In the 1860 US Census for Jefferson, Schoharie County, New York the family of Joseph Barnum was enumerated as follows:
Dwelling #52; Family #52
Joseph Barnum, 23, M, Farmer, Real property $1,900, Personal property $265, b. New York
Naomi Barnum, 21, F, b. New York
In the 1870 US Census for Jefferson, Schoharie County, New York the family of Joseph Barnum was enumerated as follows:
Dwelling #1; Family #77
Barnum, Joseph; 33; M; W; Farmer; Real property $6,000; Personal property $1,278; b. New York; Male citizen of US of 21 years of age and upwards
Barnum, Naoma; 31; F; W; Housekeeping; b. New York
Smith, Buck; 21; M; W; Farmer; b. New York; Male citizen of US of 21 years of age and upwards
In the 1880 US Census for Jefferson, Schoharie County, New York the family of Joseph Barnum was enumerated as follows:
Dwelling #264; Family #275
Barnum, Joseph; W; M; 43; Married; Farmer; b. New York; Both parents b. New York
Barnum, Naomi A.; W; F; 41; Wife; Married; Keeping house; b. New York; Both parents b. New York
Barnum, John M.; W; M; 11; Adopted son; Single; At school; Attended school within the census year; b. New York; Both parents b. Ireland