I’m doing the Inferential statistics course in Udacity. I theoretically understand the Central Limit theorem, but I’m unable to associate any story to it. So my questions are what are some real life examples/applications of the Central Limit theorem.
According to me CLT is used to guess about the population statistic from sample statistic which is easier to obtain in comparison to population.
For eg : Lets imagine a situation in which you would want to calculate the mean salary of professionals working in india in fmcg sector. The problem here is you can never get the whole population data. So CLT was designed to address this issue.
Now what you can do is take say 1000 samples of say 100 professionals and plot the 1000 means of them . You will see they somewhat resemble a normal distribution. As you increase the number of samples, the more it will resemble a normal distribution. And as you increase your sample size,the more narrower it will become.
Here, the mean of the new distribution you obtain will give an estimate of the population mean.
The more the sample size, the greater confidence in the population mean.
Hope this helps.
Thanks Neeraj. More Ideas are welcome.