Video Tutorial – Rolling 2 Dice: An Intuitive Explanation of The Central Limit Theorem

April 15, 2014

(This article was originally published at The Chemical Statistician » Statistics, and syndicated at StatsBlogs.)

According to the central limit theorem, if

$n$ random variables, $X_1, ..., X_n$ , are independent and identically distributed,
$n$ is sufficiently large,

then the distribution of their sample mean, $\bar{X_n}$ , is approximately normal, and this approximation is better as $n$ increases.

One of the most remarkable aspects of the central limit theorem (CLT) is its validity for any parent distribution of $X_1, ..., X_n$ . In my new Youtube channel, you will find a video tutorial that provides an intuitive explanation of why this is true by considering a thought experiment of rolling 2 dice. This video focuses on the intuition rather than the mathematics of the CLT. In a later video, I will discuss the technical details of the CLT and how it applies to this example.

You can also watch the video below the fold!