▁then ▁moving ▁forward ▁one ▁place ▁by ▁dro pping ▁the ▁oldest ▁value ▁and ▁introdu cing ▁a ▁new ▁value ▁at ▁the ▁other ▁end ▁of ▁the ▁list , ▁and ▁so ▁on . ▁This ▁is ▁the ▁simplest ▁form ▁of ▁moving ▁average . ▁More ▁complicated ▁forms ▁involve ▁using ▁a ▁weight ed ▁average . ▁The ▁weight ing ▁can ▁be ▁used ▁to ▁enh ance ▁or ▁suppress ▁various ▁periodic ▁behavior ▁and ▁there ▁is ▁very ▁extensive ▁analysis ▁of ▁what ▁weight ings ▁to ▁use ▁in ▁the ▁ ▁literature ▁on ▁filtering . ▁In ▁digital ▁signal ▁processing ▁the ▁term ▁" mov ing ▁average " ▁is ▁used ▁even ▁when ▁the ▁sum ▁of ▁the ▁weights ▁is ▁not ▁ 1 . 0 ▁( so ▁the ▁output ▁series ▁is ▁a ▁scale d ▁version ▁of ▁the ▁aver ages ). ▁The ▁reason ▁for ▁this ▁is ▁that ▁the ▁anal yst ▁is ▁usually ▁interested ▁only ▁in ▁the ▁tr end ▁or ▁the ▁periodic ▁behavior . ▁ ▁History ▁ ▁Origin ▁ ▁The ▁first ▁recorded ▁time ▁that ▁the ▁arithmetic ▁mean ▁was ▁extended ▁from ▁ 2 ▁to ▁n ▁cases ▁for ▁the ▁use ▁of ▁estimation ▁was ▁in ▁the ▁six teenth ▁century . ▁From ▁the ▁late ▁six teenth ▁century ▁on wards , ▁it ▁gradually ▁became ▁a ▁common ▁method ▁to ▁use ▁for ▁reducing ▁errors ▁of ▁measurement ▁in ▁various ▁areas . ▁At ▁the ▁time , ▁astronom ers ▁wanted ▁to ▁know ▁a ▁real ▁value ▁from ▁no isy ▁measurement , ▁such ▁as ▁the ▁position ▁of ▁a ▁planet ▁or ▁the ▁diameter ▁of ▁the ▁moon . ▁Using ▁the ▁mean ▁of ▁several ▁measured ▁values , ▁scient ists ▁assumed ▁that ▁the ▁errors ▁add ▁up ▁to ▁a ▁relatively