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# Advanced Math/Average Whole Numbers and Percentages

Question
QUESTION: Working on a project that we have to roll up percentages.  The question is one of the stats we are rolling up is a whole number.

Stat#1 = 68%
Stat#2 = 687 (whole number)
Stat#2 is a roll up of
455, 650, 658, 725, 735, 899

Stat#3 = 54%

How do we get the rolled up average of these 3 numbers?

ANSWER: It looks to me like the whole number 687 is supposed to represent 68.7%. If this is the case, then the average would just be

average = (68 + 68.7 + 54)/3

expressed as a percent.

---------- FOLLOW-UP ----------

QUESTION: How did you get 68.7% from 687?  So if I turn 687 into a percentage it will be 687%

We are trying to roll up percentages and whole number together into 1 percent.

ANSWER: It just looked to me that somebody had taken 5 percentages (the ones you list), which have 3 significant digits, converted then to whole numbers by multipying by 1000 (=10^3) after dropping the % sign, averaged them to get 687 and then forgot to change the number back. I guess the real question is where did you get 687? If 687 is supposed to represent a percentage (way larger than the others you list, and frankly, I can't believe it is the proper interpretation), then just tacking a percent sign on it would be consistent with the other numbers (i.e, for Stat #3, 58 percent is 58%).

I think you need to look more carefully at what your whole numbers are supposed to represent. I don't know where the numbers came from and they look inconsistent to me. Let me know what you come up with.

---------- FOLLOW-UP ----------

QUESTION: Ok, I see how you would of gotten there but that isn't what we are trying to do.

Basically we have 3 stats.  2 are percentage goals and 1 is a dollar amount goal.  We then want to roll them up to 1 overall outcome of those goals.

So hierarchy is like this:

- Overall Roll Up
- Stat#1
- Stat#1 elements
- Stat#2
- Stat#2 elements
- Stat#3
- Stat#3 elements

So solve for (x)

x = Average(Stat#1(Average(Stat#1 elements)),Stat#2(Average(Stat#2 elements)),Stat#3(Average(Stat#3 elements)))

Stat#1 are all percentages.
Stat#2 are all whole numbers.
Stat#3 are all percentages

So what I get is 229.41%

Is this the correct?

I honestly don't understand what you are trying to do in your problem. I take it that "rolling up" means finding the average. Averaging the percentage values (68 and 54) with the whole number(s) (687 or the 5 other ones) is mixing different types of quantities and as such does not make sense. A percentage is a ratio of numbers while a dollar amount isn't.

If I average 68, 687 and 54, I get

(68+687+54)/3 = 269.67

which is close to your "answer" but not the same.

The equation you list for x doesn't really require solving for x since it equates x to a (mysterious) quantity. Evaluating x would be a better term.

Stat#2 is the odd man out here. Does it represent a change from a previous amount? Such as \$Y, in which case

\$687/\$Y = ratio (fraction) that could be turned into a percentage and then averaged (rolled up) ith the other percentages.

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#### randy patton

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college mathematics, applied math, advanced calculus, complex analysis, linear and abstract algebra, probability theory, signal processing, undergraduate physics, physical oceanography

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