Here:Maximum class frequency \\\\(=20\\\\)The class corresponding to Maximum class frequency is the modal class.So, Modal class \\\\(=160-165\\\\)Lower limit \\\\(=L=160\\\\)Modal class size \\\\(=h=5\\\\)Frequency of class preceding the modal class \\\\(=f0=8\\\\)Frequency of the modal class \\\\(=f1=20\\\\)Frequency of class succeeding the modal \\\\(=f2=12\\\\)Mode formula is given by,Mode \\\\(=L+\\left( \\dfrac{f_1 -f_0}{2f_1 - f_0 -f_2}\\right)\ imes h\\\\)Mode \\\\(=160+\\left( \\dfrac{20-8}{2(20)-8-12}\\right)\ imes 12\\\\)\\\\(=160+12/20\ imes 5\\\\)\\\\(=163\\\\)The modal height is \\\\(163\\ cm\\\\), which implies maximum number of students have model height \\\\(163\\ cm\\\\)HeightMid Point \\\\((x_i)\\\\)No. of students \\\\((f_i)\\\\)\\\\(f_i x_i\\\\)\\\\(150-155\\\\)\\\\(152.5\\\\) \\\\(15\\\\)\\\\(2287.5\\\\)\\\\(155-160\\\\) \\\\(157.5\\\\) \\\\(8\\\\) \\\\(1260\\\\)\\\\(160-165\\\\)\\\\(162.5\\\\)\\\\(20\\\\)\\\\(3250\\\\)\\\\(165-170\\\\)\\\\(167.5\\\\)\\\\(12\\\\)\\\\(2010\\\\)\\\\(170-175\\\\)\\\\(172.5\\\\)\\\\(5\\\\)\\\\(862.5\\\\)\\\\(\\sum{fi}=60\\\\) \\\\(\\sum {fixi}=9670\\\\)We know,\\\\(\\bar x =\\dfrac{\\sum_{i}f_i x_i}{\\sum_{i}f_1}\\\\)\\\\(=9670/60\\\\)\\\\(=161.17\\\\)Mean is \\\\(161.17\\\\)Thus, \\\\(161.7\\ cm\\\\) is the average height of all the students.