document.write( "Question 1073041: find the mean and the standard deviation of the first n natural numbers. \n" ); document.write( "

Algebra.Com's Answer #687961 by Fombitz(32388) $\"\"$ $\"About$

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So think of an arithmetic series that starts at 1 and advances by 1.
\n" ); document.write( "The sum of that series would be,
\n" ); document.write( " $\"S%5Bn%5D=%28n%2F2%29%281%2Bn%29\"$
\n" ); document.write( "So then the average would be the sum divided by n.
\n" ); document.write( " $\"A%5Bn%5D=%28n%2B1%29%2F2\"$
\n" ); document.write( "So then to find the standard deviation, find the sum,
\n" ); document.write( " $\"sum%28%28k-%28n%2B1%29%2F2%29%5E2%2Ck=1%2Cn%29=%28n%28n%5E2-1%29%29%2F12\"$
\n" ); document.write( "Now divide that sum by n and take the square root,
\n" ); document.write( " $\"sigma=sqrt%28n%28n%5E2-1%29%29%2F%2812n%29\"$
\n" ); document.write( " $\"sigma=sqrt%28%28n%5E2-1%29%29%2F12%29\"$ \n" ); document.write( "

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