Sorry I don’t understand. The central limit theorem describe the distribution of the sample means from a population. It describes the distribution of the mean, not the distribution of the population itself. The shape of the distribution of the sample mean isn’t super interesting when you’re interested in the distribution of the samples themselves as a proxy for a population. So I’m not sure I understand your assertion. Could you explain more your reasoning? Maybe I’m missing something, but the estimation of the sample mean distribution isn’t the only metric that’s useful, and almost nothing in nature is normally distributed otherwise. Normal distributions are generally a useful assumption mostly because of the analytic form of the Gaussian and our understanding of how to work with it. But that estimation isn’t useful as it might seem. A Poisson distribution is much more common for instance.
I't appears you don't understand the central limit theorem fully. You gave the definition you find in textbooks, but you don't see how it applies to real world measurements and already explains your question. I can only recommend to visit a university level statistics course at this point. Maybe you will understand when you actually deal with some real data. Then you will indeed see its consequences pop up everywhere. The issue (also for the blog author) is that it is often implicitly assumed. It is one of many common pitfalls in statistics. You should also learn what the difference is between a poisson and a gaussian distribution. They may look similar, but there is a drastic difference in their definition and they are used in very different circumstances.
The GP here did not claim a poisson was the same thing as a Gaussian. They also don’t look similar.
As far as I can tell you’re making the introductory student error of thinking the central limit theorem means any sufficiently large sample makes a distribution look normal.
Yes precisely. I’m also frankly shocked at the condescension. If you weren’t making that typical mistake then please explain the uses you meant. I would rarely use a box plot for a CLT distribution. Why? I would most often use it with a population sample I want to get the distribution of. Yes the mean of those would be a Gaussian under the CLT but it’s not useful useful as such.
Most natural distributions are not Gaussian upon sampling even if they’re bell shaped. They often have fatter tails, model some complex process, etc. The box plot is sometimes deceptive as is demonstrated in the original link. I don’t think that’s easy to argue against as they provide a totally reasonable and common sample distribution and show it failing to be descriptive of the most important features.
I fail to see how the CLT even remotely addresses the concerns or obviates them in any useful sense. The CLT and box plots aren’t very often applied together for these reasons.
