Lesson WHAT IS Average, Why do we need it?
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The word "<A HREF=Average.wikipedia>Average</A>" is used in many ways. Here I will try to explain the use of average that you would encounter in school algebra class. Mathematically, an average of some numbers is expressed as their sum, divided by how many numbers you have. For example, the average of FOUR numbers 5, 7, 9, 11 is: <CENTER>{{{average = (5+7+9+11)/4}}}</CENTER> <U>The rule for computing an average is very simple</U>: add all the numbers together, and divide by how many numbers you added. For those of you brave enough to dive into the depths of math, mathematicians express average of N numbers {{{V[1]}}}, ..., {{{V[N]}}} as <CENTER>{{{Average = sum( V[i], i=1, N ) / N}}}</CENTER> If you feel terrified about this formula, just remember that you need to <U>add up the numbers and divide their sum by how many numbers you added</U>. I wrote a handy <A HREF=compute-average-calculator.solver>Algebra Average Calculator</A> that you can use to calculate averages. Try it! <H4>Algebra Problems involving average</H4> Usually, school algebra problems are of two kinds. One kind of problem with average is giving you a bunch of numbers, and asking to calculate their average. You know how to do that already if you read my lesson up to here. Just add them and divide that sum by the quantity of numbers that you added. Example: calculate the average of 5,6,7,2. Solution: {{{Average = (5+6+7+2)/4 = 20/4 = 5}}} The other kind of problem is they give you an average and some numbers that went into that average, except one, and ask you to figure out the number that is missing. Example: <I>Jack and Joe Jones are two brothers. Their average age is 10. Jack is 8 years old. How old is Joe?</I> This may be intimidating to some people. The solution is actually simple. Just write down what average is: {{{Average = (Jack+Joe)/2}}} Then replace words with what you know (average is 10, Jack is 8): {{{10 = (8+Joe)/2}}} Then it becomes an easy algebra problem. Multiply both sides by 2: {{{10*2 = (8+Joe)/2*2}}} {{{20=8+Joe}}} {{{20-8=8+Joe-8}}} {{{12 = Joe}}} That's the answer! Joe's age is 12!
