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Why is everything so normal (-y distributed)?

A lot of quantitative research assume that certain types of random variables, given a large enough sample size, will converge towards a normal distribution. The usefulness of this assumption combined with its relative complexity leaves some researchers partly in the dark about the quantitative methods they are using. To explain the emergence of the normal distribution to peers and pupils alike I found that visual aid is a more than words or formulas.


This is a simulation of balls falling. Each line can be thought of as a coin flip, as there are 2 outcomes and a 50% chance for both, e.g. Heads = Left and Tails = Right.


The balls follow some very simple rules:

  1. At the start, flip a coin. Fall in the direction of the result.

  2. At each white line the ball passes, flip a coin. This happens 9 times.

  3. The color of the ball is dependent on its position on the x-axis.


Each flip is random and independent of each other. A ball can end up anywhere, but very quickly the histogram starts showing signs of a normal distribution. Very few observations end up completely blue or red, roughly 0.2% of the balls are expected to land in each extreme.


Music by Lexin_Music, the song can be found here.




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