1850 census of Morgan Co., Ky, enumerated 23 Aug, lists on p. 58 as family #371:
Wiley Barker, 25, laborer; Elizabeth, 20; Thomas, 2; John, 3/12. All born in Kentucky.

The preceding household is headed by Elizabeth’s parents, Thomas R. Loveless age 46 and Malinda (Day) age 38.

1860 census of Morgan Co., Ky, division 2, West Liberty P.O., enumerated 27 June, lists on p. 19 as family #117:
Wiley Barker, 38, farmer; Elizabeth, 28; Thomas, 11; John M., 8; Sarah, 6; Malinda, 5; Mary, 2.

1870 census of Morgan Co., Ky, Black Water precinct, enumerated 26 Aug, lists on p. 1 as family #3:
Barker, Wiley, 47, farmer; Elizabeth, 38; John M., 20; Sarah, 17; Malina, 15; Mary, 13; Travis, 8; Malinda, 6; Perlina, 3; Priscilla, 1. All born in Kentucky.

1880 census of Morgan Co., Ky, Black Water precinct, enumerated 8 June, lists on p. 11 as family #85/87:
Barker, Wiley, 58, b. Ky SC Va, farmer; Elizabeth, 48, wife, b. Ky Ky Ky; Malenia D., 24, dau; Travis, 19, son; Malinda A., 16, dau; Perlina, 13, dau; Precilla, 11, dau; Williamson B., 8, son; Margaret E., 5, dau; Mary A. Pery, 23, dau, married; Lilliean, 3/12, b. Feb, granddau. All children born Ky Ky Ky.

1895 census of Linn Co., Kansas, Liberty township, lists on p. 13 as family #90:
Elizabeth Barker, 63; Bruce Barker, 23; Perlina Barker, 26; Lillie Perry, 15. All born in Kentucky.

1900 census of Miami Co., Kansas, Osawatomie, enumerated 13 June, lists on p. 14B as family #312/326:
Barker, Elizabeth, 67, b. Jan 1833, Ky Illinois Ky, widowed, mother of 4 children, 4 living; Thomas, son, 52, b. Oct 1847, Ky Ky Ky, restaurant; John, son, 50, b. March 1850, Ky Ky Ky, carpenter; William B., son, 37, b. June 1872, Ky Ky Ky, day laborer. Chase, Magie, dau, 25, b. Aug 1874, Ky Ky Ky, widowed, mother of 2 children, 2 living; Boyd, grandson, 3, b. June 1896, Kans NY Ky; Bruce, grandson, 1, b. Aug 1898, Kans NY Ky.

Elizabeth seems to have interpreted the “number of children” question to be the number living in the household.