Probably:
Cath Jane Faragher, baptised 30 August 1868, Braddan, Isle of Man, England. Parents were Philip Faragher and Margaret Cain.
Kate Ann Farrar, born 11 October 1868, baptised 20 August 1874, Wesleyan Methodist Chapel, Carlton Street, Castleford. Parents were Henry and Ann Farrar.
Kate Ann Farrar, birth registered in Pontefract, Yorkshire West Riding, England during the fourth quarter of 1869.

Katherine Ann Faragher was born on 13 May 1868 in the Malew Parish, Isle of Man. Her parents were Edward and Margaret Faragher, nee Gordon. She was baptised on 31 May 1868 and emigrated with her parents to the USA in 1872. Her marriage to Thomas R. Rook took place in Livingston, Illinois, USA on 15 October 1891. She died in Fairbury, Livingston, Illinois, USA on 13 June 1955.

The Pantagraph, Bloomington, Illinois, 14 June 1955:
Mrs. Kathryn A. Rook
Forrest - Mrs. Kathryn A. Rook, 87, of Forrest, died at 8:05 a. m. Monday at Fairbury Hospital in Faorbury.
Her funeral will be at the Culkin Funeral Home at 2 p. m. Wednesday. The Rev. H- Leland Walls will officiate. Burial will be in Forrest Cemetery.
Mrs. Rook was born May 13, 1868, on the Isle of Man, a daughter of Edward and Margaret Gordon Faragher. She accompanied her parents to this country at the age of three. She was married to Thomas Rook Oct. 15, 1891. He preceded in death.