Well, first... I've meditated in a lot of different places in my life, and I have yet to experience any sort of violence while sitting. Worst case I can think of was once when a bunch of hyped-up kids came running through the meditation room, but I was already deep in when that happened, so that was just, you know: that. We generally choose to meditate in peaceful spots — this fosters the development of the practice — so the risk of violence during meditation is extremely remote. Not impossible, granted, but remote.
And yes, I've intentionally misconstrued the question so that I could make a point. I know you were talking about violence in the surrounding world, but part of the practice is to create a mental context in which we (for some short period of time) don't have anything to do, don't have anything to think, don't have anything to worry about or fuss over, all so that we can practice putting down the egoic mind. There is no violence here and now within that meditative space; if we are disturbed by violence anyway it is violence that our mind has brought with us from somewhere or somewhen else. In meditation we should focus on removing our attachments to those thoughts of violence, and save worrying about the violence itself for some other time.
Dealing with violence itself requires perspective and understanding. Violence is merely one of the more graphic expressions of ignorance. People are caught by a desire — which could be just about anything — and their failure to achieve that desire ties them to more egoic desires: needs to claim respect, protect their sense of self worth, be treated fairly, etc, etc. When they get tangled deeply enough in these psychological knots it limits them so they can't do the 'human' things: compromise, negotiate, cede ground to others, express themselves clearly. All that comes out when they try is tinged by a seething vitriol squeezed through their own bonds. In that state, violence can seem like a normal, effective, reasonable, even pleasurable course of action. People in that state are just primed to explode, because an explosion blows apart the mental bindings they've imposed on themselves for a few moments, allowing them to breathe freely until the knots reassert themselves.
Understood this way, violence isn't something enraging or frightening. It's pitiable, like watching a wounded animal caught in a trap. Is a wounded animal dangerous? Undoubtably yes, but that wouldn't stop most of us from trying to help it. A human caught and wounded in a trap of desire and ignorance is no different. Of course, it's often hard to see that, because we work within a framework where we see animals as innocent (accruing no blame) and humans as potentially malevolent (blame-worthy). But that framework is itself a set of attachments that we should allow meditation to cure us of.