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?
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Let’s agree there are generally 3 “classes” of things that determine a trait in a population.
1. Things are consistent for every single member of the population, let’s call these the ‘natural tendency’ of a population. For example, every apple tree wants to grow 1,000 apples. You can think of this as the hardwired, “nature” part of determining how something with turn out.
2. Things are consistently *random* for every single member of a population. This is the noise, for example, some trees get visited by more bees, or some trees got a little extra fertilizer, or a little more sun, This makes some trees produce fewer, and others more apples. You can think of this as the experiential “nuture” part of determining how something will turn out.
3. Things are NOT random NOR consistent for every member of a population, for example, 1/3 of the trees producing 20,000 apples for some reason, and 1/10th of the trees producing 0 apples.
The third example is shows us there is a problem with our data. It tells us our data comes from 3 entirely different groups, the 1/10th are probably just not apple trees in the first place. The 1/3 super-producers and the remaining trees might just be different species. Either way with the information given, you *won’t* get a bell curve because your data is garbage. Best thing to do is throw away the 0 apple trees entirely and separate the super-producers and remaining trees into two groups.
Look at those two groups and should get nice bell curves. Why? What “law” of existence means a bell curve “must” happen?
I’d argue you have it backwards, it’s not that the universe demands bell curves but rather that the universe demands IF something has a ‘natural tendency’ (somethings don’t) and IF that natural tendency is exposed to noise that causes it vary a bit (somethings don’t) THEN the result is a bell curve. Specifically it’s the natural tendency that creates the peak, called the AVERAGE or MEDIAN, and its the noise that creates the tails on the curve.
That’s why bell curves are so important, because in science and physics and in daily life we’re almost always talking about systems that work like this. Test scores, heights, weights, apples growing on a tree, whatever. These are things that can be described as having a ‘natural tendency’ and then being subject to noise that combine to create a bell curve.
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