The analyses on the statistical response spectra have an important role in determining the earthquake demand. Elastic and inelastic spectra on acceleration of the 205 records on medium-stiff soil site for SDOF systems are presented in statistical analyses. The empirical probability distributions of the spectral values are derived according to the Kolmogorov-Smirnov (KS) goodness-of-fit test. The formula for statistical average spectra of the ground motion ensemble are recommended, which are valuable for current research and code revisal. The results show that the statistical averaged elastic α spectra fits well to the design spectra prescribed in Chinese code when the period is smaller than 2s. The inelastic responses decrease with the increase of ductility demand μ when μ<4. The coefficients of variance of the elastic and inelastic spectra are still large and the dispersion cannot be ignored. The probabilistic distribution of the spectra value on acceleration is validated as the lognormal distributions. The proposed formulas give a good fit to the statistical average values.