We discussed these and other statistics, as “a single number to represent the whole”, in Three Kinds of “Average”. It all depends on what you want to do with the data. For some purposes, that is just what we want for others, the set of possible values is of more interest. But together, they give a useful picture of how the variable varies. True, the range alone doesn't tell you much the same can be said of the median. 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). Why a difference? Why do we use this single number, when a broader sense (a pair of limits, or a set of numbers) gives more information? That’s what we mean when we talk about “ranging from 72 to 94”. There is a second aspect to the question: If we think as we do about functions, it makes more sense to talk about the entire interval (from the lowest to the highest number), rather than just the distance between them. Math dictionaries define this usage because it is not obvious from the everyday meaning. 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. In math, technical uses and common uses coexist we are, after all, speaking English, with special words used only where needed. These led to the mathematical usages, where a variable or data can “range” (“roam”) from one end of the “range” to the other.ĭefinition 8a above is the range of a function, as described in Finding the Range of a Function, at the bottom of which I refer to the same definition, as well as that of “domain”. Later, it took on meanings like “roam” (intransitive verb, 1a) and “region over which something roams” (noun, 3a). We are told that the word was used originally in English to mean “a row” (noun, 1a1) and “to set in a row” (transitive verb, 1a). Looking currently at the same dictionary, we get a better sense of the range of meanings of a word: (I don’t always trust general dictionaries fully for technical terms, but they can still be a good place to start.)Īs you can see from the numbering, there are other meanings as both noun and verb, and these can give a sense of why we use the words as we do in math. So the verb usage is not specifically mathematical, and is omitted from math dictionaries the noun usage found in math dictionaries is also found in general dictionaries, but is specialized enough to single out in math dictionaries. 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:ħ a : a sequence, series, or scale between limitsī : the limits of a series: the distance orĬ : the difference between the least and greatest values of an attribute or of theĨ a : the set of values a function may take onī : the class of admissible values of a variable 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. I answered, starting with a definition from a standard American English dictionary: Thanks for writing to Dr. The anonymous student finds only this definition, as a noun, in math dictionaries why don’t they say what it means as a verb? And isn’t the fact that the values range from 72 to 94 more important than the mere difference? (If you think that’s wrong, we’ll get to that soon …) If the only definition of range is the difference, why do we say "They range."? 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.". I can find only one definition of range in the math dictionaries - the difference between the smallest and the largest number in a set. I’ll start with a question from 2003: Definitions of Range What is range? Mathematical and other usage Is “range” defined as the interval containing the data, or the difference between largest and smallest values, or 1 more than that? Yes! All three are used, and are useful. A recent question about two interpretations of the range of a data set in statistics leads us into some older questions and some mysteries.
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