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

Explanation

Case I. Computation of modal Age of Group A:
In group A, class 18-20 has the maximum frequency
So, 18-20 is the modal class and its frequency is 78
`therefore x_k=18, f_k=78, f_(k-1)=50, f_(k+1)=46 and h=2`
`therefore ` mode , ` M_o=x_k+{hxx((f_k-f_(k-1)))/(2f_k-f_(k-1)-f_(k+1)}`
`=18+{2xx((78-50))/((2xx78-50-46))}=18+{(2xx28)/(60)}`
`18+(14)/(15)=18+0.93=18.93`
Case II. Computation of Modal Age of Group B
In group B , class 18-20 has the maximum is 89
So , 18-20 is the modal class and its frequency is 89
`x_k=18, f_k=89, f_(k-1)=54, f_(k+1)=40 and h=2`
`therefore ` mode , ` M_o=x_k+{hxx((f_k-f_(k-1)))/(2f_k-f_(k-1)-f_(k+1)}`
`=18+{2xx((89-54))/((2xx89-54-40))}=18+((2xx35))/((178-94))`
`=18+(70)/(84)=18+5/6=18+0.83=18.83`
Hence , the modal ages of students in group A and are 18.93 years respectively .
`therefore " (modal age in group A)" gt "(modal age in group B)"`