



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 
