Why is it useful to know something about the shape of a set of numbers?

Answer 1

That would be easier to answer with examples.

But once you start graphing things, pictures are very instructive, and mathematical techniques that spare you the trouble of drawing pictures still implicitly rely on some of the "shapes" you may be talking about.

Pretty much all of science depends on calculus and/or statistics, for example (and statistics really depends on calculus too). And those areas of math are covered by what I just said.