Biografia Frequentò la Bradford Grammar School e conseguì la maturità al Trinity College, Cambridge laureandosi poi nel 1914. Nel 1924 divenne lettore presso la London School of Economics, dove rimase fino al pensionamento. Scrisse per Biometrika e il Journal of the Royal Statistical Society
Rhodes propose l'algoritmo di Rhodes nella programmazione lineare. Collaborò con Arthur Lyon Bowley e con Alexander Morris Carr-Saunders al suo studio sulla delinquenza giovanile. Contribuì a studi sulla popolazione e sugli esami, scrivendo assieme a Philip John Hartog il libro An Examination of Examinations.
Pubblicazioni On the relationship of the condition of the teeth in children to factors of health and home environment, Eugenics Laboratory Memorial, 1921 Smoothing, tesi di dottorato, 1921 On a certain Skew Correlation Surface, Biometrika, 1922 Reducing Observations by the Method of Minimum Deviations, Phil. Magazine 7th Series. Pp. 974 – 992, 1930 Elementary statistical methods, 1935 An examination of examinations : being a summary of investigations on the comparison of marks allotted to examinations scripts by independent examiners and boards of examiners, together with a section on a viva voce examination, coautore Philip John Hartog, 1936 Young Offenders, an Enquiry Into Juvenile Delinquency, coautori A.M. Carr-Saunders e Hermann Mannheim, 1942 The platinum metals industry in Germany, 1945