1.

Compare the modal ages of two groups of students appearing for an entrance test:

Answer»

For Group A: 

Here, 

the maximum frequency is 78, the corresponding class interval 18 -20 is modal class 

l=18, h=2, f=78, f1=50, f2 =46

Mode = I + \(\frac{f-f_1}{2f-f_1-f_2}\times h\)

\(=18+\frac{78-50}{2\times78-50-46}\times2\)

\(=18+\frac{56}{60}\)

=18 + 0.93 =18.93 years

For Group B:

Here, 

the maximum frequency is 89, the corresponding class interval 18 -20 is modal class

l=18, h=2, f=89, f1=54, f2 =40

Mode = I + \(\frac{f-f_1}{2f-f_1-f_2}\times h\) 

\(=18+\frac{89-54}{2\times89-54-40}\times 2\)

\(=18+\frac{70}{84}=18+0.83=18.33\)

Hence, 

the modal age of group A is higher than that of group B.


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