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. For more information on weighted averages, please see: 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/
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