(Q13) 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 15-20 20-25 25-30 30-35 35-40 40-45 45-50 50-55
Number of states 3 8 9 10 3 0 0 2

Answer :

Number of students (C.I) Number of states (fi) Class Marks (xi) ui =
xi - a
h

(h = 5) 		fiui
15-20 3 17.5 -3 -
20-25 8 22.5 -2 -
25-30 9 27.5 -1 -
30-35 10 32.5 a 0
35-40 3 37.5 1
40-45 0 42.5 2
45-50 0 47.5 3
50-55 2 52.5 4
- ∑fi = 35 - - ∑fiui = -

Since the maximum number of states '10' lies in the class interval 30-35, this is the modal class.

Lower boundary of the modal class, l = 30

Frequency of the modal class, f1 = 10

Frequency of the class preceding the modal class f0 = 9

Frequency of the class succeeding the modal class f2 = 3

Height of the class, h = 5

∴ Mode (Z) = l +
f1 - f0
2f1 - f0 - f2
 × h
Mode (Z) = 30 +
-
( - )+( - )
 × 5
Mode (Z) = 30 +
= .625 Mean = x̄ = a +
∑fiui
∑fi
 × h

a = assumed mean = 32.5; h = height of the class = 5

∴ x = 32.5 -
35
 × 5 = .22

Mean = .22

Mode = .625

Mode states have a students - teacher ratio.625. and on an average this ratio is .22