Try using the following setup:

\RequirePackage{graphicx}
\documentclass[dissertation,draft]{univthesis}


This loads graphicx before the draft option is set. Alternatively (preferred), don't load graphicx but reset the package option using

\setkeys{Gin}{draft=false}


Gin contains the family of keys associated with graphics/graphicx.

Displaying images in draft mode for books
I am attempting to plot the most populous cities on a world map.

Currently, I have the line of code:

numberofpeople = 
  Map[{#, Length[CityData[#, "Population"]]} &amp;, CityData[All]];


which should give me the City name, and the population. However, when I type in the line of code

Reverse[SortBy[numberofpeople, Last]][[1 ;; 20]]


I am getting odd data, which is that the most populous cities have 1 person. 

Could somebody debug my code, and answer any future questions I have on the matter?
Much appreciated.

EDIT: How do I plot these points on a World Map? Currently I have

Graphics[{EdgeForm[Black], , CountryData[#, "SchematicPolygon"]} &amp; /@ 
  CountryData[]]

but I have no idea what goes between the points.
