The Barnum Family, 1517-1904 provides the note: "There are 5 sons. See other sheet." But no other sheet could be found. Other records do exist, however, for all five sons.
Joseph I. Barnum apparently had at least one sister, who has not been identified. He received a letter in 1908 from his niece Helene R. Warnock, living at 205 Miles Street in Cranford, New Jersey. In the letter, she asked him to come and visit because "We have so few relatives that Mother clings closer to those we have."
In the 1880 US Census for District 637, New York (Manhattan), New York City-Greater, New York the family of Joseph I. Barnum was enumerated as follows:
Dwelling #21; Family #48
Barnum, Joseph I.; W; M; 42; Husband; Married; Retired; b. Connecticut; Both parents b. Connecticut
Barnum, Theresa; W; F; 42; Wife; Married; Keeps House; b. New York; Both parents b. Virginia
Barnum, Fayette; W; M; 20; Son; Single; Bank clerk; b. New York, Father b. Connecticut; Mother b. New York
Barnum, Charles E.; W; M; 14; Son; Single; Scholar; b. New York, Father b. Connecticut; Mother b. New York
Barnum, William A.; W; M; 12; Son; Single; Scholar; b. New York, Father b. Connecticut; Mother b. New York
Barnum, Edward A.; W; M; 10; Son; Single; Scholar; b. New York, Father b. Connecticut; Mother b. New York
Barnum, Hannah A.; W; F; 73; Father's mother; Widowed; At home; b. Connecticut; Both parents b. Connecticut
Lee, Laura J.; W; F; 40; Single; Household servant; Cannot read or write; b. Virginia; Both parents b. Virginia
In the 1910 US Census for District 679, Manhattan Ward 12, New York, New York the family of Joseph I. Barnum was enumerated as follows:
179th Street and Fort Washington Avenue
Family #149
Barnum, Joseph; Head; M; W; 72; Married 52 years; b. Connecticut; Both parents b. Connecticut; Speaks English; Secretary; Insurance Company; Wage earner; Employed full year; Can read and write; Rents house
Barnum, Theresa A.; Wife; F; W; 74; Married 52 years; b. New York; Father b. Germany; Mother b. New York; Speaks English; Can read and write
Barnum, Edward A.; Son; M; W; 39; Single; b. New York, Father b. Connecticut; Mother b. New York; Speaks English; Manufacturer; Millinery gents; Employee; Employed full year; Can read and write
Butler, Katherine; Servant; F; W; 40; Single; b. Ireland; Both parents b. Ireland; Speaks English; Servant; Private family; Wage earner; Can read and write
Seves, Marie E.; Boarder; F; W; 18; Single; b. New York; Father b. New York; Mother b. Ireland; Speaks English; Saleswoman; Dry goods; Wage earner; Employed full year; Can read and write
Travis, Elizabeth; Nurse; F; W; 47; Single; b. New York; Both parents b. New York; Speaks English; Nurse; Private family; Wage earner; Employed full year; Can read and write The Barnum Family, 1350-1907 gives a birth date of 1930.
From the New York Times, June 16, 1912: Joseph I. Barnum, 75 years old, Secretary and General Manager of the National Accident Company, died on Friday night (June 14, 1912) in his home in the Hudson Arms Apartments, Fort Washington Avenue and 179th Street, Manhattan. Death was due to shock following the death of his daughter-in-law, Mrs. Edward Barnum a week ago. Mr. Barnum, who was born in Norwalk, Connecticut, organized the National Accident Society, becoming its Secretary and General Manager.