The Barnum Family, 1350-1907 shows an additional child of Levi, Horace W. Barnum (1817-1858), who is shown by other sources as Levi's brother. The confusion may be with Levi's son Horace Barnum (1837-1838).
In the 1850 US Census for East hartford, hartford County, Connecticut the family of Levi P. Barnum was enumerated as follows:
Dwelling #364; Feqmily #407
Levi Barnum, 33, M, Hatter, $700, b. Connecticut
Julia A. Barnum, 38, F, b. Connecticut
Adeline Barnum, 10, F, b. Connecticut, Attended school within the year
Harriet Barnum, 6, F, b. Connecticut, Attended school within the year
Levi Peck Barnum should not be confused with Levi Barnum, son of David Barnum and Jemima Stevens, who has the same years of both birth and death, but different days and months.