Background: I'm teaching an intro course to stats, and this term, I have decided to use real-world public data sets to demonstrate the methods on, instead of synthetic data. I was surprised that I wouldn't find basic data such as height/weight/IQ of men and women (which are famously well-approximated by Gaussian). I do find parameters (mean/variance of weight of Americans, for example), but I don't want to synthesize a Gaussian based on parameters. Rather, I'm looking for actual data, so the students experience the noisy-ness of real data, and how approximations work. I have the same problem for finding non-Normal data, e.g., wealth distribution and other heavy-tailed ones. Parameters exist but I cannot find actual data sets.
TLDR: For an introductory Stats course, I'm looking for publicly available data sets with medium-size sample sizes, i.e., $N=O(10^3)$ or $O(10^4)$. Preferably, with close-to-Gaussian distributions, but anything is useful.