# The following distribution gives the step-wise teacher-student ration in higher secondary schools of India. Find the mode and mean of this data. Interpret the two measures.

## 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 :

$$\bar{x}$$ = $$\sum f_ix_i\over \sum f_i$$ = $$1022.5\over 35$$ = 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