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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.

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Since the maximum number of states ‘10’ lies in the class interval 30-35, this is the modal class. 

Lower boundary of the modal class, l = 30 

Frequency of the modal class, f1 = 10 

Frequency of the class preceding the modal class = f0 = 9 

Frequency of the class succeeding the modal class = f2 = 3 

Height of the class, h = 5 

a = assumed mean = 32.5; h = height of the class = 5 

∴ x = 32.5 – \(\frac{23}{35 }\) × 5 

= 32.5 – 3.28 

= 29.22 

Mean = 30.625 

Mode = 29.22 

Mode states have a students – teacher ratio 29.22 and on an average this ratio is 30.625.

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