In the 1881 Census, William and Margaret Docherty are both 57 years old. William's occupation is Coal Miner (also that of his sons William and Edward). The family was dwelling at 11 Byrehill Row in Kilwinning.
In the 1881 Census, Thomas' occupation is listed as Coal Miner and the family dwelling was Corsehill in Kilwinning.
1 The framework for the Docherty lineage was provided by David Bruce Docherty from records maintained by LDS in Salt Lake City. I am not precisely sure how he determined that this particular Docherty lineage was the relevant one, but I presume that he had knowledge from his father.
2 International Genealogical Index Record at LDS provides name as Thomas Childs Docherty, birth date of Jan. 4, 1873 at Stevenston, Ayr, Scotland, parents Thomas Docherty and Janet Strachan
3 International Genealogical Index Record at LDS provides name as Thomas Docherty; birth date of Jan. 4,1873 at Stewarton, Ayr, Scotland, parents Thomas Docherty and Janet Strachen
4 Ancestral File Frame at LDS provides name as Thomas Docherty; birth date of Jan. 4, 1873 at Stewarton, Ayr, Scotland, parents Thomas Docherty and Janet Strachan, spouse Margaret Brown; submitted by a descendant of Margaret Palmer Docherty. Furthermore, this Pedigree provides a good deal of information on both Docherty and Strachan.
5 Although both Stevenston and Stewarton are mentioned by different researchers, Stevenston seems more likely since it's much closer to Kilwinning and this is confirmed by the 1881 Scotland Census; for all future references, Stevenston will be used
6 From 1881 Scotland Census; see Docherty Research for citations
7 According to both of the sources cited at footnotes #4 and #6, the eldest son is William Docherty, aged 11 in 1881 Census. Not clear why the marriage date is almost three years after his birth!