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### Average

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Date: 05/10/2001 at 10:34:45
From: Rick Wright
Subject: Averages

Dr. Math -

My fourth grader tells me that the average of a set of data is always
computed by adding all the numbers together and dividing by the total
number. Isn't this a misconception? I need to provide some specific

Thank you.
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Date: 05/10/2001 at 13:17:06
From: Doctor Twe
Subject: Re: Averages

Hi Rick - thanks for writing to Dr. Math.

It depends on how strictly you want to define the term "average."
Merriam-Webster's OnLine Dictionary at:

http://www.m-w.com/

defines "average" as:

1a: a single value (as a mean, mode, or median) that summarizes
or represents the general significance of a set of unequal
values

b: MEAN

2a: an estimation of or approximation to an arithmetic mean

b: a level (as of intelligence) typical of a group, class, or
series <above the average>

3:  a ratio expressing the average performance especially of an
athletic team or an athlete computed according to the number
of opportunities for successful performance

- on average or on the average: taking the typical example of the
group under consideration <prices have increased on average by
five percent>

Later, the dictionary goes on to say:

"AVERAGE is exactly or approximately the quotient obtained by
dividing the sum total of a set of figures by the number of
figures (scored an average of 85 on tests)."

This is what mathematicians define as the "mean," and it is the most
common meaning of the term "average." (Note that this is exactly
definition 1b, and definition 2a also refers to the mean.)

The mean is one of three common measures of central tendency, the
others being the median and the mode. Medians and modes are also
sometimes referred to as averages, as supported by the dictionary's
definition 1a. (The median is the middle value of the data set when
arranged in ascending order, and the mode is the most frequently
occurring value(s) in the data set.)

There are also "weighted averages," where some values are given more
weight (or counted more often) than other values in the data set.

However, for a fourth grader, understanding what an average is and how
to compute it (in the common usage of the term) is more important than
making distinctions among other types of "average" measures. When your
measures and tools, and will learn about these other "averages."

I hope this helps. If you have any more questions, write back.

- Doctor TWE, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Elementary Definitions
Middle School Definitions
Middle School Statistics

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