Given below is the frequency distribution of the heights pof the players in a school

Find the average height of the maximum number of students?

Explanation

The given data is an inclusive series.So, we convert it into an eaculsive form,as given below .

Clearly, the class 165.5-168.5 has maximum frequency , so its the modal class.`therefore x_k=165.5,f_(k-1)=127 and h =3 `
Mode,`M_0=x_k+{hxx((f_k-f_(k-1)))/((2f_k-f_(k-1)-f_(k+1)))}`
`=165.+{3xx((142-118))/((2xx142 -118-127))}`
`=165.5+{(3xx24)/39}=165.5 +24/13`
`=165.5+1.85 =167.35`
Thus , modal height =167.35 cm
This mens that the height of maximum number of players in the school is cm (approx)