How people perceive their level of "smartness" is a very interesting topic.
Intelligence comes in many forms; natural, learned, common sense, life experience among others.
Here we focus on IQ intelligence or academic intelligence. This is determined by taking an IQ test.
Generally speaking the average IQ is 100. If you achieve a score higher than 100, you are smarter than the average person, and a lower score means you are less so.
IQ Scale
Over 140 - Genius or almost genius
120 - 140 - Very superior intelligence
110 - 119 - Superior intelligence
90 - 109 - Average or normal intelligence
80 - 89 - Dullness
70 - 79 - Borderline deficiency in intelligence
Under 70 - Feeble-mindedness
Average IQ in each state of the U.S.
Map of World IQ's
Studies find that some of the least smartest people are also some of the most arrogant about their "brightness."
My humble submission for your consideration.