A 3 is professional rating, in that it is the rating of someone who has just started out making a living at doing it. It is a regular beat cop, security guard, military grunt, college athlete, go-ganger, or someone with an Associate's degree.
It is not the average for every NPC. Someone with a Master's degree, an Ancients go-ganger, someone on a SWAT team - they will have skills of 5. Shadowrunners will tend to be around the 5-6 mark in their specialties. Even the archetypes, which are far from optimized, bear this out - there are a lot of them with 5's, and the ones that don't have 5's are generally the ones with a wider spread of skills and/or skill groups.
On Attributes, remember that, just like skills, it is a 7 that is truly maximum potential (before adding SURGE and geneware, of course).
What really makes shadowrunners pull out of the pack, though, are the dice pool bonuses - some from boosting their Attributes, some from boosting their skills, and some from tech or 'ware that directly boosts the dice pool. There has been a bit of power creep, but dice pools in the 15-18 range are fairly easy to get, at least for some skills, even with the basic book.
Now, for a low-powered campaign - something like gang kids, who are supposed to be less powerful - the best way is to limit Availability, Magic rating (otherwise everyone will just be a mage or an adept), starting skill ratings, and resources. Let them pour their points into having a wider spread of skills and more contacts, instead. Dice pools (the main measure of character power) will be lower because skills will be lower and those pervasive dice pool modifiers will be less common.