AVERAGE OF SIGNED NUMBERS

To average [beautiful math coming... please be patient] $\,N\,$ numbers, add them up and divide by [beautiful math coming... please be patient] $\,N\,$.

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 [beautiful math coming... please be patient] $\,x_3\,$ (read as ‘$\,x$ sub $3\,$’), the number [beautiful math coming... please be patient] $\,3\,$ is a subscript.
When you look at [beautiful math coming... please be patient] $\,y_b\,$ (read as ‘$\,y$ sub $b\,$’), the letter [beautiful math coming... please be patient] $\,b\,$ is a subscript.

In subscript notation, we can let [beautiful math coming... please be patient] $\,x_1\,$ denote the first number, [beautiful math coming... please be patient] $\,x_2\,$ denote the second number, and so on.

AVERAGE OF $\,N\,$ NUMBERS
Let [beautiful math coming... please be patient] $\,x_1, x_2, x_3, \ldots, x_N\,$ denote [beautiful math coming... please be patient] $\,N\,$ numbers.
Then, the average of these $\,N\,$ numbers is: [beautiful math coming... please be patient] $$ \frac{x_1 + x_2 + x_3 + \cdots + x_N}{N} $$

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: [beautiful math coming... please be patient] $\,-1\,$, $\,4\,$, and $\,6\,$.
Put equal-weight pebbles at locations [beautiful math coming... please be patient] $\,-1\,$, $\,4\,$ 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, for perfect balance! [beautiful math coming... please be patient] $$ \text{average } = \frac{-1 + 4 + 6}{3} = \frac{9}{3} = 3 $$

illustrating the concept of average on a number line

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).

EXAMPLE:
Question: Find the average of [beautiful math coming... please be patient] $\,5\,$, $\,6\,$, and $\,-2\,$.
Solution:
[beautiful math coming... please be patient] $\displaystyle\text{average} = \frac{5 + 6 + (-2)}{3} = \frac{9}{3} = 3$
Master the ideas from this section
by practicing both exercises at the bottom of this page.

When you're done practicing, move on to:
Identifying Place Values

 
 
    
(an even number, please)
CONCEPT QUESTIONS EXERCISE:
On this exercise, you will not key in your answer.
However, you can check to see if your answer is correct.
PROBLEM TYPES:
1 2 3 4 5 6 7 8 9 10 11 12
AVAILABLE MASTERED IN PROGRESS

(MAX is 12; there are 12 different problem types.)