Pre Algebra Finding the Mean
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On the Average
Finding the Mean

 
 There's this thing that math types love to do when they have a bunch of numbers. 
 It's called finding the average.
 
 It goes like this. 
 Say you have a bunch of numbers (like maybe exam scores). 
 First you add them up. 
 Then you divide the total you get by how many numbers you added together.
 
 Watch:
 
 Say you have test scores of 83, 89, 96, and 90. 
 What is the average of your scores?
 
 Step 1: Add the numbers:
 

Calculators can help with this kind of stuff,
but estimate you answer before
you start punching the buttons!

 
 Step 2: Divide the total by the number of scores you added together.
 

 
 The average is 89.5
 
 So the average is 89.5, so what? What does that mean?
 
 Between all of the tests, you got 358 points. 
 
 If you had gotten the same score on each test AND had gotten 358 total points, 
 each score would have been 89.5.
 
 So let's say that this is your grade for some class. 

 The teacher says that the grades for the class 

 are only based on the average of the test scores. 
 For 90 to 100 you get an A. 
 For 80 to 89.99 you get a B. 
 For 70 to 79.99 you get a C. 
 BUMMER. 
 Some teachers might just give you the A. 
 Some might let you do some extra work to get the A. 
 This teacher says: "You can take one more test. 
 Whatever your average is after THAT test is your final grade." 
 So if you get your average up to 90, you get the A.
 
 Great. So just what do you need to get on that last test?
 
 You have to get more than 90 to bring your average up. 
 How much more? 91? 96?
 Who knows?
 
 I know.
 
 And in a minute, you will too.
 
 You took 4 tests so far. 
 After this one, you will have taken 5. 
 Averaging 90 is like getting a 90 on each. 
 If you got a 90 on each, how many points would you have?
 

 
 So to average 90 for 5 tests, you need 450 total points. 
 So far, you have 358 points. 
 How many do you need on the last test?
 

 
 You need a 92. Not too bad.
 
 BUT WAIT! What if you CRASH! 
 How bad would you have to do to move your grade down to a C?
 
 To get a C, you need to have an average of less than 80. 
 The easiest way to do this is to see how many points you need to average 80, 
 then subtract 1.
 
 To average 80 for 5 tests you need:
 

 

 
 To get a C you need one less point. So 399.
 
 You already HAVE 358 points so:
 

 
 A 41 hey that should be no problem to beat.
 
 So you're pretty safe from the C, and have a fair shot at the A.
 
 Let's do another one ...
 
 Example:
 
 Sometimes one test counts more than another. 
 Like maybe the final exam counts twice as much as the other tests. 
 Say that was so, and you got these scores:
 
Test 1: 78
Test 2: 84
Final: 100
 
 What is the average score?
 OK, since the final counts more than the other tests, 
 we can't just add up all of the scores and divide by 3. 
 But this one's not TOO bad. 
 
 Since the final counts exactly TWICE as much as the other tests, 
 just add it in twice!
 

 

 
 And now divide BY FOUR! Since we added the final in twice we had 4 scores.
 ("Four Scores" haven't I heard something like that in a speech somewhere?)
 



The middle part here is a bit tricky. 
Be sure to look at it.

36 - 36 = 0
Bring down the 2.
The two is less than the 4,
so bring down the next number.
 
 The average is 90.5.
 

   copyright 2005 Bruce Kirkpatrick

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