What Does "Mean" Mean?
Date: 14 Apr 1995 13:02:13 -0400 From: Richard Brown Dear Dr. Math, In Webster's dictionary one of the definitions of average is MEAN and another is "being about midway between extremes." Mean's definition is "a middle point between extremes." Additionally, mean also has two calculations defined as 1) "a value computed by dividing the sum of a set of terms by the number of terms" and 2) "a value computed by dividing the sum of two extremes of a range of values by two." Can the terms average and mean be used interchangeably? Definitions 1 and 2 of mean can yield different results with the same numbers. What examples can you give that would make it clear when to use mean definition 1 and mean definition 2? Any help in clearing this up for me would be appreciated. Regards, Richard Brown Phoenix Arizona USA
Date: 14 Apr 1995 14:25:10 -0400 From: Dr. Ken Hello there! The word "mean" is actually used to "mean" a whole bunch of things. In general, it purports to give a value that is somehow typical or in the middle of the rest of the values. Usually when people talk about means, they say whether they mean the arithmetic mean (the average) or the geometric mean (this is defined as the nth root of a1 * a2 * a3 * ... * an. ) for example, if you have the numbers 5, 15, and 45, the arithmetic mean is 65/3 = 21 2/3, and the geometric mean is (5*15*45)^1/3 = 15. As far as deciding which mean to use when, it's pretty valuable to see what any of them are, and then you'll know that much more about your data. For instance, the two values for mean above tell us that the data values aren't grouped that close together, since the two means are pretty well separated. This stuff shows up a bunch in statistics, and statisticians have some pretty well-developed techniques for analyzing means. -Ken "Dr." Math
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