▁ 1 3 ▁and ▁orders ▁it ▁to ▁read ▁ 1 , ▁ 3 , ▁ 7 , ▁ 1 3 . ▁Then ▁the ▁ 1 ▁and ▁ 1 3 ▁are ▁removed ▁to ▁obtain ▁the ▁list ▁ 3 , ▁ 7 . ▁Since ▁there ▁are ▁two ▁elements ▁in ▁this ▁remaining ▁list , ▁the ▁median ▁is ▁their ▁arithmetic ▁mean , ▁( 3 ▁+ ▁ 7 )/ 2 ▁= ▁ 5 . ▁ ▁Mid - range ▁ ▁The ▁mid - range ▁is ▁the ▁arithmetic ▁mean ▁of ▁the ▁highest ▁and ▁lowest ▁values ▁of ▁a ▁set . ▁ ▁Sum mary ▁of ▁types ▁ ▁The ▁table ▁of ▁mathematical ▁symbols ▁explains ▁the ▁symbols ▁used ▁below . ▁ ▁Mis cell aneous ▁types ▁ ▁Other ▁more ▁s oph istic ated ▁aver ages ▁are : ▁tr ime an , ▁trim ed ian , ▁and ▁normal ized ▁mean , ▁with ▁their ▁general izations . ▁ ▁One ▁can ▁create ▁one ' s ▁own ▁average ▁metric ▁using ▁the ▁generalized ▁f - mean : ▁▁▁▁ ▁where ▁f ▁is ▁any ▁invert ible ▁function . ▁The ▁harm onic ▁mean ▁is ▁an ▁example ▁of ▁this ▁using ▁f ( x ) ▁= ▁ 1 / x , ▁and ▁the ▁geometric ▁mean ▁is ▁another , ▁using ▁f ( x ) ▁= ▁log   x . ▁ ▁However , ▁this ▁method ▁for ▁generating ▁means ▁is ▁not ▁general ▁enough ▁to ▁capture ▁all ▁aver ages . ▁ ▁A ▁more ▁general ▁method ▁for ▁defining ▁an ▁average ▁takes ▁any ▁function ▁g ( x 1 ,   x 2 ,   ...,   x n ) ▁of ▁a