## Friday, February 1, 2013

I am a fourth grade teacher and we are currently working with mean, median, mode and range.  I received a parent email asking to clarify the definition of range.  Her email is as follows:

“ A question came up during homework on the definition of range. Apparently the kids' textbook says that the "range is the difference between the least number and the greatest number".  Range = greatest value - least value. That is not the correct definition. Range is the least number to the greatest. For example, if the test scores in one class range are between 90 to 100, and another class between 60-70. The textbook definition would say the range for scores in both classes is 10, which obvious does not make sense. (I think their textbook is defining what is known as the span of the data but that is rarely used.) A number of parents were puzzled about it but we don't know if this needs to be corrected or at this level the textbook definition should stand. Would you please clarify.”

Am I correct that finding the range does require students to subtract the greatest from the least amount in the data set?  I am not sure how to respond to her question.

Jillian, New York

Definition of Range:
There are many places one can check on the definition - wikipedia quoted reliable mathematics / statistics textbooks. This is another source for a definition.

You can send the parent some of these links.

We are often interested about the 'average' in a data set as well how the data distributes itself around the average. Examples of average include mean and median. examples of a measure of this distribution includes range and standard deviation.

Range is the size of the smallest interval that contains all the data and tells us about statistical dispersion.

I tried checking what the parent referred to as "span of the data" but could not find any entry on the internet. Apparently, it is not a conventional term. Range is a more conventional term to describe the idea under discussion.

1. Wow. What a great question. The teacher certainly describes everyday usage of the word range and after looking at http://mathworld.wolfram.com/search/?query=span&x=0&y=0, I would say his or her use of the word span is correct.

Furthermore, http://mathworld.wolfram.com/Range.html clearly supports his or her usage of the word range in math.

In short, the teacher is correct and our textbooks are simply WRONG. Truth is not established by a vote (Webster's Second people). On the other hand, we can say that the word Range is used ambiguously to those who support all definitions for all words (Webster's Third people)

I will start using the word span.

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