As of the 1881 Wales Census Ann, age 6 (born in Llanfairfechan) lives at:
Street address: Brynhyfryd 3
Occupation: Scholar
Registration district: Bangor
Sub registration district: Llanllechid, with her father John, age 31, and her mother Allice, age 32.
Sources
"England and Wales Census, 1881," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:Q2WS-VTMN : 1 September 2017), Ann Williams in household of John Williams, Llanfair-Fechan, Caernarvonshire, Wales; from "1881 England, Scotland and Wales census," database and images, findmypast (http://www.findmypast.com : n.d.); citing p. 13, Piece/Folio 5580/81, The National Archives, Kew, Surrey; FHL microfilm 101,775,520.
Ancestry.com and The Church of Jesus Christ of Latter-day Saints. 1881 Wales Census [database on-line]. Provo, UT, USA: Original data: Census Returns of England and Wales, 1881. Kew, Surrey, England: The National Archives of the UK (TNA): Public Record Office (PRO), 1881. Class: RG11; Piece: 5580; Folio: 81; Page: 13; GSU roll: 1342340
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DNA Connections
It may be possible to confirm family relationships with Ann by comparing test results with other carriers of her ancestors' mitochondrial DNA.
However, there are no known mtDNA test-takers in her direct maternal line.
It is likely that these autosomal DNA test-takers will share some percentage of DNA with Ann:
~12.50%Kim Williams :
AncestryDNA, GEDmatch A448727[compare], yourDNAportal KIM7b51fe75, Ancestry member williams_kimj
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Family Tree DNA Family Finder, GEDmatch A448727[compare], yourDNAportal KIM7b51fe75, FTDNA kit #B706290