Q. 104.9( 7 Votes )

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:

Answer :

To find: The mean and mode of the given table.

Mode is calculated as:


l=lower limit of modal class

h=width of the modal class

f=frequency of the modal class

f1=frequency of the class preceding the modal class

f2= frequency of the class following the modal class

Since, the maximum class frequency is 10

Hence, modal class interval= 30-35

h= 5, l=30, f= 10,f1=9 and f2=3

⇒ Mode = 30 + 0.625
⇒ Mode = 30.625
Now to find mean,
Use the formula,


A = assumed mean


h=length of class intervals

ui= (xi-A)/h

N=sum of all frequencies

Here A = 32.5
h = 5
N = 35

⇒ Mean = 32.5-3.28
⇒ Mean = 29.21

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