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# 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 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

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 $$\sum f_i \ = \ 35$$ $$\sum f_i x_i \ = \ 1022.5$$

$$\overline{x} \ = \ \frac{ \sum \ f_i x_i}{ \sum f_i}$$

$$= \ \frac{1022.5}{35} \ = \ 29.2$$

$$\therefore$$ mean = 29.2