SOLUTION: find the mean and the standard deviation of the first n natural numbers.

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Question 1073041: find the mean and the standard deviation of the first n natural numbers.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
So think of an arithmetic series that starts at 1 and advances by 1.
The sum of that series would be,
S%5Bn%5D=%28n%2F2%29%281%2Bn%29
So then the average would be the sum divided by n.
A%5Bn%5D=%28n%2B1%29%2F2
So then to find the standard deviation, find the sum,
sum%28%28k-%28n%2B1%29%2F2%29%5E2%2Ck=1%2Cn%29=%28n%28n%5E2-1%29%29%2F12
Now divide that sum by n and take the square root,
sigma=sqrt%28n%28n%5E2-1%29%29%2F%2812n%29
sigma=sqrt%28%28n%5E2-1%29%29%2F12%29