William Edward Farquharson was born in Liverpool, Lancashire, England in late 1873, later being baptised on 14 April 1874 in Holy Trinity Church, Liverpool.

He was the son of George Walter Farquharson (b. 1840), an engineer, and Elizabeth, née Fletcher (b. 1840), both Liverpudlians who had married in their native city on 1 January 1861.

He had seven known siblings: Isabella (b. 1862), George James (b. 1865), Elizabeth Ann (b. 1867), William Francis (b. 1869), David (b. 1872), Thomas (b. 1876) and Florence (b. 1888).

William first appears on the 1881 census when he and his family were living at 22 Gwydir Street, Toxteth Park, Liverpool. When the 1891 census was conducted he and his family were living at 87 Admiral Street, Toxteth Park and he, like several of his sibling, were described as apprentice fitters, following in their father's footsteps. He served his apprenticeship with Messrs. Higginson of Liverpool and then joined the Anglo-American Tool Company. He went to sea at the age of 22 years, initially with Johnson & Co. Ltd and then aboard ships owned by John Markwood of Liverpool. He joined the White Star line in 1900 as Assistant Second Engineer aboard the Teutonic, later transferring to the Seuvic on which he served for over three years before moving to the Majestic as Junior Second Engineer. Later he held the rank of Senior Second Engineer aboard the Teutonic and the Oceanic.

William was married in Liverpool in 1894 to Martha Ellen McAllister (b. 1874 in Liverpool) and the couple went on to have three children: George Walter (1895-1980), William Pearson (b. 1905) and Millicent (1906-1930). William was absent from the 1901 census, likely at sea, but his wife and first child were listed as living at 88 Jacob Street, Toxteth Park. The family moved to Southampton sometime around 1907 and show up on the 1911 census living at Preston House, Manor Farm Road, Bitterne Park, Southampton.

William apparently "stood-by" the Titanic during the latter stages of her construction at Harland & Wolff. When he signed on to the ship on 6 April 1912, he gave his address as 90 Wilton Avenue, (Southampton). His previous ship had been the Oceanic and as Senior second engineer he could expect to earn monthly wages of £22.

William  Farquharson died in the sinking. His body, if recovered, was never identified. His wife and children were later assisted by the Titanic Relief Fund.

Number 98. Farquharson, Martha, widow. Children: George; William; Millicent. All class A dependants. — Mansion House Titanic Relief Fund

No. 98. Farquharson, Mrs. Martha: Address for cheques: Head office. net monthly allowance to widow £7 13 10 two children £1 3 10 total £8 17 8d.  — Mansion House Titanic Relief Fund

His estate, worth £428, 7s was administered to his widow on 24 May 1912.

Farquharson, William Edward, of 90 Wilton Avenue, Southampton. Ships engineer. Administration, London 24th May 1912 to Martha Ellen Farquharson, widow. Effects £428.7.0d.

His widow Martha was never remarried and relocated to her native Liverpool. She later lived at Rivington Avenue, St Helens, Lancashire and died on 13 February 1934.