Data source was Richard I. Luht, now deceased.
1870 Census, MD, Baltimore, District 4, dwelling 198, page 252
Cole, Noah H., 33, teacher, b: MD
" , Sophia, wife, 33, keeping house, b: MD
" , Wm A, 6, b: MD
" , Carrie L., 4, b: MD
" , Emily, 2, b: MD
1880 Census MD, Baltimore, District 5
Cole, Noah H., 43, school teacher, b: MD/MD/MD
" , Sophine, 43, wife, keeping house, b: MD/MD/MD
" , William A., 16, son, at school, b: MD/MD/MD
" , Emily S., 11, dau, at school, b: MD/MD/MD
" , Noah H., 9, son, b: MD/MD/MD
" , Annie, 7, dau, b: MD/MD/MD
" , Joseph O., 5, son, b: MD/MD/MD
" , Mary, 3, dau, b: MD/MD/MD
In the 1900 census, Noah H Cole is listed 2 times. It would appear that he was living in Washington DC with 2 of his daughters, Annie and Mary. Sophia is not in the household when the census was taken on June 4th. On July 11th, both of them are enumerated as living with their son, Noah in New Jersey. Ages and birth years do not appear to have been given or recorded accurately. Perhaps Sophia was visiting her son on June 4th and that is why she was not enumerated with Noah.
1900 Census, Washington, DC, 7th Street, ED 62, 4th June
Cole, Noah H., head, Sept 1839, 60, married 36 yrs, 8 children, 6 living, b: MD/MD/MD, no occupation.
" , Mary B, dau, Jan 1880, 20, single, b: MD/MD/MD stenographer
Childs, Annie, dau., Nov 1875, m: 8 yrs, no children, b: MD/MD/MD, clerk
1900 Census, NJ, Hudson Co., Jersey City Ward 6, 222 Whiton Street.
Cole, Noah, head, Sept 1870, 29, m: 7 yrs. b: MD/MD/MD, RR conductor
" , Sarah O., wife b., July 1875, 24, m: 7 yrs., 4 children 3 living, b: MD/MD/MD
" , Sophia, dau, Feb 1895, 5, single, b: MD/MD/MD
" , Joseph O., son, Dec 1897, 2, single, b: NJ/MD/MD
" , Emily, dau, Sep 1899, 8/12, single, b: NJ/MD/MD
" , Joseph O, brother, Dec 1875, 24, m: 3 yrs, b: MD/MD/MD, RR firem
" , Agnes, sister-in-law, Mar 1878, 22, m: 3 yrs, 1 child, 1 living, b: MD/MD/MD
" , Joseph W., nephew, Oct 1898, 1, single, b: MD/MD/MD
" , Noah N., father, Mar 1857, 43, m:26 yrs., b: MD/MD/MD, retired
" , Sophia D., mother, Sept 1849, 50, m: 26 yrs, 4 children, 3 living
1910 Census Washington, DC, Precinct 7, 2808 27th Street, dwelling 291, ED 135
Cole, Noah H., head, 70, m1, 45 yrs, b: MD/MD/MD, no occupation
" , Sophia D., wife, 68, m1, 45 yrs., b: MD/MD/MD
Childs, Annie C., dau., 32, divorced, b: MD/MD/MD
" , Annie A., granddau., 8, single, b: MD/MD/MD
Noah Hooker Cole's tombstone can be viewed at
https://www.findagrave.com/cgi-bin/fg.cgi?page=gr&GRid=39208816
An image of his death certificate is available from Family Search confirming his place of burial and death date. Age appears to have been recorded in error.