Why the “Bell Curve” is so Normal
An intuitive explanation of why summing random variables gives rise to a normal distribution.
Did you ever wonder why bell curves are everywhere? Heights, weights, neurons firing, the apparent brightness of stars… why should they all just happen to follow a similar bell curve distribution?
“It reigns with serenity and complete self-effacement amidst the wildest confusion. The larger the mob, the greater the apparent anarchy, the more perfect is its sway. It is the supreme law of unreason.” — Francis Galton
To explain, let’s start with a random event familiar to all of us — rolling a pair of dice.
There are 6 × 6 = 36 equally likely outcomes for the pair of dice, but you may know that the median sum of 7 is much likely than the minimum possible sum of 2 or the maximum possible sum of 12.
The probability for each 2-dice sum is proportional to the length of a diagonal on a 6 × 6 grid. The most likely sum of 7 is the main diagonal from top-left to bottom-right.
