   SEARCH HOME Math Central Quandaries & Queries  Question from Chris: Ok I'll give you a simple example of what I'm doing. Lets say that on one forum, a member has made 52 posts out of the 412 posts made altogether. Then on another forum, the same person has made 10 posts out of the 60 posts altogether. What percentage of the posts has this person made in these 2 forums combined. Ok, I have 2 ways of doing this. One is correct, one is incorrect. Can you tell me which one is correct? First way: (52 + 10)/(412 + 60) = 62/472 = 0.131 = 13.1% Second way: In this method I find the percentage of each one and average it. 52/412*100 = 12.6% 10/60*100 = 16.7% (12.6 + 16.7)/2 = 14.5% Chris,

One way to approach this problem is to try some extreme numbers.

Lets say that on one forum, a member has made 10 posts out of the 10 posts made altogether. Then on another forum, the same person has made 1 posts out of the 1000 posts altogether. What percentage of the posts has this person made in these 2 forums combined.

First way:
(10 + 1)/(10 + 1000) = 11/1010 = 1.1%

Second way:
10/10 × 100 = 100%
1/1000 × 100 = 0.1%

(100 + 0.1)/2 = 50.05%

Has this person really made over half of the postings? I don't think so! The second way is clearly wrong.

Harley

Lets say that on one forum, a memebr has made 52 posts out of the 412 posts
made altogether. Then on another forum, the same person has
made 10 posts out of the 60 posts altogether.
What percentage of the posts has this person made in these 2 forums combined.

This means: of the total posts to both forums, what proportion are made by the person?

Ok, I have 2 ways of doing this. One is correct, one is incorrect. Can you tell me whch one is correct?
First way:
(52 + 10)/(412 + 60) = 62/472 = 0.131 = 13.1%

This is obviously right, as you find the numbers needed and
use them correctly.

Second way:
In this method I find the percentage of each one and average it.
52/412*100 = 12.6%
10/60*100 = 16.7%

What you really want to know is "why is this one wrong?" The simple answer is "because you are not doing what was asked for, and what you did is not mathematically equivalent."

To cultivate a better feeling for why you should not believe in the second method, consider an extreme case. Suppose in the second forum there is only one post, and our friend made it (100%). It is surely clear that the overall percentage should not be

(12.6% + 100%)/2 = 56.3%.

and that this figure is irrelevant for most purposes.

Good Hunting!
RD     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.