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 Originally Posted by DJAbacus
Yes, it is extremely unlikely that you will get exactly 5000 heads if you flip a coin 10000 times but it is still the most likely outcome. It is highly likely that you will be close to 5000, in other words, it is highly likely that you will be between slightly lucky and slightly unlucky.
For n = 10,000 trials, the variance is n/4 = 2,500.
The standard deviation is sqrt(var) = sqrt(n)/2 = 100/2 = 50
This means that ~76% of the data will fall between -50 and +50.
For n = 1,000,000 trials, the standard deviation is sqrt(n)/2 = 1,000/2 = 500
This means that ~76% of the data will fall between -500 and +500.
So you see that while the data is "clumped" near zero... the spread of the clump is ever widening.
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