# How is central limit theorem applied?

All resources I find online state that when you sample from the population, the means form a normal distribution. I also found out that the "mean of the sample means equals the population mean".

This is fair enough. What I do not understand is how this is applied in real life. In real life, don't we usually take just one sample? So doesn't that mean that the rule that the mean sample means equals the population mean not hold when we take one sample? And when we take one sample, won't that not form a normal distribution?

Or is the central limit theorem just a theoretical idea and is not applied in real life?

• CLT is arguably the most widely applied theorem in all of science. Mar 23, 2020 at 10:00
• Unfortunately, the word sample means something different to a statistician than it means in plain English. A statistical sample of a population means n-tuple realizations. In other words, a sample for a statistician could refer to many blood samples to a biologist.
– Carl
Mar 23, 2020 at 11:14