Question :
| 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 |
Solution :
The class (30 – 35) has the maximum frequency. Therefore, this is the modal class.
Here, l = 30, h = 5, \(f_1\) = 10, \(f_0\) = 9 and \(f_2\) = 3.
Now, let us substitute these values in the formula
Mode = l + (\(f_1 – f_0\over 2f_1 – f_0 – f_2\))\(\times\) h
Mode = 30 + \(10 – 9\over 20 – 9 – 3\) \(\times\) 5
Mode = 30 + 0.625 = 30.625
Calculation of mean :
Number of students per teacher
Number of states/U.T.
Mid-point (\(x_i\)
\(f_iu_i\)
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
105.5
Total
35
40
1022.5
\(\bar{x}\) = \(\sum f_ix_i\over \sum f_i\) = \(1022.5\over 35\) = 29.2
Mean = 29.2
Thus, most states/U.T have a student teacher ration of 30.6 and on average, the ratio is 29.2
