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.