  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
galaxies. 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 center. While R has been measured in a
number of individual galaxies, its distribution remains unknown. Here we report
the distributions of R and the kinetic luminosities of quasars outflows, using
the statistical properties of broad absorption line variability in a sample of
915 quasars from the Sloan Digital Sky Surveys. The mean and standard deviation
of the distribution of R are 10^{1.4+/-0.5} parsecs. The typical outflow
distance in this sample is tens of parsec, which is beyond the theoretically
predicted location (0.01 ~ 0.1 parsecs) where the accretion disc line-driven
wind is launched, but is smaller than the scales of most outflows that are
derived using the excited state absorption lines. The typical value of the
mass-flow rate is of 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.
