Under　the　condition　that　comparison　results　are　Gaussian　distributed　with　a　common　mean,　a　chi-square　statistics　of　arithmetic　mean　is　proposed　and　investigated　through　the　Monte　Carlo　simulation.　Simulation　results　show　that　the　arithmetic　mean　has　its　own　(n-1)th-order　chi-square　statistics　under　the　condition　that　the　uncertainties　of　participants　are　comparable.　Furthermore,　the　density　curve　of　the　proposed　statistics　is　confined　between　the　(n-1)th-order　and　first-order　chi-square　under　the　condition　that　the　uncertainties　of　participants　are　incomparable.　However,　the　expected　value　of　this　statistics　equals　n-1,　which　is　unaffected　by　the　uncertainties.　Based　on　these　properties,　the　proposed　statistics　is　applied　to　the　consistence　testing　of　arithmetic　mean　by　examples.