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

Not necessarily.

Bell curves ( normal distributions) arise when a group has a single average value, and additive fluctuations around that.

If the fluctuations are multiplicative (for example, % changes or probability changes, and factors influencing growth) then a log normal distribution will occur (looks similar to bell curve, but skewed towards lower values). Human weight is an example of this.

Sometimes these can be hard to distinguish from a normal distribution though, if the skew is small.

Some traits, like those whose likelihood changes over time at a fixed rate, will give an exponential distribution. For example, age of death in an ideal population (although bc of factors like birth rate, war, and health care accessibility, in reality it may not follow an exponential distribution).

Some traits depend on multiple underlying groups, which can create a bimodal (or several average value) distribution. This will have multiple peaks. For example, if you scored people based on their ability to distinguish colors, you would see 2 peaks: a higher peak for normal color vision and a lower peak for colorblind people. If you isolate one peak, it will tend to have a normal or log normal distribution.

In general, the fewer factors that influence a trait, the further from a bell curve it will look. Bell curves (and log normal) curves are special and common because they are a “stable” point in probability theory, if you add another underlying factor, you still get a bell curve. As you have fewer factors creating variation, the distribution can become more skewed.

Essentially, Bell curves arise when there are so many unmeasured factors in a dataset that they blur out the more intricate variations and underlying distributions of individual factors.