Will every population always converge to a “middle” that contains greatest amounts of whatever is being measured with “increasing” number of traits on wither side in order to make a bell curve visual distribution?

Question

Or are there populations where the curve graphs will converge on either end instead of the middle? Is it a fixed rule in Statistics that we “should” always have a bell curve distribution? If not, why does it seem like my data must make a bell curve distribution? Is it a rule in nature that that are greatest amounts of something in a group while slope downwards by number and value of trait towards the gretest middle and from it downwards? What is the special trait about the bell curve that it is underscored so much?

In: 2

Answer 1

> Is it a fixed rule in Statistics that we “should” always have a bell curve distribution

No there isn’t, and there are lots of other distributions besides the normal distribution. Another common one is the [Pareto distribution](https://en.wikipedia.org/wiki/Pareto_distribution).

However, there is a mathematical reason why the normal distribution is so common – the central limit theroem. This states that if you take the average of N random variables, the distribution of that average will tend towards a normal distribution as N gets larger. Therefore, any quantity which represents an average of many contributing factors, will tend to be at least approximately normally distributed.

Note that a normal distribution covers the entire real line – all values have a nonzero probability. So a quantity like the height of a human population cannot strictly be normally distributed, because that would imply that a nonzero proportion of the population has negative height. But it is *approximately* normally distributed.