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 is =  30

Frequency (f₁) of modal class = 10

Frequency (f₀) of the preceding modal class = 9

Frequency (f₂) of the succeeding modal class = 3

`Mode = l+((f_1-f_0)/(2f_1-f_0-f_2) xxh)`

= `30+((10-9)/2(10)-9-3)xx(5)`

=`30+(1/(20-12))xx 5`

=` 30 + 5/8`

= 30.625

Mode = 30.6

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

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

`"Class mark" = ("Upper class limit + Lower class limit")/2`

Taking 32.5 as the 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.	`u_i=d_i/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

Mean, `barx = a+((sumf_iu_i)/(sumf_i))xxh`

= `32.5 +((-23)/35)xx5`

= `32.5 - 23/7 `

= 32.5 - 3.28

= 29.22

Therefore, the mean of the data is 29.2.

It represents that, on average, the teacher-student ratio was 29.2