The height/width ratio depends on the particular typeface, some (e.g., Times Roman) being inherently narrower than others (such as Bookman). Many typefaces have Compressed, Condensed, Regular and/or Extended fonts in the family. Obviously the height/width average is very different for each. The range spans a wide spectrum from the incredibly narrow (Universe 39 Thin Ultra-Condensed) to the ridiculously wide (Blackoak).
Depending on the needs of a particular project, a designer will choose a wider or narrower typeface.