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### What Does Average Mean?

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Date: 12/05/2001 at 21:50:18
From: John Profeta
Subject: Average

Can someone explain what average is? For example what is the average
rainfall in New York? I understand the formula needed to find the
average, but what is the meaning of average?

Thanks,
John
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Date: 12/05/2001 at 23:24:11
From: Doctor Peterson
Subject: Re: Average

Hi, John.

Sometimes "average" just means "normal." Other times it refers to some
number "in the middle"; there are several different ways to define an
average. But the usual average, which you are familiar with, called
the "arithmetic mean," is calculated by summing all the values of
something and then dividing by the number of values you used.

What this really means is that you are finding a single number that
you could use in place of all the different numbers and still get
the same total. For example, suppose that the rainfall one day is
2 inches, the next day 0 inches, and the next day 1 inch. The total
rainfall over the three days is 3 inches, so it is just as if there
had been 1 inch each day. So the average daily rainfall over that
period is 1 inch.

Do you see that an average "smooths out" the numbers? It's as if there
were two inches of dirt on one block of sidewalk, none on the next,
and one on the third. If I spread all the dirt out evenly, so it was
all the same level, there would be one inch over the whole sidewalk.
In the same way, if we spread the rain out evenly over all three days,
there would be one inch every day. Of course, everything isn't "just
as if it rained an inch every day"; then you could never have a picnic
in Central Park! But just from the perspective of the total amount of
rain, it's the same. And that's why there are different kinds of
average: if something else is important other than the total, then you
can get a different "average."

It's also important to ask what data are represented by the average
you are talking about. Is the "average rainfall in New York" the
average per day over some particular number of days? Is it the average
over a whole year? Is it the average per year over a number of years?
Or the average amount on December 5 over several years? The actual
amount will vary with the season as well as from year to year, and you
can average the data to eliminate either variation, or both, depending

That may not fully answer your question, so write back if you have

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

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