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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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