Can one individual represent and entire population? Why or why not

A representative does his/her utmost to convey the feelings of the majority of the group they speak for, and stands up for their interests. This might be for negotiation, voting, litigation, diplomacy, etc.

A leader, ideally, inspires their constituents and brings out the best in them, as in strength, ethics, spirituality, and so on.

Short version: a rep is an agent or conduit. A leader is a catalyst. Either job can be hard. And yes, it can be done for most of a population. Maybe not all, but not everyone can fit into the same mold.