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;+xNN
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).
