A histogram won't necessarily extend from one side to the other. If there is a wide range of brightness in the scene, e.g. dark shadows to bright light, it will, or it may even be clipped on one end or the other, or both. A scene with low contrast may only have a spike in the middle. Changing the exposure for the scene will push the graph to the right (with more exposure) or left (with less exposure).

The practice of "exposing to the right" is often used when shooting RAW as this gives the file the most data. The image may look too bright, but the exposure can be corrected in post processing to the level you want. This technique applies mostly to RAW, not so much if you shoot JPEGs.

Alan