The story extrapolates to great lengths (including a complete overthrow of humanity by smartly evolved canines) a simple principle: what might happen if we found a perfectly average man who had quantitative qualities representative of the population averages of those qualities (like having number of teeth equal to the average teeth per capita, etc.) The protagonist in the story, George Abnego, is that perfectly normal, perfectly average man who, owing to a sudden appreciation of normality in a post-apocalyptic world, goes on to become a 6-term US president and then a World leader, leading to usual peace and recidivism in human civilization before the canines takes over (the author may have had "abnegate" in mind while naming his hero, given the evolution of the story). The title of the story refers to the concept of "null hypothesis" in statistical inference, presumably taken here to mean that the "averageness" of man is a base case hypothesis and it is the deviations from this null hypothesis that are suppressed and smoothed out in the world ruled by Abnego.
There are scattered references to statistics & averages and two pieces are striking: the tag line, which says, "Not for George was the piddling triumph of non-Aristotelian logic or non-Euclidean geometry. For him, the unsought and undreamed-of miracle: non-Platonic Politics - the everlasting rule of the Average Man!" and the observation by a Biology professor, "All he is, I am afraid, a bell-shaped curve with ambition, the median made flesh".