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Question

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.
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

Mode: The class which have highest frequency.
In this case, class interval $$30-35$$ is the modal class.
Now,
Lower limit of modal class, $$l = 30, h = 5, f_1, = 10, f_0 = 9, f_2 = 3$$
We know that,
Mode =$$ l + \left(\dfrac{f_1- f_0}{2f_1-f_0-f_2 }\right) \times h$$$$= 30 + \left(\dfrac{10- 9}{2(10)-9-3 }\right) \times 5$$
$$= 30+ \left(\dfrac{1}{20-12}\right) 5$$
$$= 30 + \dfrac{1}{8} \times 5$$
Mode $$= 30.625 \equiv 30.6$$
for mean,
Mean, $$\bar x = \dfrac{\sum f_iu_i}{\sum f_i}$$
$$\bar x = \dfrac{1022.5}{35} = 29.2$$
Therefore, 
Most states/U.T. have a student teacher ratio of $$30.6$$ and on an average, the ratio is $$29.2$$.

498551_465489_ans_7c9188d7eb7c44a88f01aed0112bb86a.png

Mathematics
RS Agarwal
Standard X

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