Would adding together random values create a bell curve?

Question

I feel like this is a statistical law that I can't remember the name of or something. If you took a series of random variables from a normal distribution and added them together in chunks, say, 10 at a time, and then you plotted out all the sums, would the sums be a normal distribution? More importantly, would the distribution be narrower than the initial distribution?

Sqdancefan · Answer

The sums would have a normal distribution with a mean 10 times that of the underlying distribution, and a variance 10 times that of the underlying distribution.

If you were to divide the sum by 10 so you had a distribution of the average of 10 values, you would find it narrower by a factor of √10. That is, the sd of the mean of 10 samples is 1/√10 that of the original distribution.

nbsale (Freond) · Answer

Look up Central Limit Theorem.

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Would adding together random values create a bell curve?

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