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### Definitions of Range

```Date: 10/20/2003 at 15:37:55
From: glockhart@satx.rr.com
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

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/
```
Associated Topics:
High School Definitions
High School Statistics
Middle School Definitions
Middle School Statistics

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