The eldest of four daughters and third of eight children of William Alexander Elderton (1839–1890) and his wife, Sarah Isabella, née Lapidge (1852–1931), who, after her husband’s death, took charge of a local school to support the family.
Ethel’s three sisters all became schoolmistresses. Her elder brother Sir William Palin Elderton (1877–1962) became an actuary, was president of the Equitable Life Assurance Society, and wrote a number of works on statistical problems. Another brother, Sir Thomas Howard Elderton (1886–1970), took a first in the Cambridge mathematical tripos and became chairman of the Calcutta Port Trust.
Ethel Elderton attended Streatham High School. She lived with her widowed mother and siblings at 4 Valley Road.
She became Galton Scholar and Fellow and Assistant Professor at University College London. She retired in 1933.