Barr's parents were Charles George Barr (1845-1922), Church of England minister (Perpetual Curate of All Saints, Old Swan, Lancashire, 1875-87; Rector of Acrise, Folkestone, Kent, 1888-1906; Vicar of St Nicholas, Codsall, Wolverhampton, 1906-19) and his wife Rebecca Emily Palmer (1841-93), daughter of Henry Norton Palmer.
Barr was educated privately in Cheltenham, then at Rossall School, going on to Pembroke College, Cambridge. On 31 May 1892 "Barr, Pembroke" gained honours in the Cambridge Mathematical Tripos Part I; ranked 53rd in the list, he was a Senior Optime (the grade below Wrangler, the top grade).
Barr, jointly with Percy Dealtry, was headmaster of the school from its foundation. After Percy's retirement in 1925, Barr continued as joint headmaster with Percy's son Tim Dealtry, and retired from The Leas in 1930.
Barr does not appear to have married. His younger sister Mildred must have helped with school admin: she is the contact in an ad in the Wellington Journal,11 Sep 1909, for a Head Waitress "for a boys' preparatory school, Hoylake, Cheshire".
Michael Longson (The Leas 20t3-24t2) writes in his autobiography A Classical Youth (Anthony Blond, 1985):