An estimated one-third of American children live in homes with firearms, according to public health research, and 43 percent of these homes have at least one unlocked firearm lying about as an invitation to accidental mayhem.

The inevitable results are appalling. Federal data says that between 2007 and 2011 a yearly average of 62 children, age 14 and under, were killed every year while playing with a family gun left loaded and unsecured, and 660 were injured badly enough to require hospitalization.

But the actual toll could be even greater — with 100 youngsters or more shot to death each year in grossly careless family settings — according to a detailed new study of child deaths by firearm conducted by Everytown for Gun Safety, former Mayor Michael Bloomberg’s gun research and lobbying organization.

The report tracked fatalities in 35 states since the shooting massacre in 2012 when 20 children were massacred at school in Newtown, Conn. Individual shooting deaths have gone far less noticed, for all the public concern for children and guns that was prompted by Newtown.