Averages: The Average Pie
To get the average, what should you do next ?
Incorrect.
Remember the average formula?
Incorrect.
Remember the average formula?
Now what if you had the "total" and the "average", and the question asked what is the "number of things"?
What should you do next?
Incorrect.
Remember the average formula?
Incorrect.
Remember the average formula?
Now what if you had the "number of things" and the "average", and the question asked what is the "total"?
What should you do next?
Incorrect.
Remember the average formula?
Incorrect.
Remember the average formula?
Having covered all possible variations by now, memorize the relations between the different parts of the average pie.
To sum up:
[[summary]]
Consider the following question:
What is the average of 3, 7, and 8 ?
Use the average formula $$Average=\frac{Total}{Number\ of\ Things}=\frac{3+7+8=18}{3}=6$$.
The average formula is made up of three parts: average, total, and number of things.
GMAT questions are usually about organizing your information clearly. For averages questions, it's convenient to organize the average formula in the average pie format.
Some call it the average wheel or the camping plate.
Let's find the average of 3, 7, and 8 using the average pie.
First, draw an average pie. Don't forget to label the various regions, so you don't get confused.
Second, organize your information; There are 3 "things" and the total is 18.
Correct.
This is exactly what you did a few moments ago using the average formula, hence the average is 18÷3= 6. Write it down in the right spot. Note that the relation of "total" to "number of things" in the average pie is the same as in the average formula.
Remember that any two parts of the formula allow you to calculate the third part.
Correct.
This is exactly what you did a few moments ago using the average formula, hence the number of things is 18÷6=3. Write it down in the right spot. Again, the relation of "total" to "average" in the average pie is the same as in the average formula.
Remember that any two parts of the formula allow to get the third.
Correct.
This is exactly what you did a few moments ago using the average formula, hence the total is 6×3=18. Write it down in the right spot. Once more, the relation of "average" to "number of things" in the average pie is the same as in the average formula.
Remember that any two parts of the formula allow you to get the third part.
