2 , ▁or ▁ 2 0 %. ▁This ▁means ▁that ▁the ▁total ▁return ▁over ▁the ▁ 2 - year ▁period ▁is ▁the ▁same ▁as ▁if ▁there ▁had ▁been ▁ 2 0 % ▁growth ▁each ▁year . ▁The ▁order ▁of ▁the ▁years ▁makes ▁no ▁difference ▁– ▁the ▁average ▁percentage ▁returns ▁of ▁+ 6 0 % ▁and ▁− 1 0 % ▁is ▁the ▁same ▁result ▁as ▁that ▁for ▁− 1 0 % ▁and ▁+ 6 0 %. ▁ ▁This ▁method ▁can ▁be ▁generalized ▁to ▁examples ▁in ▁which ▁the ▁periods ▁are ▁not ▁equal . ▁For ▁example , ▁consider ▁a ▁period ▁of ▁a ▁half ▁of ▁a ▁year ▁for ▁which ▁the ▁return ▁is ▁− 2 3 % ▁and ▁a ▁period ▁of ▁two ▁and ▁a ▁half ▁years ▁for ▁which ▁the ▁return ▁is ▁+ 1 3 %. ▁The ▁average ▁percentage ▁return ▁for ▁the ▁combined ▁period ▁is ▁the ▁single ▁year ▁return , ▁R , ▁that ▁is ▁the ▁solution ▁of ▁the ▁following ▁equation : ▁, ▁giving ▁an ▁average ▁return ▁R ▁of ▁ 0 . 0 6 0 0 ▁or ▁ 6 . 0 0 %. ▁ ▁Mov ing ▁average ▁ ▁Given ▁a ▁time ▁series ▁such ▁as ▁daily ▁stock ▁market ▁prices ▁or ▁year ly ▁temper atures ▁people ▁often ▁want ▁to ▁create ▁a ▁sm o other ▁series . ▁This ▁helps ▁to ▁show ▁underlying ▁tr ends ▁or ▁perhaps ▁periodic ▁behavior . ▁An ▁easy ▁way ▁to ▁do ▁this ▁is ▁the ▁moving ▁average : ▁ ▁one ▁cho oses ▁a ▁number ▁n ▁and ▁creates ▁a ▁new ▁series ▁by ▁taking ▁the ▁arithmetic ▁mean ▁of ▁the ▁first ▁n ▁values ,