Interplanetary coronal mass ejections (ICMEs) are often observed to travel much faster than the ambient solar wind. If the relative speed between the two exceeds the fast magnetosonic velocity, then a shock wave will form. The Mach number and the shock standoff distance ahead of the ICME leading edge is measured to infer the vertical size of an ICME in a direction that is perpendicular to the solar wind flow. We analyze the shock standoff distance for 45 events varying between 0.5 AU and 5.5 AU in order to infer their physical dimensions. We find that the average ratio of the inferred vertical size to measured radial width, referred to as the aspect ratio, of an ICME is 2.8 ± 0.5. We also compare these results to the geometrical predictions from Paper I that forecast an aspect ratio between 3 and 6. The geometrical solution varies with heliocentric distance and appears to provide a theoretical maximum for the aspect ratio of ICMEs. The minimum aspect ratio appears to remain constant at 1 (i.e., a circular cross section) for all distances. These results suggest that possible distortions to the leading edge of ICMEs are frequent. But, these results may also indicate that the constants calculated in the empirical relationship correlating the different shock front need to be modified; or perhaps both distortions and a change in the empirical formulae are required.