Outlets(receptacles) not grounded "properly"... what to do?
I embarked on a project to replace all the 15amp duplex wall receptacles in my living room yesterday because I wanted white outlets instead of the black ones that were installed. So I turned off the power and started to swap them out. They are 15amp duplex, 125-volt u-grounded receptacles. Much to my surprised, when I got the cover plates off and the receptacles out of the wall, NONE of them were grounded! Two hot and two neutral connected to the receptacles, but the ground was not connected. I'm not sure if there was even a ground in there. If I looked to the back of the box, there were two cables coming into it. Each had a copper wire wrapped around the cable just above where the insulation was removed. Out of each cable came the hot and neutral wires that were connected to the receptacle.
I'm a little concerned that my outlets are not grounded. Should I be concerned? What are some issues I might encounter as a result of the outlets not being grounded? The copper wire that is wrapped around each cable coming into the box, is that the ground wire? Should I pigtail these and attach them to the receptacle ground screw?
Thanks in advance for help/advice.