 50−55	3 0 0 2

Answer 1

Number of students per teacher	Number of states/U.T. (fi)	xi	f i xi
15−20	3	17.5	52.5
20−25	8	22.5	180.0
25−30	9	27.5	247.5
30−35	10	32.5	325.0
35−40	3	37.5	112.5
40−45	0	42.5	0
45−50	0	47.5	0
50−55	2	52.5	105.0

Here, the maximum frequency is 10 so the modal class is 30−35.

Therefore,

Thus, the mode of the data is 30.6.

Now,
Mean of the data = $\frac{\sum _{}{f}_i{x}_i}{\sum _{}{f}_i}=\frac{1022.5}{35}=29.2$
Thus, the mean of the data is 29.2.

The mode of the number of students per teacher in the states is more than the mean of the number of students per teacher in the states.