▁the ▁even ▁integer ▁nearest ▁to ▁. ▁Thus , ▁for ▁example , ▁+ 2 3 . 5 ▁becomes ▁+ 2 4 , ▁as ▁does ▁+ 2 4 . 5 ; ▁while ▁− 2 3 . 5 ▁becomes ▁− 2 4 , ▁as ▁does ▁− 2 4 . 5 . ▁This ▁function ▁minim izes ▁the ▁expected ▁error ▁when ▁sum ming ▁over ▁rounded ▁figures , ▁even ▁when ▁the ▁inputs ▁are ▁mostly ▁positive ▁or ▁mostly ▁negative . ▁ ▁This ▁variant ▁of ▁the ▁round - to - near est ▁method ▁is ▁also ▁called ▁conver gent ▁round ing , ▁stat istic ian ' s ▁round ing , ▁Dutch ▁round ing , ▁Gaussian ▁round ing , ▁odd – even ▁round ing , ▁or ▁bank ers ' ▁round ing . ▁ ▁This ▁is ▁the ▁default ▁round ing ▁mode ▁used ▁in ▁IE EE ▁ 7 5 4 ▁floating - point ▁operations ▁( see ▁also ▁Near est ▁integer ▁function ), ▁and ▁ ▁used ▁when ▁round ing ▁to ▁significant ▁figures . ▁ ▁By ▁elimin ating ▁bias , ▁repeated ▁rounded ▁addition ▁or ▁sub tra ction ▁of ▁independent ▁numbers ▁will ▁give ▁a ▁result ▁with ▁an ▁error ▁that ▁tends ▁to ▁grow ▁in ▁proportion ▁to ▁the ▁square ▁root ▁of ▁the ▁number ▁of ▁operations ▁rather ▁than ▁linear ly . ▁See ▁random ▁walk ▁for ▁more . ▁ ▁However , ▁this ▁rule ▁dist ort s ▁the ▁distribution ▁by ▁increasing ▁the ▁probability ▁of ▁ev ens ▁relative ▁to ▁odd s . ▁Typ ically ▁this ▁is ▁less ▁important ▁than ▁the ▁bi ases ▁that ▁are ▁elimin ated ▁by ▁this ▁method . ▁ ▁Round ▁half ▁to