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Averaging Percentages

```
Date: 12/11/98 at 00:34:39
From: Dominic Dionisio
Subject: Average of percentages

Hi,

I am having difficulties in explaining to several friends that you
cannot take percentages by totalling them up and then averaging the
total of the percentages. It does not equal the percentage of the
total of the numbers.

Is there a rule or theory that can explain this better?
```

```
Date: 12/11/98 at 12:11:37
From: Doctor Peterson
Subject: Re: Average of percentages

Hi, Dominic. I'm not entirely sure what kind of problem you are
referring to. Certainly there are at least some situations where you
can average percentages. For example, if there are 50 questions on an
exam, and three students got 20%, 30%, and 40% of them right, then the
average number of questions they got right is 30%, or 15 questions.

I suspect what you are thinking of is cases where the percentages are
taken from different totals, in which case weighted averaging is
needed. For example, if I survey 20% of 50 people, and 80% of 500 other
people, then I have not surveyed (20+80)/2 = 50% of the total
population, but:

.20 * 50 + .80 * 500   10 + 400   410
-------------------- = -------- = --- = 74.5%
50 + 500           550      550

The problem is simply that the percentages in such a problem do not
represent fractions of the same total, so they can't be added.

http://mathforum.org/dr.math/problems/smith11.2.98.html

For another explanation of weighted averages, if you want another
perspective, see:

http://mathforum.org/dr.math/problems/riggins11.16.95.html

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Fractions
Middle School Statistics

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