Question: I was asked by a friend what it means for something to become more and more like a Gaussian and I was unable to come up with a satisfactory answer. Therefore my question is:
How would you explain to a layperson what it means for something to become more and more like a Gaussian?
Thank your for your time.
If the question is unclear or unfit, please let me know and I will do my best to improve it.
Think of someone making a study about the height of adult humans. He measures $10$ persons in his neighborhood and puts them in classes an inch wide. Now he has classes with $0$, $1$ or maybe $2$ crosses. Then he steps to $100$ individuals, makes crosses in their classes, and then draws a pillar for each class, where the number of crosses is translated into the height of the pillar. The tops of these pillars form a praenatial realization of a curve. In the next round he measures $1000$ people, and maybe makes the classes only $1$ cm wide. Again the crosses in each class, and the pillars showing the number of crosses for each class. The tops of the pillars now already make a reasonable curve. Continuing in this way we obtain a sequence of more and more curvelike curves, and these curves look more and more like a Gaussian.