I noticed in two of the three censuses that I looked at that Arthur stated his mother was born in England and his father in OH.
I found this family in the 1880 census for East Cleveland, Cuyahoga Co, OH: KING, C.S. age 32 b. OH wife Hannah age 25 b. England son Leanord age 6 b. OH son Arthur age 6 b. OH son Harry age 4 b. OH son Claude age 3 b. OH dau Carry age 1 b. OH
In 1900 this family is located in Mattoon, Coles Co, IL, the same town, county and state as Arthur and Gertrude's family: KING, Chas.S. b. Jan 1848 in OH, married 36 yrs, both parents b. RI wife Hannah b. Aug 1853 in England, 12 children born, 11 children living, both parents b. England son Harry C. b. Mar 1876 in OH son Bert H. b. Aug 1880 in OH son Ralph M. b. June 1883 in IL son William S. b. Oct 1886 in IL dau Emma M. b. Aug 1888 in IL son George T. b. Mar 1890 in IL dau Ruth G. b. Dec 1891 in IL son Paul J. b. Apr 1894 in IL
By 1910 Hannah is listed as a widow.She and the youngest 4 children are still in Mattoon.