Why does the same bell shape keep turning up?
One coin toss has only two outcomes; a total from many independent tosses has many more. Middle totals can arise in more ways than extreme ones. The central limit theorem explains a broader pattern in sums and averages under its assumptions, without making every individual measurement bell-shaped.
Questions you could explore
- What happens if all the contributions move together instead of independently?
Start reading
- OpenStax; Rice University7.1 The Central Limit Theorem for Sample Means (Averages)
The textbook distinguishes the distribution of original observations from the distribution of repeated sample means.
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