[1] Allan was born on 11 July 1905 in St Kilda, Victoria; her parents were both journalists with The Argus, and she was one of four sisters.
[3] She studied mathematics at the University of Melbourne,[3][4] earning a bachelor's degree in 1926 and a master's in 1928 for her work with John Henry Michell on solitary waves on liquid-liquid interfaces.
A year later, she travelled to Rothamsted Experimental Station in Hertforshire to work alongside Ronald Fisher studying crop experiments and developing statistical methods.
[8] During her time at CSIRO, Allan also taught at Canberra University College and the Australian Forestry School.
[1] In 2019 the Statistical Society of Australia and Data61 created a joint travel award named in her honour.