You never hold a population mean in your hand… you hold a sample mean. That mean isn’t a replica; it’s a messenger. Its message carries error, and that error has a shape. When your sample is honest and big enough, the shape becomes comfortably bell-ish even when the population isn’t. That’s the quiet magic of sampling distributions: the statistic becomes predictable before the world does. So don’t apologize for using a sample. Name how you got it, show how its mean behaves across many possible samples, and act on that predictability. Decisions don’t need perfection… they need a mean you can hold.
