Margaret was the daughter of Thomas Mann Randolph and Martha Jefferson. She was born 2 Nov 1803 in Virginia and lived there until her death 29 Mar 1876A picture of the Memorial at Monticello is available at Find a Grave
In 1870, Margaret is living with her sister and husband, Virginia and Nicholas Trist
It is assumed that she died unmarried, as she is the only daughter buried with her maiden name and no family members. 
↑ "United States Census, 1870," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MFL6-NYV : 12 April 2016), Mary Randolph in household of Nicholas P Trist, Virginia, United States; citing p. 62, family 496, NARA microfilm publication M593 (Washington D.C.: National Archives and Records Administration, n.d.); FHL microfilm 553,131
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It may be possible to confirm family relationships with Mary by comparing test results with other carriers of her ancestors' mitochondrial DNA.
Mitochondrial DNA test-takers in the direct maternal line: