Average of Three Signed Numbers

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AVERAGE OF THREE SIGNED NUMBERS

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The concepts for this exercise are summarized below. For a complete discussion, read the text.

To average N numbers, add them up and divide by N .

A convenient way to talk about N numbers is to use subscript notation.
A subscript is a character (usually, a number or letter) that is written slightly below another character.
For example, when you look at x3 (read as "x sub three"), 3 is a subscript.
When you look at yb (read as "y sub b"), b is a subscript.

In subscript notation, we can let x1 denote the first number, x2 denote the second number, and so on.

AVERAGE OF N NUMBERS
Let x1, x2,&ldots;, xN denote N numbers.
Then, the average of these N numbers is:

x1+ x2+&cdots;+ xN N

When more than two numbers are averaged, the concept of balancing point becomes the central idea.
To illustrate the idea, consider finding the average of three numbers: -1 , 4 , and 6 .

Put equal-size pebbles at locations -1 , 4 and 6 on a number line.
If you think of the number line as a see-saw from a childhood playground, the support must be placed at the average, -1+4+ 63= 93=3 , for perfect balance!

It is clear from the "balancing point" interpretation of the average that the average of numbers always lies between the greatest number (the one farthest to the right) and the least number (the one farthest to the left).

Click here to play with the "balancing point" concept using Geometer's Sketchpad!

EXAMPLE:
Find the average of 5 , 6 and -2 .

Solution: average = 5+6+ (-2)3= 93=3

CONCEPT QUESTIONS EXERCISE:
On this exercise, you will not key in your answer.
However, you can check to see if your answer is correct.