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