Data obtained recently by the Mars Orbiter Laser Altimeter (MOLA) were used to study the statistical properties of the topography and slopes on Mars. We find that the hemispheric dichotomy, manifested as an elevation difference, can be described by long baseline tilts but in places is expressed as steeper slopes. The bimodal hypsometry of elevations on Mars becomes unimodal when referenced to the center of figure, contrary to the Earth, for which the bimodality is retained. However, ruling out a model in which the elevation difference is expressed in a narrow equatorial topographic step cannot be done by the hypsometry alone. Mars' slope distribution is longer tailed than those of Earth and Venus, indicating a lower efficiency of planation processes relative to relief-building tectonics and volcanics. We define and compute global maps of statistical estimators, including the interquartile scale, RMS and median slope, and characteristic decorrelation length of the surface. A correspondence between these parameters and geologic units on Mars is inferred. Surface smoothness is distinctive in the vast northern hemisphere plains, where slopes are typically <0.5¿. Amazonis Planitia exhibits a variation in topography of <1 m over 35-km baselines. The region of hematite mineralization in Sinus Meridiani is also smooth, with median slopes lower than 0.4¿, but does not form a closed basin. The shallower long-wavelength portion of the lowlands' topographic power spectrum relative to the highlands' can be accounted for by a simple model of sedimentation such as might be expected at an ocean's floor. The addition of another process such as cratering is necessary to explain the spectral slope in short wavelengths. Among their application, these MOLA-derived roughness measurements can help characterize sites for landing missions. ¿ 2001 American Geophysical Union