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August 14th, 2011, 07:02 AM  #21  
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,963 Thanks: 1148 Math Focus: Elementary mathematics and beyond  Re: Arithmetic mean: Why use its computation as its definiti Quote:
 
August 14th, 2011, 01:20 PM  #22  
Newbie Joined: Aug 2011 Posts: 9 Thanks: 0  Re: Arithmetic mean: Why use its computation as its definiti Quote:
There's also methods for multiplying (yes, multiplying) on your fingers, and probably lots of other cool math methods. I have my own method of multiplying longhand (especially squaring) that's more efficient and involves much fewer "carries". Quote:
However, you could calculate it stepwise, beginning with some nominal value (eg, zero seems like a good value to begin for the estimate â). Then, calculating the sum of the residuals, and using the result to determine which way to move the estimate along the number line. For example, using the set of {4, 5, 9}, the sum of residuals is as follows: â ? ? 0 ? 18 1 ? 15 2 ? 12 3 ? 9 4 ? 6 5 ? 3 6 ? 0 7 ? 3 8 ? 6 9 ? 9 etc The estimate â can be adjusted until the sum of the residuals equals zero (and then the mean would equal the value of â at that point), or the sum of residuals can be set to zero and the mean determined from it.  

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