Quasar outflows carry mass, momentum and energy into the surrounding environment, and have long been considered a potential key factor in regulating the growth of supermassive black holes and the evolution of their host galaxies1-4. A crucial parameter for understanding the origin of these outflows and measuring their influence on their host galaxies is the distance R between the outflow gas and the galaxy centre5,6. Although R has been measured in a number of individual galaxies7-15, its distribution remains unknown. Here we report the distributions of R and the kinetic luminosities of quasar outflows, using the statistical properties of broad absorption line variability in a sample of 915 quasars from the Sloan Digital Sky Survey. The mean and standard deviation of the distribution of R are 101.4±0.5 parsecs. The typical outflow distance in this sample is tens of parsecs, which is beyond the theoretically predicted location (0.01 to 0.1 parsecs) at which the accretion disk line-driven wind is launched16,17, but is smaller than the scales of most outflows that are derived using the excited-state absorption lines7-14. The typical value of the mass flow rate is tens to a hundred solar masses per year, or several times the accretion rate. The typical kinetic-to-bolometric luminosity ratio is a few per cent, indicating that outflows are energetic enough to influence the evolution of their host galaxies.