What Does Average Mean?
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
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 on what your goal is. That may not fully answer your question, so write back if you have more to ask. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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