possible use case of central limit theorem for analysts This is a bit of a long shot but I would appreciate any help please.
I have to do a basic stats course for our analysts, which I try to make as applicable and useful as possible using our data (e.g. showing skewed distributions and promoting the median over the arithmetic mean - basic stuff). Our analysts deal mainly with observational data but AFIK they never have to estimate the population mean of some external process. This is one of the main applications of the CLT. I am looking for any other use case for our analysts and would appreciate a possible example. We will later on also talk about bootstrapping, which is somewhat related but I want to keep it simple for now.
PS:
I think my main issue is, that we do not have a population and samples from it. Internally we have processes and we may want to compare process A vs process B. However, I would use bootstrapping for this. I just cannot see the direct application for CLT as we never intentionally collect several samples from a population ....
 A: The CLT allows to talk about the asymptotic distribution of the mean, which is useful for providing inference on it. For example, that an experiment has led to a change in the mean of group A vs group B. It is true that for right-tailed distribution it is more convenient (IMHO) to talk about the median instead, but making inference on the median is harder (e.g.: requires bootstrapping). In such cases, the CLT can be useful since if a transformation of the data (e.g.: log) will make the data approximately normal, then using a t-test on the log-transformed data will be allow us to make inference on a difference in medians in the original scale. Note, though, that the inference in such a case will be on the ratio of the medians, and not their difference.
The benefit here is that the queries for running such analysis are easily available in many SQL implementations (E.g.: Presto), and even excel. While bootstrapping requires getting the data to a more advanced environment such as R or Python.
