Statistics on murders BY children are exceedingly difficult to find. I did however find the following very interesting.
Incarceration of children
2,000 studies show that children from single-mother households (SMHs), compared to children with father present, are more likely to go to prison by twenty times.
Suicide by children
Fatherless children are more likely to commit suicide by five times.
Murder by children
Fatherless children are more likely to commit murder by eight times.
Children's behavioral problems
Fatherless children are more likely to have behavioral problems by twenty times.
Likelihood of children to become rapists
Fatherless children are more likely to become rapists by fourteen times.
Become runaways
Fatherless children are more likely to run away by thirty two times.
Drug users
Fatherless children are more likely to abuse chemical substances by ten times.
Drop outs
Fatherless children are more likely to drop out of high school by nine times.
From: http://christianparty.net/aa.htm