For the Sun, the answer is a few 10^-16 solar masses per year, or a few percent of the total mass lost through the steady solar wind. However, coronal mass ejections (CMEs) are associated with energetic flares, with the average mass being thrown out in each event increasing with flare energy, and in particular, total radiated X-ray energy. The middle-aged Sun is quite an inactive star magnetically.  More rapidly rotating (generally younger) stars can be much more active, with magnetically-driven X-ray luminosities factors of up to 10,000 times that of the Sun. These stars exhibit immense, energetic flares, How much mass is involved in the CMEs that are likely associated with these superflares?  We took CME data for the Sun, and made an average relation between CME mass and associated flare X-ray fluence.  We scaled this relation to other stars, assuming their X-ray output was dominated by flaring activity. We found that such a relation predicts uncomfortably large mass loss rates for active stars - several 10^-10 solar masses/year, compared with the Sun's 10^-14. We know this cannot be right because it would take 10% of the star's energy output to power such a CME mass loss rate. Still, active star mass loss is very likely to be dominated by CMEs and its probably larger than we thought and perhaps 100 times the solar value.  This is important for understanding habitability of exoplanets around active M dwarf stars, and might also help solve the Faint Young Sun problem if we can find a way to bump up the estimate by a factor of ten. This work was published in the 2013 February 20 edition of the Astrophysical Journal.