<p>When I run the supplied code I see a plot which is a great deal closer to normality than the original sample so I find it hard to see what is going on here. The code itself seems to show more understanding of the central limit theorem than the quoted explanation of what the central limit theorem in fact states. I would suggest the OP edits the question in the light of the comments made here and under the original question to clarify exactly what they do not understand. I would suggest also inserting as an image the plots so readers who do not use R can join into the conversation.</p>
