If Anne Gordon or Anderson was described as a pauper, the implication is that she was in receipt of relief from a parochial board. There are quite extensive surviving records from
some of the parishes in Aberdeenshire, and these are in the care of Aberdeen archives
https://www.aberdeencity.gov.uk/services/libraries-and-archives/aberdeen-city-and-aberdeenshire-archives. The question is which parochial board.
From the 1871 census, John Anderson was born in Peterhead
Ann Gordon was born in Fraserburgh
John Noble Anderson and Ann Gordon were married in Aberdeen St Nicholas in 1864
From the index at SP, I see that the children were all born in different parishes
Helen Ross, 17 May 1865, Aberdeen St Nicholas
Annabella Gordon Noble, 13 January 1867, Kintore
Elizabeth Paterson, 6 September 1868, Rhynie and Essie
Mary Jane Gordon, 15 April 1870, Auchindoir
John Noble, 24 January 1873, Clatt
Agnes Hunter, 5 June 1874, Auchterless
In 1871 the family was living in Aberdeen St Nicholas
Ann Gordon or Anderson died in Fraserburgh in 1877
John Noble Anderson died in Aberdeen Old Machar in 1894
so there could be references to them in any, or indeed all, of the parochial boards of these parishes.
Apart from Ann herself, none of them were born or lived for any length of time in Fraserburgh. So I would expect the Fraserburgh parochial board to have generated the records relating to Ann Gordon or Anderson, but possibly not the children; the parochial board would have expected John to support (i.e. pay for the keep) of his family, even if he could not look after them himself, unless he himself was 'disabled' (i.e. physically or mentally incapacitated to the extent of being unable to earn a living). In that case the parochial board would probably have sent the children either to the poorhouse or boarded them out, almost certainly not all in the same household.
In the 1881 census there is a 15-year-old Helen Anderson, born Aberdeenshire, a servant in the household of Janet Singer at 8 St Catherine's Wynd, Aberdeen. She would exactly fit Helen Ross Anderson, but her parish of birth is not recorded.
Elizabeth Anderson, 13, birthplace said to be Auchterless, and Helen Anderson, 7, also born Auchterless, are in the household of Mary Mitchell at 183 King Street, Aberdeen. This household includes a matron and assistant matron and dozens of young girls, all described as scholars, so I assume that this is some kind of institution, possibly an orphanage. However the birthplace and Helen's age do not fit with the daughters of John Anderson and Ann Gordon; and they do match two of the daughters of James Anderson and Margaret Cowie, who were born in Auchterless.
There's a Mary J Anderson, 11, listed as the adopted daughter of Mary J Noble, seaman's wife, in Fraserburgh. However her parish of birth is said to be Fraserburgh, which is a long way from Auchindoir, where Mary Jane was born. But worth looking into.
Perhaps the others were also adopted, and recorded in the later censuses by their adopted names? If so you will struggle to find them because formal adoption did not exist until 1930, so there are no adoption records from the 1870s and 1880s.
