system
Given the following post, respond as if you're commenting on Reddit:
human
Dumb question: What is so special about normal distribution ?

We care about error being normally distributed, For a variety of purposes we prefer normally distributed data. Why is it so ? Is it because at higher count of data values, the distribution slowly resembles normal distribution in nature (law of large numbers) ? If that's the case then is it safe to assume that other distributions are only prevalent in data with sample size less than 30 ?
gpt
The normal distribution has lots of nice properties that not only make certain calculations easy, but makes them possible in the first place.

For example: you mention errors being normally distributed. With this assumption, we can formulate things like linear regression with all of its useful properties. 

> at higher count of data values, the distribution slowly resembles normal distribution in nature 

This is false. If the underlying distribution is not normal, then taking more samples from that distribution will not suddenly make it look normal. It will still resemble the underlying distribution.

You are confusing data with the Central Limit Theorem, which says that certain *calculations* of data begin to resemble a normal distribution as you feed more data into those calculations (for example, the mean or sum of a dataset).

Often times, people are only interested in the mean or sum of a dataset, so they invoke the CLT - which is where you're seeing references to normality. Note that, in reality, people usually care about a lot more than just the mean/sum, but they don't know how to test for anything else, or are unaware of the limitations/dangers of only looking at the mean/sum.

> is it safe to assume that other distributions are only prevalent in data with sample size less than 30 ?

No.