The 1850 US Census for Carlton, Barry, Michigan enumerates the family of Henry P. Barnum [note the difference in middle initial] as follows:
Household #751; Family #770
Barnum, Henry P; 26; M; Farmer; real estate value $2,000; b. N York
Barnum, Sarah A; 25; F; b. N York
Barnum, Austin C; 3; M; b. Michigan
Barnum, Biola A; 8/12; F; b. Michigan
Living next door, in Household #752; Family #771 was Barnum, Betsey; 65; F; N York [Henry's mother]
In household #753; Family #772 lived Seth P. Fester, 21, who may have been a relative, since Henry's mother's maiden name appears as Ferster.
The 1850 census shows at least eight other Barnum family groups, as well as the families of several in-laws, located in the same town.