The many known excited states of some medium-weight nucleides are analysed in terms of the total number of states as a function of the excitation energy. Low-energy nuclear temperatures can be determined and are found to agree well with those obtained from evaporation spectra. There is a marked odd-even difference in the number of states of odd and even nuclei, appearing as a displacement of the curves with respect to each other by the pairing energy. Information on the spin distribution among the excited states is obtained and is related to a nuclear moment of inertia. The theoretical interpretation of the odd-even effect and a constant temperature is discussed in terms of an energy-gap model.