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No 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 :
The class 30-35 has the maximum frequency, therefore, this is the modal class.
Here l = 30,
h = 5, f1 = 10,
f0 = 9 and
f2 = 3
Now, let us substitute these values in the formula
Mode \(= \ l \ + \ ( \frac{f_1 \ - \ f_0}{2f_1 \ - \ f_0 \ - \ f_2}) \ × \ h \)
\( = \ 30 \ + \ ( \frac{10 \ - \ 9}{2 \ × \ 10 \ - \ 9 \ - \ 3}) \ × \ 5 \)
\(= \ 30 \ + \ \frac{10 \ - \ 9}{20 \ - \ 9 \ - \ 3} \ × \ 5 \)
\(= \ 30 \ + \ \frac{1}{8} \ × \ 5 \ = \ 30 \ + \ 0.625 \)
\( = \ 30.625 \ = \ 30.6 \)
Calculation of mean :
Class Interval | Frequency \( (f_i) \) | Mid-point \( (x_i) \) | \( f_i x_i \) |
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 |
\( \sum f_i \ = \ 35 \) | \( \sum f_i x_i \ = \ 1022.5 \) |