Hi, Bob. Welcome back! Don't have time for an extended discourse just now, but am thinking about it. Did have one quick reaction, below:
On Thu, 19 Feb 2004, Robert Frick wrote in part: > So I was looking for a formula that did not involve addition. Maybe > the first moment (terminology?) is the more natural formula? The > first moment, if I have my terminology correct, is the number such > that summation of each number minus the first moment is zero. Sorry to disillusion you, but "summation" surely involves addition. > That formula does not make addition salient -- the only addition is in > the error term, and everything is supposed to cancel out to zero. Only after having done (or at least thought about doing) a subtraction for every datum. And subtraction is a subset of addition: if one permits the objects being added to be signed numbers, "subtraction" as a separate operation becomes entirely unecessary. > Instead, that formula emphasizes a comparison of the average to every > number, with the amount the average is greater (than a number in the > set) balancing out the amount the average is less (than a number in a > set). There are different ways of making a comparison. The method you describe carries out the comparison by subtracting each datum from a comparison value; and it arrives at a value that minimizes the sum of the squares of those differences. One could instead simply observe whether the datum were larger than, or smaller than, the comparison value; then one arrives at a different average, commonly called "median", as the value for which the number of data larger is equal to (or nearest to, when there are ties) the number of data smaller than the comparison value. This value minimizes the sum of the absolute values of the differences, if one envisions carrying out the subtractions referred to above. Or you could seek a value that minimizes the total number of data values that are not equal to the comparison value: this way lies the "mode". > Well, that was more than I had planned to think about this! Thanks > everyone for your responses. > > Bob Cheers! -- Don. ------------------------------------------------------------ Donald F. Burrill [EMAIL PROTECTED] 56 Sebbins Pond Drive, Bedford, NH 03110 (603) 626-0816 . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
