Most data in our world follow a certain probabilistic distribution where the y axis shows the frequency or probability density and the x axis showing the actual values. It's been determined that many naturally occurring phenomenon follow a normal distribution that is symmetrical around the mean.
Many folks in probability and statistics wonder why the normal distribution comes up many times when sampling. One of the reasons is that as you sample more data randomly from a population, the sample mean tends to converge towards the population mean because of the central limit theorem. In addition, the distribution of the samples will start to have a normal distribution even if the original population did not. This makes it easier to study this data.
Finally, the law of large number just states that as your sample size increases, its mean and variance/standard deviation will start to approach that of the larger population. This makes intuitive sense. For example, if we want to determine the life expectancy of the US population and we start sampling a few people, say ten. We will not get an accurate average but as our number increases to a really high number, say a few millions, the life expectancy will start to mirror that of the US.
