Little is known about Eliza T. Frederick. She apparently was born c. 1856 in Person County, North Carolina, and died before the death of her father on May 27, 1888. This is based upon the following:

Death Notice: The Roxboro Courier, Thursday, 14 June 1888: "At his residence in Person County, on Sunday the 27th of May, 1888, Mr. Ransom Frederick, age about 73 years. He leaves a wife, five children and many relatives and friends to mourn his death."

The five children known living on May 27, 1888, were. Cicero S. Frederick; Matilda Frederick; Arasmus Donald Frederick; Lucy A. Frederick; and Leonidas Pointer Frederick. Elizabeth Walton Frederick died June 16, 1886. This leaves George W. Frederick and Eliza T. Frederick.
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See: Frederick Family History Omnibus Memorandum

1860 United States Federal Census
Name: Eliza T Fedrick
Age in 1860: 4
Birth Year: abt 1856
Birthplace: North Carolina
Home in 1860: Person, North Carolina
Gender: Female
Post Office: Hurdles Mills
Household Members: Name Age
Ransom Fedrick 45
Joanna Fedrick 40
Cicero Fedrick 20
Erasmus P Fedrick 18
Itilda C Fedrick 16
Elizabeth W Fedrick 14
Lucy A Fedrick 12
George W Fedrick 9
Leardoor P Fedrick 5
Eliza T Fedrick 4
Martha G Walton 53
Mary E Wood 21
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The Frederick Family Omnibus Memorandum explores the history of the Frederick family of Person County, North Carolina: https://www.ncccha.org/pdf/frederick/frederickfamilyhistoryomnibusmemorandum.pdf

The Caswell County Genealogy online database contains extensive information about the Frederick family: https://www.caswellcountync.org

The Frederick Family Photograph Collection contains hundreds of Frederick family photographs: https://www.flickr.com/photos/ncccha/albums/72157600255950540