Arthur was 9 in 1881, so born ~1872, but his mother Elizabeth didnt marry until 1883. Therefore, this first record is the most likely:
Name: Arthur Eddowes Year of Registration: 1872 Quarter of Registration: Oct-Nov-Dec District: Wrexham (1837-1974) County: Cheshire, Denbighshire, Flintshire Volume: 11b Page: 296
Name: Arthur Roberts Year of Registration: 1871 Quarter of Registration: Jan-Feb-Mar District: Wrexham (1837-1974) County: Cheshire, Denbighshire, Flintshire Volume: 11b Page: 305
Name: Arthur Roberts Year of Registration: 1873 Quarter of Registration: Oct-Nov-Dec District: Wrexham (1837-1974) County: Cheshire, Denbighshire, Flintshire Volume: 11b Page: 281