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.

Question :

Number of students per teacherNumber of states/U.T.
15 – 203
20 – 258
25 – 309
30 – 3510
35 – 403
40 – 450
45 – 500
50 – 552

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 :

Number of students per teacherNumber of states/U.T.Mid-point (\(x_i\)\(f_iu_i\)
15 – 20317.552.5
20 – 25822.5180.0
25 – 30927.5247.5
30 – 351032.5325.0
35 – 40337.5112.5
40 – 45042.50
45 – 50047.50
50 – 55252.5105.5
Total35401022.5

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

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