About May K Rogers
The Sources tab has a reproduction of Mary/May's death record because of age questions that may come up when viewing her documents. Indeed her death record says she was born in 1857. But that is consistent with the 1900, 1910, and 1920 census. Her death record also says she was born in Vermont to Stephen Rogers and unknown Stone. That definitely establishes her identity as this person, the Mary K Rogers born 1850 as enumerated in the 1860 census of Ohio Grove Township, Mercer County, Illinois.
In the 1880 census her age would put her birth in 1852, when already using the name May.