The National Survey of Children’s Exposure to Violence from OJJDP (Office of Juvenile Justice & Delinquency Prevention) has issued a number of reports. The latest is Children’s Exposure to
Violence and the Intersection Between Delinquency and
Victimization.

It concludes that somewhere around a third of victimized children end up committing delinquent acts.  (This is a very rough numerical interpretation, leaving out the children who have not been victimized from the charts in the article.) Get the full picture in the publication itself.