Alfred E. Mingus and Ephragm Mingus may actually be the same person. Their apparent birth dates are within the same range.
"Ephragm" was found on 1850 census with apparent parents and siblings. "Alfred" was not present with this family on the 1850 census.
"Alfred E." was found on a death certificate which gave his parents' names, which links him to this family.
I personally haven't yet found a documented record that shows both full names for the same person, but am inclined to believe that they are. Future editions of this family may be updated to combine them into one person.