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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.

4.   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.

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The class having maximum frequency is the modal class.

The maximum frequency is 10 and hence the modal class = 30-35

Lower limit (l) of modal class = 30, class size (h) = 5

Frequency ( f_1 ) of the modal class = 10 frequency ( f_0 ) of class preceding the modal class = 9, frequency ( f_2 ) of class succeeding the modal class = 3

Mode = l + \left(\frac{f_1-f_0}{2f_1 - f_0 - f_2} \right).h

\\ = 30 + \left(\frac{10-9}{2(10)-9-3} \right).5 \\ \\ = 30 + \frac{1}{8}.5

= 30.625

Thus, Mode of the data is 30.625

Now,

Let the assumed mean be a = 32.5 and h = 5

Class

Number of

states f_i

Class mark

x_i

d_i = x_i -a u_i = \frac{d_i}{h} f_iu_i
15-20 3 17.5 -15 -3 -9
20-25 8 22.5 -10 -2 -16
25-30 9 27.5 -5 -1 -9
30-35 10 32.5 0 0 0
35-40 3 37.5 5 1 3
40-45 0 42.5 10 2 0
45-50 0 47.5 15 3 0
50-55 2 52.5 20 4 8
 

\sum f_i

=35

     

\sum f_ix_i

= -23

Mean, 

\overline x =a + \frac{\sum f_iu_i}{\sum f_i}\times h 
= 32.5 + \frac{-23}{35}\times5= 29.22

Thus, the Mean of the data is 29.22

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