▁small ▁number ▁when ▁compared ▁to ▁the ▁total ▁of ▁all ▁measured ▁values . ▁The ▁method ▁of ▁taking ▁the ▁mean ▁for ▁reducing ▁observation ▁errors ▁was ▁indeed ▁mainly ▁developed ▁in ▁astronom y . ▁A ▁possible ▁prec ursor ▁to ▁the ▁arithmetic ▁mean ▁is ▁the ▁mid - range ▁( the ▁mean ▁of ▁the ▁two ▁extreme ▁values ), ▁used ▁for ▁example ▁in ▁Arab ian ▁astronom y ▁of ▁the ▁nin th ▁to ▁ele vent h ▁centuries , ▁but ▁also ▁in ▁met all ur gy ▁and ▁navigation . ▁ ▁However , ▁there ▁are ▁various ▁older ▁vague ▁references ▁to ▁the ▁use ▁of ▁the ▁arithmetic ▁mean ▁( which ▁are ▁not ▁as ▁clear , ▁but ▁might ▁reason ably ▁have ▁to ▁do ▁with ▁our ▁modern ▁definition ▁of ▁the ▁mean ). ▁In ▁a ▁text ▁from ▁the ▁ 4 th ▁century , ▁it ▁was ▁written ▁that ▁( text ▁in ▁square ▁brackets ▁is ▁a ▁possible ▁missing ▁text ▁that ▁might ▁clarify ▁the ▁meaning ): ▁ ▁In ▁the ▁first ▁place , ▁we ▁must ▁set ▁out ▁in ▁a ▁row ▁the ▁sequence ▁of ▁numbers ▁from ▁the ▁mon ad ▁up ▁to ▁nine : ▁ 1 , ▁ 2 , ▁ 3 , ▁ 4 , ▁ 5 , ▁ 6 , ▁ 7 , ▁ 8 , ▁ 9 . ▁Then ▁we ▁must ▁add ▁up ▁the ▁amount ▁of ▁all ▁of ▁them ▁together , ▁and ▁since ▁the ▁row ▁contains ▁nine ▁terms , ▁we ▁must ▁look ▁for ▁the ▁nin th ▁part ▁of ▁the ▁total ▁to ▁see ▁if ▁it ▁is ▁already ▁naturally ▁present ▁among ▁the ▁numbers ▁in ▁the ▁row ; ▁and ▁we ▁will ▁find ▁that ▁the