Definitions of Range
Date: 10/20/2003 at 15:37:55 From: firstname.lastname@example.org Subject: Definition of Range I can find only one definition of range in the math dictionaries - the difference between the smallest and the largest number in a set. We are always talking about "They range in age from, or they range in height, or they range in weight, or they range in size, etc". If the only defintion of range is the difference, why do we say "They range..."?
Date: 10/20/2003 at 22:40:07 From: Doctor Peterson Subject: Re: Definition of Range Thanks for writing to Dr. Math. Math definitions generally give only the specific technical sense of words; your use of "range from this to that" is a common-language sense, which can be found in ordinary dictionaries, and doesn't need a special definition. In fact, if you look up "range" in, for example, Merriam-Webster (m-w.com), you find the technical definition of the noun as 7c, among other related uses within mathematics: 7 a : a sequence, series, or scale between limits (a wide range of patterns) b : the limits of a series: the distance or extent between possible extremes c : the difference between the least and greatest values of an attribute or of the variable of a frequency distribution 8 a : the set of values a function may take on b : the class of admissible values of a variable Your use as a verb is 5 : to change or differ within limits In math, technical uses and common uses coexist; we are, after all, speaking English, with special words used only where needed. Here the range as the difference between maximum and minimum is, more specifically, a "statistic", a single number used to indicate one aspect of the behavior of some variable; that needs precise definition, as the other uses do not. Why do we use this single number, when a broader sense (a pair of limits, or a set of numbers) gives more information? If you think about it, you will recognize that the whole idea of statistics is to boil down large amounts of information to single numbers (mean, standard deviation, and so on). True, the range alone doesn't tell you much; the same can be said of the median. But together, they give a useful picture of how the variable varies. For some purposes, that is just what we want; for others, the set of possible values is of more interest. It all depends on what you want to do with the data. If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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