We report on the variability of 443 flat-spectrum, compact radio sources monitored using the VLA for 3 days in four epochs at image4 month intervals at 5 GHz as part of the Micro-Arcsecond Scintillation-Induced Variability (MASIV) survey. Over half of these sources exhibited 2%-10% rms variations on timescales over 2 days. We analyzed the variations by two independent methods and find that the rms variability amplitudes of the sources correlate with the emission measure in the ionized interstellar medium along their respective lines of sight. We thus link the variations with interstellar scintillation of components of these sources, with some (unknown) fraction of the total flux density contained within a compact region of angular diameter in the range 10-50 muas. We also find that the variations decrease for high mean flux density sources and, most importantly, for high-redshift sources. The decrease in variability is probably due either to an increase in the apparent diameter of the source or to a decrease in the flux density of the compact fraction beyond image. Here we present a statistical analysis of these results, and a future paper will discuss the cosmological implications in detail.