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 20 – 25 25 – 30 30 – 35 35 – 40 40 – 45 45 – 50 50 – 55 | 3 8 9 10 3 0 0 2 |
As per the question:
Modal class = 30-35
l = 30
h = 5
f1 = 10
f0 = 9
f2 = 3
= 
= 30.625
Class interval | fi | xi | di= xi-a | ui | 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 |
∑fi=35 | ∑fiui =-23 |
Hence, the mean can be calculated as below:
= 32.5 -
= 29.22
10