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 teacherNumber 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 $$29.2$$.MathematicsRS AgarwalStandard X

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