▁Example : ▁Ge ometric ▁mean ▁of ▁ 2 ▁and ▁ 8 ▁is ▁ ▁Harm onic ▁mean ▁Harm onic ▁mean ▁for ▁a ▁non - empty ▁collection ▁of ▁numbers ▁a 1 ,   a 2 ,   ...,   an , ▁all ▁different ▁from ▁ 0 , ▁is ▁defined ▁as ▁the ▁reci pro cal ▁of ▁the ▁arithmetic ▁mean ▁of ▁the ▁reci pro cal s ▁of ▁the ▁a is : ▁▁▁▁ ▁One ▁example ▁where ▁the ▁harm onic ▁mean ▁is ▁useful ▁is ▁when ▁exam ining ▁the ▁speed ▁for ▁a ▁number ▁of ▁fixed - distance ▁tri ps . ▁For ▁example , ▁if ▁the ▁speed ▁for ▁going ▁from ▁point ▁A ▁to ▁B ▁was ▁ 6 0   km / h , ▁and ▁the ▁speed ▁for ▁returning ▁from ▁B ▁to ▁A ▁was ▁ 4 0   km / h , ▁then ▁the ▁harm onic ▁mean ▁speed ▁is ▁given ▁by ▁ ▁I ne quality ▁concerning ▁AM , ▁G M , ▁and ▁H M ▁A ▁well ▁known ▁inequality ▁concerning ▁arithmetic , ▁geometric , ▁and ▁harm onic ▁means ▁for ▁any ▁set ▁of ▁positive ▁numbers ▁is ▁▁▁▁ ▁( The ▁alphabet ical ▁order ▁of ▁the ▁letters ▁A , ▁G , ▁and ▁H ▁is ▁preserved ▁in ▁the ▁inequality .) ▁See ▁I ne quality ▁of ▁arithmetic ▁and ▁geometric ▁means . ▁ ▁Thus ▁for ▁the ▁above ▁harm onic ▁mean ▁example : ▁AM ▁= ▁ 5 0 , ▁G M ▁ ≈ ▁ 4 9 , ▁and ▁H M ▁= ▁ 4 8   km / h . ▁ ▁Statist ical ▁location ▁The ▁mode , ▁the ▁median , ▁and