The effective dose equivalent was defined in the International Commission on Radiological Protection Publication 26 in 1977 and later adopted by the U.S. Nuclear Regulatory Commission. To calculate organ doses and effective dose equivalent for external exposures using Monte Carlo simulations, sex-specific anthropomorphic phantoms and sex specific weighting factors are always employed. This paper presents detailed mathematical derivation of a set of sex specific tissue weighting factors and the conditions which the weighting factors must satisfy. Results of effective dose equivalent calculations using female and male phantoms exposed to monoenergetic photon beams of 0.08, 0.3, and 1.0 MeV are provided and compared with results published by other authors using different sex-specific weighting factors and phantoms. The results indicate that females always receive higher effective dose equivalent than males for the photon energies and geometries considered and that some published data may be wrong due to mistakes in deriving the sex-specific weighting factors.